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Antidiff: 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.

Antidiff

Test
?
Student response
Teacher answer
Opt
Mark
Answer note
Antidiff 
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.
Antidiff 
1/0
 
1
 
x
 -1 ATAntidiff_STACKERROR_SAns.
Antidiff 
1
 
1/0
 
x
 -1 ATAntidiff_STACKERROR_TAns.
Antidiff 
0
 
0
 
1/0
 -1 ATAntidiff_STACKERROR_Opt.
Antidiff 
0
 
0
 
[x,1/0]
 -1 ATAntidiff_STACKERROR_Opt.
Antidiff 
0
 
0
 
[x,NOCONST,1/0]
 -1 ATAntidiff_STACKERROR_Opt.
Basic tests
Antidiff 
x^3/3
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3+1
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3+c
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3-c
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3+c+1
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3+3*c
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
(x^3+c)/3
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^(k+1)/(k+1)
 
x^(k+1)/(k+1)
 
x
 1 ATAntidiff_true.
Antidiff 
x^(k+1)/(k+1)+c
 
x^(k+1)/(k+1)
 
x
 1 ATAntidiff_true.
Antidiff 
(x^(k+1)-1)/(k+1)
 
x^(k+1)/(k+1)
 
x
 1 ATAntidiff_true.
Antidiff 
(x^(k+1)-1)/(k+1)+c
 
x^(k+1)/(k+1)+c
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3+c+k
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3+c^2
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3+c^3
 
x^3/3
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3*c
 
x^3/3
 
x
 0 ATAntidiff_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!
Antidiff 
X^3/3+c
 
x^3/3
 
x
 0 ATAntidiff_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: \[0\] so you must have done something wrong!
Antidiff 
sin(2*x)
 
x^3/3
 
x
 0 ATAntidiff_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!
Antidiff 
x^2/2-2*x+2+c
 
(x-2)^2/2
 
x
 1 ATAntidiff_true.
Antidiff 
(t-1)^5/5+c
 
(t-1)^5/5
 
t
 1 ATAntidiff_true.
Antidiff 
(v-1)^5/5+c
 
(v-1)^5/5
 
v
 1 ATAntidiff_true.
Antidiff 
cos(2*x)/2+1+c
 
cos(2*x)/2
 
x
 1 ATAntidiff_true.
Antidiff 
(x-a)^6001/6001+c
 
(x-a)^6001/6001
 
x
 1 ATAntidiff_true.
Antidiff 
(x-a)^6001/6001
 
(x-a)^6001/6001
 
x
 1 ATAntidiff_true.
Antidiff 
6000*(x-a)^5999
 
(x-a)^6001/6001
 
x
 0 ATAntidiff_diff.
It looks like you have differentiated instead!
Antidiff 
4*%e^(4*x)/(%e^(4*x)+1)
 
log(%e^(4*x)+1)+c
 
x
 0 ATAntidiff_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
Antidiff 
x^3/3+c
 
x^3/3+c
 
x
 1 ATAntidiff_true.
Antidiff 
x^2/2-2*x+2+c
 
(x-2)^2/2+k
 
x
 1 ATAntidiff_true.
Antidiff 
x^3/3
 
x^3/3
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
x^3/3+c
 
x^3/3
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
x^2/2-2*x+2
 
(x-2)^2/2+k
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
x^3/3+1
 
x^3/3
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
x^3/3+c^2
 
x^3/3
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
n*x^n
 
n*x^(n-1)
 
x
 0 ATAntidiff_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!
Antidiff 
n*x^n
 
(assume(n>0), n*x^(n-1))
 
x
 0 ATAntidiff_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
Antidiff 
exp(x)+c
 
exp(x)
 
x
 1 ATAntidiff_true.
Antidiff 
exp(x)
 
exp(x)
 
x
 1 ATAntidiff_true.
Antidiff 
exp(x)
 
exp(x)
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Student differentiates by mistake
Antidiff 
2*x
 
x^3/3
 
x
 0 ATAntidiff_diff.
It looks like you have differentiated instead!
Antidiff 
2*x+c
 
x^3/3
 
x
 0 ATAntidiff_diff.
It looks like you have differentiated instead!
Sloppy logs (teacher ignores abs(x) )
Antidiff 
ln(x)
 
ln(x)
 
x
 1 ATAntidiff_true.
Antidiff 
ln(x)
 
ln(x)
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
ln(x)+c
 
ln(x)+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(k*x)
 
ln(x)+c
 
x
 1 ATAntidiff_true.
Fussy logs (teacher uses abs(x) )
Antidiff 
ln(x)
 
ln(abs(x))+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(x)+c
 
ln(abs(x))+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(x)
 
ln(abs(x))+c
 
[x, NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
ln(abs(x))
 
ln(abs(x))+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(abs(x))+c
 
ln(abs(x))+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(k*x)
 
ln(abs(x))+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(k*abs(x))
 
ln(abs(x))+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(abs(k*x))
 
ln(abs(x))+c
 
x
 1 ATAntidiff_true.
Teacher uses ln(k*abs(x))
Antidiff 
ln(x)
 
ln(k*abs(x))
 
x
 1 ATAntidiff_true.
Antidiff 
ln(x)+c
 
ln(k*abs(x))
 
x
 1 ATAntidiff_true.
Antidiff 
ln(abs(x))
 
ln(k*abs(x))
 
x
 1 ATAntidiff_true.
Antidiff 
ln(abs(x))+c
 
ln(k*abs(x))
 
x
 1 ATAntidiff_true.
Antidiff 
ln(k*x)
 
ln(k*abs(x))
 
x
 1 ATAntidiff_true.
Antidiff 
ln(k*abs(x))
 
ln(k*abs(x))
 
x
 1 ATAntidiff_true.
Other logs
Antidiff 
ln(x)+ln(a)
 
ln(k*abs(x+a))
 
x
 0 ATAntidiff_generic.
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!
Antidiff 
log(x)^2-2*log(c)*log(x)+k
 
ln(c/x)^2
 
x
 1 ATAntidiff_true.
Antidiff ! 
log(x)^2-2*log(c)*log(x)+k
 
ln(abs(c/x))^2
 
x
 -3 ATAntidiff_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!
Antidiff 
c-(log(2)-log(x))^2/2
 
-1/2*log(2/x)^2
 
x
 1 ATAntidiff_true.
Antidiff 
ln(abs(x+3))/2+c
 
ln(abs(2*x+6))/2+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(abs(x+3))/2+c
 
ln(abs(2*x+6))/2+c
 
[x, FORMAL]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
ln(abs(x+3))/2
 
ln(abs(2*x+6))/2+c
 
[x, FORMAL]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
ln(abs(x+3))/2
 
ln(abs(2*x+6))/2+c
 
[x, FORMAL, NOC
ONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
ln(abs(x+3))/2
 
ln(abs(2*x+6))/2+c
 
[x, NOCONST, FO
RMAL]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
ln(abs(x+3))/2
 
ln(abs(2*x+6))/2+c
 
[x, NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
-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
 1 ATAntidiff_true.
Antidiff 
-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 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Irreducible quadratic
Antidiff 
ln(x^2+7*x+7)
 
ln(x^2+7*x+7)
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
ln(x^2+7*x+7)
 
ln(abs(x^2+7*x+7))
 
[x,NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
ln(x^2+7*x+7)+c
 
ln(x^2+7*x+7)+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(k*(x^2+7*x+7))
 
ln(x^2+7*x+7)+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(x^2+7*x+7)
 
ln(abs(x^2+7*x+7))+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(x^2+7*x+7)+c
 
ln(abs(x^2+7*x+7))+c
 
x
 1 ATAntidiff_true.
Antidiff 
-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 ATAntidiff_generic.
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!
Antidiff 
ln(abs(x^2+7*x+7))+c
 
ln(abs(x^2+7*x+7))+c
 
x
 1 ATAntidiff_true.
Antidiff 
ln(k*abs(x^2+7*x+7))
 
ln(abs(x^2+7*x+7))+c
 
x
 1 ATAntidiff_true.
Two logs
Antidiff 
log(abs(x-3))+log(abs(x+3))
 
log(abs(x-3))+log(abs(x+3))
 
x
 1 ATAntidiff_true.
Antidiff 
log(abs(x-3))+log(abs(x+3))+c
 
log(abs(x-3))+log(abs(x+3))
 
x
 1 ATAntidiff_true.
Antidiff 
log(abs(x-3))+log(abs(x+3))
 
log(x-3)+log(x+3)
 
x
 1 ATAntidiff_true.
Antidiff 
log(abs(x-3))+log(abs(x+3))+c
 
log(x-3)+log(x+3)
 
x
 1 ATAntidiff_true.
Antidiff 
log(x-3)+log(x+3)
 
log(x-3)+log(x+3)
 
x
 1 ATAntidiff_true.
Antidiff 
log(x-3)+log(x+3)+c
 
log(x-3)+log(x+3)
 
x
 1 ATAntidiff_true.
Antidiff 
log(x-3)+log(x+3)
 
log(abs(x-3))+log(abs(x+3))
 
x
 1 ATAntidiff_true.
Antidiff 
log(x-3)+log(x+3)+c
 
log(abs(x-3))+log(abs(x+3))
 
x
 1 ATAntidiff_true.
Antidiff 
log(abs((x-3)*(x+3)))+c
 
log(abs(x-3))+log(abs(x+3))
 
x
 1 ATAntidiff_true.
Antidiff 
log(abs((x^2-9)))+c
 
log(abs(x-3))+log(abs(x+3))
 
x
 1 ATAntidiff_true.
Antidiff 
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
 1 ATAntidiff_true.
Antidiff 
-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 ATAntidiff_true.
Antidiff 
-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 ATAntidiff_true.
Inconsistent log(abs())
Antidiff 
log(abs(x-3))+log((x+3))+c
 
log(x-3)+log(x+3)
 
x
 1 ATAntidiff_true.
Antidiff 
log((v-3))+log(abs(v+3))+c
 
log(v-3)+log(v+3)
 
v
 1 ATAntidiff_true.
Antidiff 
log((x-3))+log(abs(x+3))
 
log(x-3)+log(x+3)
 
x
 1 ATAntidiff_true.
Antidiff 
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
 1 ATAntidiff_true.
Significant integration constant differences
Antidiff 
2*(sqrt(t)-5)-10*log((sqrt(t)-
5))+c
 
2*(sqrt(t)-5)-10*log((sqrt(t)-
5))+c
 
t
 1 ATAntidiff_true.
Antidiff 
2*(sqrt(t))-10*log((sqrt(t)-5)
)+c
 
2*(sqrt(t)-5)-10*log((sqrt(t)-
5))+c
 
t
 1 ATAntidiff_true.
Antidiff 
2*(sqrt(t)-5)-10*log((sqrt(t)-
5))+c
 
2*(sqrt(t)-5)-10*log(abs(sqrt(
t)-5))+c
 
t
 1 ATAntidiff_true.
Antidiff 
2*(sqrt(t))-10*log(abs(sqrt(t)
-5))+c
 
2*(sqrt(t)-5)-10*log(abs(sqrt(
t)-5))+c
 
t
 1 ATAntidiff_true.
Trig
Antidiff 
2*sin(x)*cos(x)
 
sin(2*x)+c
 
x
 1 ATAntidiff_true.
Antidiff 
2*sin(x)*cos(x)+k
 
sin(2*x)+c
 
x
 1 ATAntidiff_true.
Antidiff 
-2*cos(3*x)/3-3*cos(2*x)/2
 
-2*cos(3*x)/3-3*cos(2*x)/2+c
 
x
 1 ATAntidiff_true.
Antidiff 
-2*cos(3*x)/3-3*cos(2*x)/2+1
 
-2*cos(3*x)/3-3*cos(2*x)/2+c
 
x
 1 ATAntidiff_true.
Antidiff 
-2*cos(3*x)/3-3*cos(2*x)/2+c
 
-2*cos(3*x)/3-3*cos(2*x)/2+c
 
x
 1 ATAntidiff_true.
Antidiff 
(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
 1 ATAntidiff_true.
Antidiff 
(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
 1 ATAntidiff_true.
Antidiff 
(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 ATAntidiff_true.
Antidiff 
tan(x)-x+c
 
tan(x)-x
 
x
 1 ATAntidiff_true.
Antidiff 
4*x*cos(x^12/%pi)+c
 
x*cos(x^12/%pi)+c
 
x
 0 ATAntidiff_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!
Antidiff 
4*x*cos(x^50/%pi)+c
 
x*cos(x^12/%pi)+c
 
x
 0 ATAntidiff_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.
Antidiff 
((5*%e^7*x-%e^7)*%e^(5*x))
 
((5*%e^7*x-%e^7)*%e^(5*x))/25+
c
 
x
 0 ATAntidiff_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!
Antidiff 
((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)
]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Inverse hyperbolic integrals
Antidiff 
log(x-3)/6-log(x+3)/6+c
 
log(x-3)/6-log(x+3)/6
 
x
 1 ATAntidiff_true.
Antidiff 
asinh(x)
 
ln(x+sqrt(x^2+1))
 
x
 1 ATAntidiff_true.
Antidiff 
asinh(x)+c
 
ln(x+sqrt(x^2+1))
 
x
 1 ATAntidiff_true.
Antidiff 
-acoth(x/3)/3
 
log(x-3)/6-log(x+3)/6
 
x
 1 ATAntidiff_true.
Antidiff 
-acoth(x/3)/3
 
log(x-3)/6-log(x+3)/6
 
[x, NOCONST]
 -1 ATAntidiff_STACKERROR_Opt.
The answer test failed to execute correctly: please alert your teacher. There is something wrong with the options given to the ATAntidiff answer test.
Antidiff 
-acoth(x/3)/3+c
 
log(x-3)/6-log(x+3)/6
 
x
 1 ATAntidiff_true.
Antidiff 
-acoth(x/3)/3+c
 
log(abs(x-3))/6-log(abs(x+3))/
6
 
x
 1 ATAntidiff_true.
Antidiff 
log(x-a)/(2*a)-log(x+a)/(2*a)+
c
 
log(x-a)/(2*a)-log(x+a)/(2*a)
 
x
 1 ATAntidiff_true.
Antidiff 
-acoth(x/a)/a+c
 
log(x-a)/(2*a)-log(x+a)/(2*a)
 
x
 1 ATAntidiff_true.
Antidiff 
-acoth(x/a)/a+c
 
log(abs(x-a))/(2*a)-log(abs(x+
a))/(2*a)
 
x
 1 ATAntidiff_true.
Antidiff 
log(x-a)/(2*a)-log(x+a)/(2*a)+
c
 
log(abs(x-a))/(2*a)-log(abs(x+
a))/(2*a)
 
x
 1 ATAntidiff_true.
Antidiff 
log(x-3)/6-log(x+3)/6+c
 
-acoth(x/3)/3
 
x
 1 ATAntidiff_true.
Antidiff 
log(abs(x-3))/6-log(abs(x+3))/
6+c
 
-acoth(x/3)/3
 
x
 1 ATAntidiff_true.
Antidiff 
log(x-3)/6-log(x+3)/6
 
-acoth(x/3)/3
 
x
 1 ATAntidiff_true.
Antidiff 
atan(2*x-3)+c
 
atan(2*x-3)
 
x
 1 ATAntidiff_true.
Antidiff 
atan((x-2)/(x-1))+c
 
atan(2*x-3)
 
x
 1 ATAntidiff_true.
Antidiff 
atan((x-2)/(x-1))
 
atan(2*x-3)
 
x
 1 ATAntidiff_true.
Antidiff 
atan((x-1)/(x-2))
 
atan(2*x-3)
 
x
 0 ATAntidiff_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 in ATInt, but works in ATAntidiff)
Antidiff 
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
 1 ATAntidiff_true.