$\int \frac{d x}{x^{2}+4 x+13}=$

$\int \frac{d x}{x^{2}+4 x+13}=$
  1. $\frac{1}{3} \tan ^{-1}\left(\frac{x+2}{3}\right)+c$
  2. $\frac{1}{6} \log \left(\frac{x-1}{x+5}\right)+c$
  3. $\frac{1}{6} \tan ^{-1}\left(\frac{x+2}{3}\right)+c$
  4. $3 \tan ^{-1}\left(\frac{x+2}{3}\right)+c$

Solution

$\int \frac{1}{x^{2}+4 x+13} d x$ $=\int \frac{1}{x^{2}+4 x+4+9} d x=\int \frac{1}{(x+2)^{2}+3^{2}} d x=\frac{1}{3} \tan ^{-1}\left(\frac{x+2}{3}\right)+c$

Asked in: MHT CET 2020 (19 Oct Shift 2)

Practice more Indefinite Integration questions on Aicharya