Question

How do you integrate `intdx/(x+xlnx^2)`?

Answer 1

We know `d/dx(lnx) = 1/x`, so we should think about that when we see an integral involving `lnx`.

`intdx/(x+xlnx^2) = int 1/(1+lnx^2) 1/x dx`

`d/dx(1+lnx^2) = d/dx(lnx^2) = d/dx(2lnx) = 2/x`

Integrate by substitution with `u = 1+2lnx` (Or `u = 1+lnx^2`, they are equal).