Question

первообразная $frac{1}{sin^25x}$ равна $-ctg5x?$

Answer 1

$intfrac{1}{sin^2(5x)}dx=[d(5x)=5dxrightarrow dx=frac{d(5x)}{5}]=intfrac{1}{sin^2(5x)}*frac{d(5x)}{5}=\=frac{1}{5}intfrac{d(5x)}{sin^2(5x)}=frac{1}{5}*(-ctg(5x))=-frac{ctg(5x)}{5}$