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Prove that int(-a)^(a) dx = {(2int(0)^(a...

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
(d) `int_(-pi//2)^(pi//2)tan^(9) xdx`.

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