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
Opt
Mark
Int
1/0
1
-1 STACKERROR_OPTION.
TEST_FAILED
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.
Int
x^3/3+c+k
x^3/3
x
0 ATInt_weirdconst.
Int
x^3/3+c^2
x^3/3
x
0 ATInt_weirdconst.
Int
x^3/3+c^3
x^3/3
x
0 ATInt_weirdconst.
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!
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.
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. 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. 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. 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. 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. 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. 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. 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 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. 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.
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.
Int
ln(abs(x+3))/2+c
ln(abs(2*x+6))/2+c
[x, FORMAL]
1 ATInt_EqFormalDiff.
Int
ln(abs(x+3))/2
ln(abs(2*x+6))/2+c
[x, FORMAL]
1 ATInt_EqFormalDiff.
Int
ln(abs(x+3))/2
ln(abs(2*x+6))/2+c
[x, FORMAL, NOC
ONST]
1 ATInt_EqFormalDiff.
Int
ln(abs(x+3))/2
ln(abs(2*x+6))/2+c
[x, NOCONST, FO
RMAL]
1 ATInt_EqFormalDiff.
Int !
ln(abs(x+3))/2
ln(abs(2*x+6))/2+c
[x, NOCONST]
-3 ATInt_EqFormalDiff.
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.
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.
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. 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. 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. 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. 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. 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.
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. 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.
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. 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.