[Math] Integrate $\int{\frac{\sin(2x)+\cos(2x)}{(\sin(2x)-\cos(2x))^{5/2}}}\,\mathrm dx$.

calculusintegration

Integrate $$\int{\frac{\sin(2x)+\cos(2x)}{(\sin(2x)-\cos(2x))^{5/2}}}\,\mathrm
dx.$$

How do I integrate such an integral?

u-substitution, no idea

by parts, no idea

this is very confusing! please help!

Best Answer

Hint:

With inside functions, in this case $(\sin 2x-\cos 2x)$, a $u$-substitution is a great place to start.

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