Integrate this function without using contour integration or feynman method

Question

$$\int_{0}^{1} \frac{(x^{2}-1)}{\ln x} \ dx$$ I tried 3 different methods: First , I tried to use the substitution $x = \frac{1}{t}$ which led to integral of $\frac{e^t}{t}$ form which I was unable to integrate analytically Then I tried to use integration by parts taking $ln$ as the second function and $x^2-1$ as the second function but it did not help Is there any way to evaluate it without using the residue theorem and differentiation under integral sign??

Answer 1

$$\int_0^1\frac{x^2-1}{\log x}dx = \int_0^1\int_0^2x^y\:dydx = \int_0^2\int_0^1x^ydxdy = \int_0^2\frac{dy}{y+1} = \boxed{\log 3}$$