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

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

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

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

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

Evaluate: int_(0)^((pi)/(4))(tan^(-1)((2cos^(2)theta)/(2-sin2 theta)))sec^(2)theta d theta

If int_0^1tan^(-1)xdx=alpha,t h e nint_0^(pi/4)tan^(-1)((2cos^2theta)/(2-sin2theta))sec^2thetadtheta is equal to: alpha (b) alpha/2 (c) 3alpha (d) 2alpha

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//2) (cos^(4) theta)/(sin^(4) theta + cos^(4) theta)d theta