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int(0)^(2)(sin x-cos x)/(1+sin x cos x)d...

int_(0)^(2)(sin x-cos x)/(1+sin x cos x)dx

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int_(0)^( pi/2)(sin x-cos x)/(1+sin x*cos x)*dx

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int(cos 2x)/(1+sin x cos x)dx

int(sin x+cos x)/(sin x-cos x)dx

Prove that int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x)dx = 0 .

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By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx

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