Integral from pi to pi sin^4x cos^5x dx how do it evaluate

He indefinite integral can be found by substitution:u=sin (x) du = cos (x) dxand use sin^2 (x) + cos^2 (x) = 1 to convert sin^4 (x) cos^4 (x) = sin^4 (x) (1-sin^2 (x)) ^2=u^4 (1-u^2) ^2SoI=integral (u^4 (1-u^2) ^2duAnd you'll soon find that the integral with limits - pi to pi, - pi to 0, 0 to pi all give 0.

To make it more understandable,∫sin4 (x) cos5 (x) dx = ∫u4 (1-u2) 2du

withu=sin (x), du=cos (x) dx