Question

Помогите найти интеграл

Answer 1

$int frac{sin^3x dx}{sqrt{cos x}} = -int frac{sin^2x d( cos x )}{sqrt{ cos x}} = int frac{(cos^2x-1) d( cos x )}{sqrt{ cos x}} = left[begin{array}{ccc}cos x = tend{array}right] =\ = int frac{t^2-1}{sqrt{t}} dt = int t^{frac{3}{2}} dt - int t^{-frac{1}{2}} dt = frac{2}{5} t^{frac{5}{2}} -2t^{frac{1}{2}} +C = frac{2}{5} t^2sqrt{t} - 2sqrt{t} +C = \ = frac{2}{5} cos^2x sqrt{ cos x} - 2sqrt{ cos x} +C$