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int(0)^((pi)/(2))(cosx-sinx)/(1+sinxcosx...

`int_(0)^((pi)/(2))(cosx-sinx)/(1+sinxcosx)dx`

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By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sinx-cosx)/(1+sinxcosx)dx

int_0^(pi/2) (cosx-sinx)/(1+sinx cosx) dx =

int_(0)^((pi)/(2))(sinx)/(sinx+cosx)dx

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

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sinx-cosx)/(1+sinxcosx)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sinx-cosx)/(1+sinxcosx)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sinx-cosx)/(1+sinxcosx)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sinx-cosx)/(1+sinxcosx)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sinx-cosx)/(1+sinxcosx)dx