int_(0)^((pi)/(2))sqrt(tan theta)d theta?

Show that int_(0)^(pi//4) sqrt(tan theta) d theta = (1)/(sqrt(2)) log(sqrt(2)-1)+(pi)/(2sqrt(2))

STATEMENT 1: int_(0)^((pi)/(4))log(1+tan theta)d theta=(pi)/(8)log2 STATEMENT 2:int_(0)^((pi)/(2))log sin theta d theta=-pi log2

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

Evaluate the following : int_(0)^(pi//2)sin theta d theta

int_(0)^((pi)/(2))(sec theta-tan theta)d theta

Evaluate: int_(0)^(a)(dx)/(x+sqrt((a^(2)-x^(2))))quad or int_(0)^((pi)/(2))(d theta)/(1+tan theta)

If int_(0)^((pi)/(2))log sin theta d(theta)=k, then find the value of int_(0)^((pi)/(2))((theta)/(sin theta))^(2)d(theta) in terms of k

Evaluate int_(0)^((pi)/(2))(cos theta d theta)/((sin theta +2)(sin theta +3)) .

Evaluate : int_(0)^((pi)/(4)) log(1+tan theta ) d theta