[int_(0)^(1)(log x)/(sqrt(1-x^(2)))dx=],[0-(pi)/(2)log2],[0-mog2],[0(pi)/(2)log2]

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

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

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

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

int_(0)^(pi//2)(2logcosx-logsin2x)\ dx=-(pi)/(2)log2

[int_(0)^(0)cot^(-1)(1-x+x^(2))dx=],[[" (A) "(pi)/(2)-ln2," (B) "(pi)/(2)+ln2],[" (C) "(pi)/(2)-ln sqrt(2)," (D) "(pi)/(2)+ln sqrt(2)]]

int_(0)^(1) ln Sin((pi x)/(2))dx=

int_(0)^(1)log sin((pi)/(2)x)dx equals

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