int cos^(2)theta d theta

int_(0) ^(pi//2) cos^(2) theta d theta =

int (sin^(2)theta d theta)/((1 + cos theta)^(2))

int(sin^(6)theta+cos^(6)theta)/(sin^(2)theta cos^(2)theta)d theta=

int_(0)^( pi/2)cos^(9)theta d theta

int_ (0) ^ ((pi) / (2)) cos ^ (4) theta d theta

int_(0)^( pi/2)cos^(9)theta d theta

int_(0)^( pi/2)cos^(3)theta d theta

Let the be an integrable function defined on [0,a] if I_(1)=int_(pi//2)^(pi//2) cos theta f(sin theta cos ^(2) theta)d theta and I_(2)=int_(0)^(pi//2)sin 2 theta f(sin theta cos ^(2) theta)d theta then

int (cos theta d theta)/((1-sin theta)(2-sin theta))