Question

Найти интеграл: (ctg(z) + 1)^4 / sin^2(z)dz)

Answer 1

$int frac{(ctgz+1)^4}{sin^2z}dz=[, t=ctgz+1,; dt=-frac{dz}{sin^2z}, ]=-int t^4, dt=-frac{t^5}{5}+C=\\=-frac{1}{5}(ctgz+1)^5+C$