Prove that `int 1/(x-a)dx=log|x-a|`

Prove that int_2^3 x/(x^2+1) dx=log sqrt2

int x ln(x-1)dx

Prove that : int 1/(a^(2)-x^(2)) dx = 1/(2a) log |(a+x)/(a-x)|+c.

int(1)/(log x)dx

Prove that int_-a^a f(x) dx=0 , where 'f' is an odd function. And, evaluate, int_-1^1 log[(2-x)/(2+x)] dx

Prove that int_(-1)^(1)log((2-x)/(2+x))^(20)dx=0

if y=log x^(x) prove that (dy)/(dx)=1+log x

int x ln(1+x)dx

int 1/(x(log x)^2)dx