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Step-by-step Solution

Integral of x/(1-x^2)

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Answer

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

Step-by-step explanation

Problem to solve:

$\int\frac{x\:dx}{1-x^2}$
1

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

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

Isolate $dx$ in the previous equation

$\frac{du}{-2x}=dx$

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Answer

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

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$\int\frac{x\:dx}{1-x^2}$

Main topic:

Integration by substitution

Time to solve it:

~ 0.8 seconds