Question

Evaluate: $\int \frac{4x+6}{2x^2+5x+3}dx$

Answer 1

$\int \frac{2(2x+3)dx}{2x^2+5x+3}$

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

$=\int \frac{2(2x+3)dx}{2x(x+1)+3(x+1)}$

$=\int \frac{2(2x+3)dx}{(x+1)(2x+3)}$

$=\int \frac{2dx}{(x+1)}$

$=2\log |x+1|+c$