List of top Mathematics and Statistics Questions on Integration of Rational Functions

Prove that \( \displaystyle \int \sqrt{a^2 - x^2} \, dx = \frac{x}{2}\sqrt{a^2 - x^2} + \frac{a^2}{2}\sin^{-1}\left(\frac{x}{a}\right) + C \).

Evaluate \( \displaystyle \int \frac{x+2}{2x^2 + 6x + 5} \, dx \) using the substitution or partial fraction method.