Question

Срочно нужно найти интеграл!!!
1. dx/sqrt(x)(x-1)
2. (cos4x - cos6x)/sin5x

Answer 1

$1); int frac{dx}{ sqrt{x}(x-1)} =[, x=t^2; ,; t= sqrt{x}; ,; dx=2t, dt; ]=int frac{2t, dt}{tcdot (t^2-1)}=\\=int frac{2, dt}{t^2-1}=2cdot frac{1}{2}cdot ln| frac{t-1}{t+1}|+C=ln| frac{ sqrt{x}-1}{ sqrt{x}+1} |+C$

$2)int frac{cos4x-cos6x}{sis5x}dx=int frac{-2cdot sin5xcdot sin(-x)}{sin5x}dx=2int sinx, dx=\\=2cdot (-cosx)+C=-2cosx+C$