(1) `int_(0)^( 2pi)cos^(7)xdx`

(i) int_(0)^( pi)x cos^(2)xdx

int_(0)^(pi/2) cos^(2) x dx

int_(0)^( pi/2)sec^(2)xdx

int_(0)^( pi/4)sec^(2)xdx

find the value of int_(0)^( pi/2)cos^(2)xdx

int_(0)^( pi)x sin^(-1)xdx

I=int_(0)^( pi)*sec^(2)xdx

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_(0)^( pi/2)x sec^(2)xdx

If I_(1)=int_(0)^(2pi)sin^(3)xdx and I_(2)=int_(0)^(1)ln((1)/(x)-1)dx , then