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

int_(0)^(1)log((1)/(x)-1)dx

int_(0)^(1)log((1)/(x)-1)dx=

The value of int_(0)^(1) (log(1+x)dx)/(1+x^(2)) is -

int_(0)^(oo)log(x+(1)/(x))(dx)/(1+x^(2))

int_(0)^(1)log((1-x)/(x))dx=0

Show that, int_(0)^(1)(1)/(x)log(1+x)dx=1-(1)/(2^(2))+(1)/(3^(2))-(1)/(4^(2))+...oo .

int _(0)^(pi/2) log(cotx)dx

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

int_(-3)^(-2)(dx)/(x^(2)-1)=(1)/(2)log.(3)/(2)

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