Find `int_0^pi xsin^2xdx`

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int_0^pi xcos^2xdx

"int_0^pi sin^(2)xdx

int_0^(pi/2)sin^2xdx =

"int_0^pi cos^(2)xdx

int_0^(pi/2) cos^5xdx

int_0^(pi/4) sec^4xdx

int_0^(pi/4) tan^3xdx

int xsin xdx=

int_0^(pi/2) xsinxsin2xdx

Prove that int_0^pi x sin^6xcos^4xdx=pi/2 int_0^pi sin^6xcos^4xdx