Integration with Sines and Cosines

[Ayesh]

Homework Statement

$$\int$$sinxcosx/sin^4x+cos^4x

Homework Equations

sin^2x=1/2-1/2cos(2x)

cos^2x=1/2+1/2cos(2x)

sinxcosx=1/2sin(2x)

The Attempt at a Solution

$$\int$$1/2 sin(2x)/(1/2-1/2cos(2x))^2 + (1/2 + 1/2cos(2x))^2

$$\int$$1/2 sin(2x)/1/2 + 1/2cos^2(2x)

...?

Am I on the right track?

 

[tiny-tim]

Hi Ayesh!

(have an integral: ∫ and try using the X² tag just above the Reply box )

… $$\int$$1/2 sin(2x)/1/2 + 1/2cos^2(2x)

...?

Am I on the right track?

Yes, that's fine.

(though it would have been quicker to notice that the original denominator is almost the square of cos²x + sin²x )

And you should be able to integrate it immediately.

 

[Ayesh]

Thank you!