Evaluate `int_(-1)^(1)sin^(5)xcos^(4)xdx`

Prove that int_(-a)^(a) dx = {(2int_(0)^(a) f(x) dx, if f(x) "is even"),(0, if f(x) "is odd"):} and hence evaluate (a) int_(-1)^(1) sin^(5)x cos^(4)xdx .

int_0^(pi) sin^(50)x.cos^(49)xdx=

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Find : int(1)/(sin^(4)x+cos^(4)x)dx .

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