integrate int[0, pi/4] ( 1 / (1 + sin(2x) + cos(2x) ) dx

[shaswata tripathy]

\(\displaystyle \displaystyle{\int_0^{\frac{\pi}{4}}}\, \dfrac{x}{1\, +\, \sin(2x)\, +\, \cos(2x)}\, dx\)

please help me to integrate this

 

[Quaid]

What have you thought about or tried, so far?


Have you considered using any trigonometric identities?

 

[pka]

View attachment 3618 please help me to integrate this

Sorry to tell you, but there is no elementary way of doing this. There is no closed form.
One has to use numerical methods.
If you simply need the answer, then look here.

 

[stapel]

\(\displaystyle \displaystyle{\int_0^{\frac{\pi}{4}}}\, \dfrac{x}{1\, +\, \sin(2x)\, +\, \cos(2x)}\, dx\)

please help me to integrate this

We'll be glad to help. Of course, "helping" doesn't mean "doing it for you"; that would be called "cheating". :lol:

Please reply with an explanation of what method(s) you believe you are supposed to be using (numerical? in a spreadsheet? approximation using summation? using midpoints? etc), so we have a better chance of understanding what is going on here. When you reply, please include a clear listing of your efforts, showing what you've tried and where you ground to a halt. Thank you! :wink: