Evaluate `int_(0)^(pi//2)(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)`

Evaluate int_(0)^(4pi)(dx)/(cos^(2)x(2+tan^(2)x)) .

Evaluate int_0^(pi/2) cos ^5 x dx

int_(0)^(pi/2)(1)/(1+cot^(4)x)dx=

Evaluate int_0^(pi//2)sin^2x/(sinx+cosx)dx .

Evaluate int_0^(pi/2) sin ^7 x d x

Evaluate int_0^pi (xsinx)/(1+cos^2x)dx

Evaluate int_0^pi (x sin x)/(1+cos ^2 x) d x

If I_(1)=int_(0)^(pi//2)(cos^(2)x)/(1+cos^(2)x)dx,I_(2)=int_(0)^(pi//2)(sin^(2)x)/(1+sin^(2)x)dx , I_(3)=int_(0)^(pi//2)(1+2cos^(2)x.sin^(2)x)/(4+2cos^(2)xsin^(2)x)dx , then

int_(-pi//2)^(pi//2)sin^(2)xcos^(2)x(sinx+cosx)dx=