`int_0^1 log(sqrt(1+x)+sqrt(1-x))dx=` (A) `1/2(log2-pi/2+1)` (B) `1/2(log2+pi/2+1)` (C) `1/2(log2+pi/2-1)` (D) none of these

int_(0)^(1)(logx)/(sqrt(1-x^(2)))dx=-(pi)/(2)(log2)

Prove that int_(0)^(1) log(sqrt(1-x)+sqrt(1+x))dx = (1)/(2) log 2 + (pi)/(4) - (1)/(2)

int_0^oo logx/(1+x^2)dx= (A) log2 (B) pi/2 (C) 0 (D) none of these

int_(log(1/2))^(log2) log(x+sqrt(x^2+1))dx= (A) 2log2 (B) 1-log2 (C) 1+log2 (D) 0

The value of int_1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dx is (a) pi/8(log)_e2 (b) pi/2(log)_e2 (c) -pi/2(log)_e2 (d) none of these

int_(0)^(1)(log|1+x|)/(1+x^(2))dx=(pi)/(8)log2

int_(0)^(1)((sin^(-1)x)/(x))dx=(pi)/(2)(log2)

Prove that 1/(log_2 pi) + 1/(log_(6)pi) > 2 .

int_(0tooo) log(1+x^2)/(1+x^2) dx equals-(A) log2(B) -a log2(C) 1/2 log2(D) -A/2 log2

int_(0)^(1)cot^(-1)(1-x+x^(2))dx=(1)(pi)/(2)-log2(2)(pi)/(2)+log2(3)pi-log2(4)pi+log2