calculus - Solving a limit with L'hospital rule or without it

So I have a limit that I want to solve:

$$\lim_{x\to0}\bigg(\frac{1+\ln(1-x^2)}{2x+1-\sin(x)}\bigg)^{\frac{1}{x^2}}$$

So I thought of using L'Hospital's rule, but it's not the $\displaystyle\frac{0}{0}$ situation.

Or Can it go for a different L'Hospital's rule situation, like it's $\displaystyle\frac{\infty}{\infty}$ but i get $1$ at the numerator?
Can I still use it or should I first manipulate the fraction somehow that it's plausible for using that rule, or is there another trick to use?

Any help would be appreciated.