Mathematics - Definite Integration Question with Solution | TestHub

${\lim }_{x\to 0}\frac{{\int }_0^x{\left(t^2+e^{t^2}\right)}^{\frac{1}{1-\cos t}}}{\left(e^x-1\right)}dt\left(\frac{0}{0}\right)$ Use L'Hôspital ${\lim }_{x\to 0}\frac{{\left(x^2+e^{x^2}\right)}^{\frac{1}{1-\cos x}}}{e^x}={\lim }_{x\to 0}\frac{e^{\left(x^2+e^{x^2}-1\right)\frac{1}{1-\cos x}}}{e^x}=e^4$