" 5."int_(0)^( pi/4)log(1+tan theta)d theta=(pi)/(8)log2

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

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

If int_(0)^( pi/2)log sin xdx=k, then the value of the definite integral int_(0)^( pi/4)log(1+tan theta)d theta( i) -(K)/(8)( ii) -(K)/(4) (iii) (K)/(8) (iv) (K)/(4)

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

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.

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

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

int_(0)^(pi//8) cos^(3)4 theta d theta=

int_(0)^(pi//8) cos^(3)4 theta d theta=

The value of int_(0)^(pi//4) log (1+ tan theta ) d theta is equal to