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Int: Answer test results

This page exposes the results of running answer tests on STACK test cases. This page is automatically generated from the STACK unit tests and is designed to show question authors what answer tests actually do. This includes cases where answer tests currentl fail, which gives a negative expected mark. Comments and further test cases are very welcome.

Int

Test
?
Student response
Teacher answer
Opt
Mark
Answer note
Int 
1/0
 
1
 -1 STACKERROR_OPTION.
TEST_FAILED
The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.
Int 
1/0
 
1
 
x
 -1 ATInt_STACKERROR_SAns.
Int 
1
 
1/0
 
x
 -1 ATInt_STACKERROR_TAns.
Int 
0
 
0
 
1/0
 -1 ATInt_STACKERROR_Opt.
Int 
0
 
0
 
[x,1/0]
 -1 ATInt_STACKERROR_Opt.
Int 
0
 
0
 
[x,NOCONST,1/0]
 -1 ATInt_STACKERROR_Opt.
Basic tests
Int 
x^3/3
 
x^3/3
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
x^3/3+1
 
x^3/3
 
x
 0 ATInt_const_int.
You need to add a constant of integration. This should be an arbitrary constant, not a number.
Int 
x^3/3+c
 
x^3/3
 
x
 1 ATInt_true.
Int 
x^3/3-c
 
x^3/3
 
x
 1 ATInt_true.
Int 
x^3/3+c+1
 
x^3/3
 
x
 1 ATInt_true.
Int 
x^3/3+3*c
 
x^3/3
 
x
 1 ATInt_true.
Int 
(x^3+c)/3
 
x^3/3
 
x
 1 ATInt_true.
Int 
x^(k+1)/(k+1)
 
x^(k+1)/(k+1)
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
x^(k+1)/(k+1)+c
 
x^(k+1)/(k+1)
 
x
 1 ATInt_true.
Int ! 
(x^(k+1)-1)/(k+1)
 
x^(k+1)/(k+1)
 
x
 -2 ATInt_true.
Int ! 
(x^(k+1)-1)/(k+1)+c
 
x^(k+1)/(k+1)+c
 
x
 -3 ATInt_weirdconst.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this.
Int 
x^3/3+c+k
 
x^3/3
 
x
 0 ATInt_weirdconst.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this.
Int 
x^3/3+c^2
 
x^3/3
 
x
 0 ATInt_weirdconst.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this.
Int 
x^3/3+c^3
 
x^3/3
 
x
 0 ATInt_weirdconst.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this.
Int 
x^3/3*c
 
x^3/3
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[x^2\] In fact, the derivative of your answer, with respect to \(x\) is: \[c\cdot x^2\] so you must have done something wrong!
Int 
X^3/3+c
 
x^3/3
 
x
 0 ATInt_generic. ATInt_var_SB_notSA.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[x^2\] In fact, the derivative of your answer, with respect to \(x\) is: \[0\] so you must have done something wrong!
Int 
sin(2*x)
 
x^3/3
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[x^2\] In fact, the derivative of your answer, with respect to \(x\) is: \[2\cdot \cos \left( 2\cdot x \right)\] so you must have done something wrong!
Int 
x^2/2-2*x+2+c
 
(x-2)^2/2
 
x
 1 ATInt_true.
Int 
(t-1)^5/5+c
 
(t-1)^5/5
 
t
 1 ATInt_true.
Int 
(v-1)^5/5+c
 
(v-1)^5/5
 
v
 1 ATInt_true.
Int 
cos(2*x)/2+1+c
 
cos(2*x)/2
 
x
 1 ATInt_true.
Int 
(x-a)^6001/6001+c
 
(x-a)^6001/6001
 
x
 1 ATInt_true.
Int 
(x-a)^6001/6001
 
(x-a)^6001/6001
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
6000*(x-a)^5999
 
(x-a)^6001/6001
 
x
 0 ATInt_diff.
It looks like you have differentiated instead!
Int 
4*%e^(4*x)/(%e^(4*x)+1)
 
log(%e^(4*x)+1)+c
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\frac{4\cdot e^{4\cdot x}}{e^{4\cdot x}+1}\] In fact, the derivative of your answer, with respect to \(x\) is: \[\frac{16\cdot e^{4\cdot x}}{e^{4\cdot x}+1}-\frac{16\cdot e^{8 \cdot x}}{{\left(e^{4\cdot x}+1\right)}^2}\] so you must have done something wrong!
The teacher adds a constant
Int 
x^3/3+c
 
x^3/3+c
 
x
 1 ATInt_true.
Int 
x^2/2-2*x+2+c
 
(x-2)^2/2+k
 
x
 1 ATInt_true.
The teacher condones lack of constant, or numerical constant
Int 
x^3/3
 
x^3/3
 
[x,NOCONST]
 1 ATInt_const_condone.
Int 
x^3/3+c
 
x^3/3
 
[x,NOCONST]
 1 ATInt_true.
Int 
x^2/2-2*x+2
 
(x-2)^2/2+k
 
[x,NOCONST]
 1 ATInt_const_condone.
Int 
x^3/3+1
 
x^3/3
 
[x,NOCONST]
 1 ATInt_const_int_condone.
Int 
x^3/3+c^2
 
x^3/3
 
[x,NOCONST]
 0 ATInt_weirdconst.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this.
Int 
n*x^n
 
n*x^(n-1)
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\left(n-1\right)\cdot n\cdot x^{n-2}\] In fact, the derivative of your answer, with respect to \(x\) is: \[n^2\cdot x^{n-1}\] so you must have done something wrong!
Int 
n*x^n
 
(assume(n>0), n*x^(n-1))
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\left(n-1\right)\cdot n\cdot x^{n-2}\] In fact, the derivative of your answer, with respect to \(x\) is: \[n^2\cdot x^{n-1}\] so you must have done something wrong!
Special case
Int 
exp(x)+c
 
exp(x)
 
x
 1 ATInt_true.
Int 
exp(x)
 
exp(x)
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
exp(x)
 
exp(x)
 
[x,NOCONST]
 1 ATInt_const_condone.
Student differentiates by mistake
Int 
2*x
 
x^3/3
 
x
 0 ATInt_diff.
It looks like you have differentiated instead!
Int 
2*x+c
 
x^3/3
 
x
 0 ATInt_diff.
It looks like you have differentiated instead!
Sloppy logs (teacher ignores abs(x) )
Int 
ln(x)
 
ln(x)
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
ln(x)
 
ln(x)
 
[x,NOCONST]
 1 ATInt_const_condone.
Int 
ln(x)+c
 
ln(x)+c
 
x
 1 ATInt_true_equiv.
Int 
ln(k*x)
 
ln(x)+c
 
x
 1 ATInt_true_equiv.
Fussy logs (teacher uses abs(x) )
Int 
ln(x)
 
ln(abs(x))+c
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(x)+c
 
ln(abs(x))+c
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(x)
 
ln(abs(x))+c
 
[x, NOCONST]
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(abs(x))
 
ln(abs(x))+c
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
ln(abs(x))+c
 
ln(abs(x))+c
 
x
 1 ATInt_true_equiv.
Int 
ln(k*x)
 
ln(abs(x))+c
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(k*abs(x))
 
ln(abs(x))+c
 
x
 1 ATInt_true_equiv.
Int 
ln(abs(k*x))
 
ln(abs(x))+c
 
x
 1 ATInt_true_equiv.
Teacher uses ln(k*abs(x))
Int 
ln(x)
 
ln(k*abs(x))
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(x)+c
 
ln(k*abs(x))
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(abs(x))
 
ln(k*abs(x))
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
ln(abs(x))+c
 
ln(k*abs(x))
 
x
 1 ATInt_true_equiv.
Int 
ln(k*x)
 
ln(k*abs(x))
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(k*abs(x))
 
ln(k*abs(x))
 
x
 1 ATInt_true_equiv.
Other logs
Int 
ln(x)+ln(a)
 
ln(k*abs(x+a))
 
x
 0 ATInt_generic. ATInt_logabs.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\frac{1}{x+a}\] In fact, the derivative of your answer, with respect to \(x\) is: \[\frac{1}{x}\] so you must have done something wrong! Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
log(x)^2-2*log(c)*log(x)+k
 
ln(c/x)^2
 
x
 0 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int 
log(x)^2-2*log(c)*log(x)+k
 
ln(abs(c/x))^2
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[-\frac{2\cdot \ln \left( \frac{\left| c\right| }{\left| x\right| } \right)}{x}\] In fact, the derivative of your answer, with respect to \(x\) is: \[\frac{2\cdot \ln \left( x \right)}{x}-\frac{2\cdot \ln \left( c \right)}{x}\] so you must have done something wrong!
Int 
c-(log(2)-log(x))^2/2
 
-1/2*log(2/x)^2
 
x
 1 ATInt_true_equiv.
Int 
ln(abs(x+3))/2+c
 
ln(abs(2*x+6))/2+c
 
x
 0 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int 
ln(abs(x+3))/2+c
 
ln(abs(2*x+6))/2+c
 
[x, FORMAL]
 1 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int 
ln(abs(x+3))/2
 
ln(abs(2*x+6))/2+c
 
[x, FORMAL]
 1 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int 
ln(abs(x+3))/2
 
ln(abs(2*x+6))/2+c
 
[x, FORMAL, NOC
ONST]
 1 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int 
ln(abs(x+3))/2
 
ln(abs(2*x+6))/2+c
 
[x, NOCONST, FO
RMAL]
 1 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int ! 
ln(abs(x+3))/2
 
ln(abs(2*x+6))/2+c
 
[x, NOCONST]
 -3 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int 
-log(sqrt(x^2-4*x+3)+x-2)/2+(x
*sqrt(x^2-4*x+3))/2-sqrt(x^2-4
*x+3)+c
 
integrate(sqrt(x^2-4*x+3),x)
 
x
 0 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int 
-log(sqrt(x^2-4*x+3)+x-2)/2+(x
*sqrt(x^2-4*x+3))/2-sqrt(x^2-4
*x+3)+c
 
integrate(sqrt(x^2-4*x+3),x)
 
[x, FORMAL]
 1 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Irreducible quadratic
Int 
ln(x^2+7*x+7)
 
ln(x^2+7*x+7)
 
[x,NOCONST]
 1 ATInt_const_condone.
Int 
ln(x^2+7*x+7)
 
ln(abs(x^2+7*x+7))
 
[x,NOCONST]
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(x^2+7*x+7)+c
 
ln(x^2+7*x+7)+c
 
x
 1 ATInt_true_equiv.
Int 
ln(k*(x^2+7*x+7))
 
ln(x^2+7*x+7)+c
 
x
 1 ATInt_true_equiv.
Int 
ln(x^2+7*x+7)
 
ln(abs(x^2+7*x+7))+c
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(x^2+7*x+7)+c
 
ln(abs(x^2+7*x+7))+c
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
-2*log(x)-(10*x^6)/3+x^3/3+5*l
og(x^4)+c
 
-2*log(abs(x))+(10*x^6)/3-x^3/
3-5/x^3+c
 
x
 0 ATInt_generic. ATInt_logabs.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[20\cdot x^5-x^2-\frac{2}{x}+\frac{15}{x^4}\] In fact, the derivative of your answer, with respect to \(x\) is: \[-20\cdot x^5+x^2+\frac{18}{x}\] so you must have done something wrong! Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
ln(abs(x^2+7*x+7))+c
 
ln(abs(x^2+7*x+7))+c
 
x
 1 ATInt_true_equiv.
Int 
ln(k*abs(x^2+7*x+7))
 
ln(abs(x^2+7*x+7))+c
 
x
 1 ATInt_true_equiv.
Two logs
Int 
log(abs(x-3))+log(abs(x+3))
 
log(abs(x-3))+log(abs(x+3))
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
log(abs(x-3))+log(abs(x+3))+c
 
log(abs(x-3))+log(abs(x+3))
 
x
 1 ATInt_true_equiv.
Int 
log(abs(x-3))+log(abs(x+3))
 
log(x-3)+log(x+3)
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
log(abs(x-3))+log(abs(x+3))+c
 
log(x-3)+log(x+3)
 
x
 1 ATInt_true_equiv.
Int 
log(x-3)+log(x+3)
 
log(x-3)+log(x+3)
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
log(x-3)+log(x+3)+c
 
log(x-3)+log(x+3)
 
x
 1 ATInt_true_equiv.
Int 
log(x-3)+log(x+3)
 
log(abs(x-3))+log(abs(x+3))
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
log(x-3)+log(x+3)+c
 
log(abs(x-3))+log(abs(x+3))
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
log(abs((x-3)*(x+3)))+c
 
log(abs(x-3))+log(abs(x+3))
 
x
 1 ATInt_true_equiv.
Int 
log(abs((x^2-9)))+c
 
log(abs(x-3))+log(abs(x+3))
 
x
 0 ATInt_EqFormalDiff.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.
Int 
2*log(abs(x-2))-log(abs(x+2))+
(x^2+4*x)/2
 
-log(abs(x+2))+2*log(abs(x-2))
+(x^2+4*x)/2+c
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
-log(abs(x+2))+2*log(abs(x-2))
+(x^2+4*x)/2+c
 
-log(abs(x+2))+2*log(abs(x-2))
+(x^2+4*x)/2+c
 
x
 1 ATInt_true_equiv.
Int 
-log(abs(x+2))+2*log(abs(x-2))
+(x^2+4*x)/2+c
 
-log((x+2))+2*log((x-2))+(x^2+
4*x)/2
 
x
 1 ATInt_true_equiv.
Inconsistent log(abs())
Int 
log(abs(x-3))+log((x+3))+c
 
log(x-3)+log(x+3)
 
x
 0 ATInt_true_equiv. ATInt_logabs_inconsistent.
There appear to be strange inconsistencies between your use of \(\log(...)\) and \(\log(|...|)\). Please ask your teacher about this.
Int 
log((v-3))+log(abs(v+3))+c
 
log(v-3)+log(v+3)
 
v
 0 ATInt_true_equiv. ATInt_logabs_inconsistent.
There appear to be strange inconsistencies between your use of \(\log(...)\) and \(\log(|...|)\). Please ask your teacher about this.
Int 
log((x-3))+log(abs(x+3))
 
log(x-3)+log(x+3)
 
x
 0 ATInt_const. ATInt_logabs_inconsistent.
There appear to be strange inconsistencies between your use of \(\log(...)\) and \(\log(|...|)\). Please ask your teacher about this.
Int 
2*log((x-2))-log(abs(x+2))+(x^
2+4*x)/2
 
-log(abs(x+2))+2*log(abs(x-2))
+(x^2+4*x)/2
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs. ATInt_logabs_inconsistent.
There appear to be strange inconsistencies between your use of \(\log(...)\) and \(\log(|...|)\). Please ask your teacher about this.
Significant integration constant differences
Int 
2*(sqrt(t)-5)-10*log((sqrt(t)-
5))+c
 
2*(sqrt(t)-5)-10*log((sqrt(t)-
5))+c
 
t
 1 ATInt_true_equiv.
Int 
2*(sqrt(t))-10*log((sqrt(t)-5)
)+c
 
2*(sqrt(t)-5)-10*log((sqrt(t)-
5))+c
 
t
 1 ATInt_true_differentconst.
Int 
2*(sqrt(t)-5)-10*log((sqrt(t)-
5))+c
 
2*(sqrt(t)-5)-10*log(abs(sqrt(
t)-5))+c
 
t
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
2*(sqrt(t))-10*log(abs(sqrt(t)
-5))+c
 
2*(sqrt(t)-5)-10*log(abs(sqrt(
t)-5))+c
 
t
 1 ATInt_true_differentconst.
Trig
Int 
2*sin(x)*cos(x)
 
sin(2*x)+c
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
2*sin(x)*cos(x)+k
 
sin(2*x)+c
 
x
 1 ATInt_true.
Int 
-2*cos(3*x)/3-3*cos(2*x)/2
 
-2*cos(3*x)/3-3*cos(2*x)/2+c
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
-2*cos(3*x)/3-3*cos(2*x)/2+1
 
-2*cos(3*x)/3-3*cos(2*x)/2+c
 
x
 0 ATInt_const_int.
You need to add a constant of integration. This should be an arbitrary constant, not a number.
Int 
-2*cos(3*x)/3-3*cos(2*x)/2+c
 
-2*cos(3*x)/3-3*cos(2*x)/2+c
 
x
 1 ATInt_true.
Int 
(tan(2*t)-2*t)/2
 
-(t*sin(4*t)^2-sin(4*t)+t*cos(
4*t)^2+2*t*cos(4*t)+t)/(sin(4*
t)^2+cos(4*t)^2+2*cos(4*t)+1)
 
t
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
(tan(2*t)-2*t)/2+1
 
-(t*sin(4*t)^2-sin(4*t)+t*cos(
4*t)^2+2*t*cos(4*t)+t)/(sin(4*
t)^2+cos(4*t)^2+2*cos(4*t)+1)
 
t
 0 ATInt_const_int.
You need to add a constant of integration. This should be an arbitrary constant, not a number.
Int 
(tan(2*t)-2*t)/2+c
 
-(t*sin(4*t)^2-sin(4*t)+t*cos(
4*t)^2+2*t*cos(4*t)+t)/(sin(4*
t)^2+cos(4*t)^2+2*cos(4*t)+1)
 
t
 1 ATInt_true.
Int 
tan(x)-x+c
 
tan(x)-x
 
x
 1 ATInt_true.
Int 
4*x*cos(x^12/%pi)+c
 
x*cos(x^12/%pi)+c
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\cos \left( \frac{x^{12}}{\pi} \right)-\frac{12\cdot x^{12}\cdot \sin \left( \frac{x^{12}}{\pi} \right)}{\pi}\] In fact, the derivative of your answer, with respect to \(x\) is: \[4\cdot \cos \left( \frac{x^{12}}{\pi} \right)-\frac{48\cdot x^{12} \cdot \sin \left( \frac{x^{12}}{\pi} \right)}{\pi}\] so you must have done something wrong!
Int 
4*x*cos(x^50/%pi)+c
 
x*cos(x^12/%pi)+c
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\cos \left( \frac{x^{12}}{\pi} \right)-\frac{12\cdot x^{12}\cdot \sin \left( \frac{x^{12}}{\pi} \right)}{\pi}\] In fact, the derivative of your answer, with respect to \(x\) is: \[4\cdot \cos \left( \frac{x^{50}}{\pi} \right)-\frac{200\cdot x^{50} \cdot \sin \left( \frac{x^{50}}{\pi} \right)}{\pi}\] so you must have done something wrong!
Note the difference in feedback here, generated by the options.
Int 
((5*%e^7*x-%e^7)*%e^(5*x))
 
((5*%e^7*x-%e^7)*%e^(5*x))/25+
c
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\frac{e^{5\cdot x+7}}{5}+\frac{\left(5\cdot e^7\cdot x-e^7\right) \cdot e^{5\cdot x}}{5}\] In fact, the derivative of your answer, with respect to \(x\) is: \[5\cdot e^{5\cdot x+7}+5\cdot \left(5\cdot e^7\cdot x-e^7\right) \cdot e^{5\cdot x}\] so you must have done something wrong!
Int 
((5*%e^7*x-%e^7)*%e^(5*x))
 
((5*%e^7*x-%e^7)*%e^(5*x))/25+
c
 
[x,x*%e^(5*x+7)
]
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[x\cdot e^{5\cdot x+7}\] In fact, the derivative of your answer, with respect to \(x\) is: \[5\cdot e^{5\cdot x+7}+5\cdot \left(5\cdot e^7\cdot x-e^7\right) \cdot e^{5\cdot x}\] so you must have done something wrong!
Inverse hyperbolic integrals
Int 
log(x-3)/6-log(x+3)/6+c
 
log(x-3)/6-log(x+3)/6
 
x
 1 ATInt_true_equiv.
Int 
asinh(x)
 
ln(x+sqrt(x^2+1))
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
asinh(x)+c
 
ln(x+sqrt(x^2+1))
 
x
 1 ATInt_true.
Int 
-acoth(x/3)/3
 
log(x-3)/6-log(x+3)/6
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
-acoth(x/3)/3
 
log(x-3)/6-log(x+3)/6
 
[x, NOCONST]
 1 ATInt_true.
Int 
-acoth(x/3)/3+c
 
log(x-3)/6-log(x+3)/6
 
x
 1 ATInt_true.
Int 
-acoth(x/3)/3+c
 
log(abs(x-3))/6-log(abs(x+3))/
6
 
x
 1 ATInt_true.
Int 
log(x-a)/(2*a)-log(x+a)/(2*a)+
c
 
log(x-a)/(2*a)-log(x+a)/(2*a)
 
x
 1 ATInt_true_equiv.
Int 
-acoth(x/a)/a+c
 
log(x-a)/(2*a)-log(x+a)/(2*a)
 
x
 1 ATInt_true.
Int 
-acoth(x/a)/a+c
 
log(abs(x-a))/(2*a)-log(abs(x+
a))/(2*a)
 
x
 1 ATInt_true.
Int 
log(x-a)/(2*a)-log(x+a)/(2*a)+
c
 
log(abs(x-a))/(2*a)-log(abs(x+
a))/(2*a)
 
x
 0 ATInt_EqFormalDiff. ATInt_logabs.
The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \(\int\frac{1}{x} dx = \log(|x|)+c\), rather than \(\int\frac{1}{x} dx = \log(x)+c\). Please ask your teacher about this.
Int 
log(x-3)/6-log(x+3)/6+c
 
-acoth(x/3)/3
 
x
 1 ATInt_true.
Int 
log(abs(x-3))/6-log(abs(x+3))/
6+c
 
-acoth(x/3)/3
 
x
 1 ATInt_true.
Int 
log(x-3)/6-log(x+3)/6
 
-acoth(x/3)/3
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
atan(2*x-3)+c
 
atan(2*x-3)
 
x
 1 ATInt_true.
Int 
atan((x-2)/(x-1))+c
 
atan(2*x-3)
 
x
 1 ATInt_true.
Int 
atan((x-2)/(x-1))
 
atan(2*x-3)
 
x
 0 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.
Int 
atan((x-1)/(x-2))
 
atan(2*x-3)
 
x
 0 ATInt_generic.
The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \[\frac{2}{{\left(2\cdot x-3\right)}^2+1}\] In fact, the derivative of your answer, with respect to \(x\) is: \[\frac{\frac{1}{x-2}-\frac{x-1}{{\left(x-2\right)}^2}}{\frac{{\left( x-1\right)}^2}{{\left(x-2\right)}^2}+1}\] so you must have done something wrong!
Stoutemyer (currently fails)
Int ! 
2/3*sqrt(3)*(atan(sin(x)/(sqrt
(3)*(cos(x)+1)))-(atan(sin(x)/
(cos(x)+1))))+x/sqrt(3)
 
2*atan(sin(x)/(sqrt(3)*(cos(x)
+1)))/sqrt(3)
 
x
 -3 ATInt_const.
You need to add a constant of integration, otherwise this appears to be correct. Well done.