Evaluate: `int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2thetadthetadot`

int_(0)^(1)tan^(-1)xdx=alpha, then int_(0)^((pi)/(4))tan^(-1)((2cos^(2)theta)/(2-sin2 theta))sec^(2)theta d theta is equal to: alpha(b)(alpha)/(2)(c)3 alpha(d)2 alpha

Evaluate: int_(0)^( pi/2)(cos theta)/((1+sin theta)(2+sin theta))dth eta

Evaluate int_0^(pi/4)sqrt(1+tan^2theta)d theta.

int_0^(pi/4) (2sinthetacostheta)/(sin^4theta+cos^4theta)d theta

I=int_(0)^( pi/4)(sin2 theta)/(sin^(2)theta+cos^(4)theta)d theta

int_(0)^(pi//2) (sin^(2)theta)/ (1+cos theta)^(2) d theta =

If costhetagtsinthetagt0 , then evaluate: int{log((1+sin2theta)/(1-sin2theta))^(cos2theta)+log((cos2theta)/(1+sin2theta))}d theta

Evaluate int _(0)^(pi//2) cosec theta tan^(-1) (c sin theta ) d theta .