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

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

STATEMENT 1: int_0^(pi/4)log(1+t a ntheta)d theta=pi/8log2. STATEMENT 2: int_0^(pi/2)logsin theta d theta =-pilog2.

Prove that int_(0)^( pi/2)log(tan theta+cot theta)backslash d theta=pi log2

Evalute: int_(0)^((pi)/(4)) log(1+tantheta)d theta .

int_(0)^((pi)/(4))log(sin2 theta)d theta=-((pi)/(4))log((1)/(2))

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

int_(0)^(10)log(1+cot theta)d theta=(pi)/(8)log2

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

If I_(n)=int_(0)^(pi//4) tan^(n)theta d theta , then I_(8)+I_(6) equals