Trigonometric Integral Question

Hello

I am trying to integrate (cosx)/(cosx+sinx).

Through my workings, I have reached a point where I believe the integral to be equal to 0.5u+0.5ln(cosu)+c (where u=x-0.25pi). I know the answer is 0.5x+0.5ln(cosx+sinx)+c. Have I gone wrong somewhere or can my answer be re-written in terms of x?

Please help me

Hello

I am trying to integrate (cosx)/(cosx+sinx).

Through my workings, I have reached a point where I believe the integral to be equal to 0.5u+0.5ln(cosu)+c (where u=x-0.25pi). I know the answer is 0.5x+0.5ln(cosx+sinx)+c. Have I gone wrong somewhere or can my answer be re-written in terms of x?

Please help me

If you let this integral be called I and define J as:
$J=\int \frac{\sin x}{\cos x + \sin x}dx$.
Consider the values of I+J and I-J, Solve these two simultaneous equations for I.

Good luck with your interview tomorrow x

If you let this integral be called I and define J as:
$J=\int \frac{\sin x}{\cos x + \sin x}dx$.
Consider the values of I+J and I-J, Solve these two simultaneous equations for I.

Thank you! I'm gonna need it.

Haha. I too have done this STEP question. I can do it using their method. I just want to know if the second answer is still correct and if so, why it is correct. If someone could show me that would be excellent. If you have an interview tomorrow, good luck with it!

I think not but good luck from me too.

Hello

I am trying to integrate (cosx)/(cosx+sinx).

Through my workings, I have reached a point where I believe the integral to be equal to 0.5u+0.5ln(cosu)+c (where u=x-0.25pi). I know the answer is 0.5x+0.5ln(cosx+sinx)+c. Have I gone wrong somewhere or can my answer be re-written in terms of x?

Please help me