The value of `int_0^1(8log(1+x))/(1+x^2)dx` is: (1) `pilog2` (2) `pi/8log2` (3) `pi/2log2` (4) `log2`

The value of int_(0)^(1)(8log(1+x))/(1+x^(2))dx is: (1)pi log2 (2) (pi)/(8)log2(3)(pi)/(2)log2(4)log2

The value of int_0^1(8log(1+x))/(1+x^2)dx is a. pilog2 b. \ pi/8log2 c. \ pi/2log2 d. log2

The value of int_0^1(8 log(1+x))/(1+x^(2)) dx is a) πlog2 b) π/8log2 c) π/2log2 d) log2

The value of int_(0)^(oo)log(x+1//x)(dx)/(1+x^(2)) is a) pilog2 b) 2pilog2 c) -pilog2 d) -2pilog2

Show that int_0^1(log(1+x))/(1+x^2)dx=pi/8log2

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

G i v e nint_0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integral int_0^(pi/2)(sinx)/(1+sinx+cosx)dx is equal to (a) 1/2log2 (b) pi/2-log2 (c) pi/4-1/2log2 (d) pi/2+log2

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

The value of the integral int_(0)^(pi)log(1+cosx)dx is a) (pi)/(2)log2 b) -pilog2 c) pi log2 d)None of these

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