int_(-pi/2)^( pi/2)sin{log(x+sqrt(x^(2)+1))}dx

STATEMENT-1 : int_(-(pi)/(2))^((pi)/(2))sin(log(x+sqrt(1+x^(2))))dx=0 and STATEMENT-2 : int_(-a)^(a)f(x)dx=0 if f(x) is an even function

STATEMENT-1 : int_(-(pi)/(2))^((pi)/(2))sin(log(x+sqrt(1+x^(2))))dx=0 and STATEMENT-2 : int_(-a)^(a)f(x)=0 if f(x) is an even function

int_0^(pi/2)sin2x log(tanx)dx

The value of int_(-pi)^( pi)(x^(2))/(1+sin x+sqrt(1+sin^(2)x))dx is

The value of the integral int_(-pi//2)^(pi//2) sin^(4) x (1+ log ((2+ sinx)/( 2- sin x))) dx is

1) int_(-pi/2)^pi sin^(-1) (sinx) dx 2) int_(-pi/2)^(pi/2) (-pi/2)/(sqrt(cos x sin^2 x)) dx 3) int_0^2 2x[x] dx

If I_(1)=int_(0)^( pi/2)(sin x)^(sqrt(3)+1)dx,I_(2)=int_(0)^(pi/2)(sin x)^(sqrt(3)-1))dx then (I_(1))/(I_(2))=

[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]]

int_(0)^((pi)/(2))log(sin2x)dx