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# Trigonometric Integral Question Watch

1. 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?

2. (Original post by Magu1re)
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?

It can be re-written; have a go.
3. (Original post by Magu1re)
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?

If you let this integral be called I and define J as:
.
Consider the values of I+J and I-J, Solve these two simultaneous equations for I.
4. (Original post by Farhan.Hanif93)
If you let this integral be called I and define J as:
.
Consider the values of I+J and I-J, Solve these two simultaneous equations for I.
Good luck with your interview tomorrow x
5. (Original post by boromir9111)
Good luck with your interview tomorrow x
Thank you! I'm gonna need it.
6. (Original post by Farhan.Hanif93)
If you let this integral be called I and define J as:
.
Consider the values of I+J and I-J, Solve these two simultaneous equations for I.
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!
7. (Original post by Farhan.Hanif93)
Thank you! I'm gonna need it.
I think not but good luck from me too.
8. (Original post by Magu1re)
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!
Find the constants, and , such that .
Then use this result to transform the integral.

(Original post by Mr M)
I think not but good luck from me too.
Thank you, your words are encouraging.
9. (Original post by Magu1re)
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?

Divide both the numerator and the denominator by cosx.
and use the tan x = t and dx=1/(1+t^2) dt substitution

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