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int(-1)^(3/2) |xsinpix|dx=[(-xcospix)/pi...

`int_(-1)^(3/2) |xsinpix|dx=[(-xcospix)/pi+(sinpix)/pi^2]_(-1)^1-[(-xcospix)/pi+(sinpix)/pi^2]_1^(3/2)`

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int_(-2)^(2)abs(xcospix)dx is equal to

int_(-(pi)/(2))^((pi)/(2))(sin^3xdx)/(1+cosx)= .

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If int_(-1)^(3//2)|xsinpix|dx = (k)/(pi^(2)) , then the value of k is :

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I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx , I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx . Then

I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx , I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx . Then

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