Find $\displaystyle\int \frac{x}{\sqrt{x^2 - 4}} \, \mathrm{d}x$. Find \(\displaystyle\int x^2 \ln

Question

Find $\displaystyle\int \frac{x}{\sqrt{x^2 - 4}} \, \mathrm{d}x$. Find $\displaystyle\int x^2 \ln (2x) \, \mathrm{d}x$. Find $\displaystyle\int \frac{\sin 2x}{1 + \cos^2 x} \, \mathrm{d}x$.

Accepted Answer

(a)$\sqrt{x^2-4}+C$ (b)$\frac{1}{3}x^3 \ln (2x) - \frac{1}{9}x^3 + C$ (c)$-\ln (1+\cos^2x)+C$

2025 MI P1 Q3

2025 MI P1 Q3