Question

Solve $\int \frac{6x-1}{3x^2-x+6}dx$

Answer 1

We have,

$I=\int \frac{6x-1}{3x^2-x+6}dx$ ……. (1)

Let $t=3x^2-x+6$

$dt=(6x-1)dx$

Therefore,

$I=\int \frac{dt}{t}$

$I=\ln \left(t\right)+C$

On putting the value of $t$, we get

$I=\ln (3x^2-x+6)+C$

Hence, this is the answer,