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Step-by-step Solution

Integral of $\frac{x}{3x^2-1}$ with respect to x

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Answer

$\frac{1}{6}\ln\left|3x^2-1\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{xdx}{3x^2-1}$
1

Solve the integral $\int\frac{x}{3x^2-1}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=3x^2-1 \\ du=6xdx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{6x}=dx$

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Answer

$\frac{1}{6}\ln\left|3x^2-1\right|+C_0$
$\int\frac{xdx}{3x^2-1}$

Main topic:

Integrals of Rational Functions

Used formulas:

4. See formulas

Time to solve it:

~ 0.77 seconds