`int(cos2x dx)/(1+sinxcosx)`

Evaluate int(cosx-sinx)/(1+2sinxcosx)dx .

int((sinx+cosx)(1-sinxcosx))/(sin^(2)x cos^(2)x)dx=

int(sinxcosx)/(sin^4x+cos^4x)dx

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

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

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

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