Question

Интеграл.$intlimits , frac{sinx-cosx}{(cosx+sinx)^5} dx$

Answer 1

$int{dfrac{sin(x)-cos(x)}{(cos(x)+sin(x))^5}}dx=begin{vmatrix}u=sin(x)+cos(x)\du=(cos(x)-sin(x))dxend{vmatrix}=-intdfrac{1}{u^5}du=dfrac{1}{4u^4}+C=dfrac{1}{4(sin(x)+cos(x))^4}+C$