Question

The value of $\int \frac{3x+5}{3x^2+10x+6}dx$ is

Answer 1

Let

$3x^2+10x+6=t$

$6x+10dx=dt$...........$\left(differentiatingwithrespecttox\right)$

$2(3x+5)=\frac{dt}{dx}$

$\int \frac{1}{2}\cdot \frac{1}{t}dt$

$=\frac{1}{2}\log t+c$

$=\frac{1}{2}\log (3x^2+10x+6)+c$