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

We know $\frac{d}{\mathrm{dx}} \left(\ln x\right) = \frac{1}{x}$, so we should think about that when we see an integral involving $\ln x$.
$\int \frac{\mathrm{dx}}{x + x \ln {x}^{2}} = \int \frac{1}{1 + \ln {x}^{2}} \frac{1}{x} \mathrm{dx}$
$\frac{d}{\mathrm{dx}} \left(1 + \ln {x}^{2}\right) = \frac{d}{\mathrm{dx}} \left(\ln {x}^{2}\right) = \frac{d}{\mathrm{dx}} \left(2 \ln x\right) = \frac{2}{x}$
Integrate by substitution with $u = 1 + 2 \ln x$ (Or $u = 1 + \ln {x}^{2}$, they are equal).