Solving $\int {\frac{2 \sin(x) \cos(x)}{\sin^4(x) + \cos^4(x)}}\, dx$ See this link here. I am having trouble with this one as well. Any hints or help appreciated.
$$\int{\frac{2\sin(x)\cos(x)}{\sin^4(x)+\cos^4(x)}}\,dx$$

Hint
For the denominator 
$$\sin^4(x)+\cos^4(x)=(\sin^2(x)+\cos^2(x))^2-2\sin^2(x)\cos^2(x)=1-\frac 12\sin^2(2x)=\frac 12(1+\cos^2(2x))$$
For the numerator $$2\sin(x)\cos(x)=\sin(2x)$$
So $$\int {\frac{2 \sin(x) \cos(x)}{\sin^4(x) + \cos^4(x)}}\, dx=\int \frac{2\sin(2x)}{1+\cos^2(2x)}\,dx$$
Changing variable $t=\cos(2x)$ looks quite promising.
