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.

Thank you.