Question

Интеграл от (tgx-ctgx)^2dx

Answer 1

$int (tgx-ctgx)^2dx=int (tg^2x-2, underbrace {tgx, ctgx}_{1}+ctg^2x)dx=\\=int Big ((frac{1}{cos^2x}-1)-2+(frac{1}{sin^2x}-1)Big )dx=int (frac{1}{cos^2x}+frac{1}{sin^2x}-4)dx=\\=tgx-ctgx-4x+C$