1) $\int \frac{dx}{x^{2}+4x+13}=$ A) $\frac{1}{3}\tan^{-1}\left(\frac{x+2}{3}\right)+C$ B) $\frac{1}{6}\tan^{-1}\left(\frac{x-1}{x+5}\right)+C$ C) $3\tan^{-1}\left(\frac{x+2}{3}\right)+C$ D) $\frac{1}{6}\tan^{-1}\left(\frac{x+2}{3}\right)+C$ Answer: Option AExplanation: We have, l= $\int \frac{dx}{x^{2}+4x+13}$ l=$\int \frac{dx}{x^{2}+4x+4+9}$=$\int \frac{dx}{(x+2)^{2}+(3)^{2}}$ l= $\frac{1}{3}\tan^{-1}\left(\frac{x+2}{3}\right)+C$
