Reduction Formula for `int sin^m x cos^n x dx`

Reduction Formula for int sin^(m)x cos^(n)xdx

Evaluate the reduction formula for I_n = int cos^n x dx and hence find int cos^4 x dx .

int sin x cos(cos x)dx

int sin x sin (cos x) dx

int sin x sin (cos x) dx

Obtain reduction formula for I_n = int sin^n x dx for an integer n ge 2 and deduce the value of int sin^4 x dx .

int sin x sin (cos x)dx

int sin x sin (cos x) dx.