Exam question - Integrals
The results of my calculus exam came and there is a question I had wrong.
Which is the integral of (sin(logx))/x?
My answer was -cos(logx) + c
I checked wolfram and the answer is the same, therefore that makes my answer correct right?
However, it says on the paper that this answer is wrong.
I did some research and realised that the derivative of -cos(logx) is not (sin(logx))/x, and maybe that's why it is wrong.
But how come I did not get the correct answer? Even wolfram says my answer is correct.
My resoltuion process was the following:
- turn (logx) into u;
- turn du into (1/x)dx -------> dx = xdu
- that gives me the integral of (xsen(u)/x);
- cutting the x's on either side gives me the integral of sen(u)
- resolving the integral gives me -cos(u)
- replacing the u gives me -cos(logx) and the add the constant +c
This method always never failed me, so what went wrong?
I have to go to college tomorrow to defend my answer, so I would like to get some replies fast... I need two points more on this exam to pass this subject.