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[" 14."int(0)^(1)(log x)/(sqrt(1-x^(2)))...

[" 14."int_(0)^(1)(log x)/(sqrt(1-x^(2)))dx=],[" 1) "pi log2quad " 2) "-pi log2],[" 3) "2^(-log2)quad " 4) "-(pi)/(2)log2]

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

[int_(-pi/4)^( pi/4)log(cos x+sin x)dx=(1)/(2)],[[" 1) "pi log2," 2) "-pi log2," 3) "-(pi)/(4)log2," 4) "-(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

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_(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)^(pi)log(1+cosx)dx=-pi(log2)

int_(0)^((pi)/(2))x^(2)csc^(2)xdx=pi log2

int_(0)^((pi)/(2))(dx)/((1-2x^(2))sqrt(1-x^(2)))=(1)/(2)log(2+sqrt(3))

int_(0)^((pi)/(2))(dx)/((1-2x^(2))sqrt(1-x^(2)))=(1)/(2)log(2+sqrt(3))