Question

Solve
$I=\int \frac{x+2}{x^2+5x+6}dx$

Answer 1

We have,

$I=\int \frac{x+2}{x^2+5x+6}dx$

$I=\int \frac{x+2}{x^2+3x+2x+6}dx$

$I=\int \frac{x+2}{(x+3)(x+2)}dx$

$I=\int \frac{1}{(x+3)}dx$

on Integrating and we get,

$I=\log (x+3)+c\because \int \frac{1}{x}dx=\log 2$

Hence, this is the answer.