An integral i am unable to solve

Question

f(x)=(1/x)*(ln(1+x^2))

i have tried to do this many times by parts and substitution but cant.This was something sent by a friend without much context.any help is appreciated

Answer 1

No, special functions are required...

Let U = -x^2....

then dU = -2x dx

dU/dx = -2x

(-1/2) du = x dx

(-1/(2x)) du = dx

the integral becomes : (1/2) [ ln(1-u)/u]

which is a special function Li_2(u)