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int(1+cosx)/(sinxcosx)dx...

`int(1+cosx)/(sinxcosx)dx`

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int(cosx)/(sinx+cosx)dx=

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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

int(dx)/(1+2sinx+cosx)