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Step-by-step Solution

Integral of x/((x^2+1)^3)

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Answer

$\frac{-\frac{1}{4}}{\left(x^2+1\right)^{2}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{x}{\left(x^2+1\right)^3}dx$
1

Podemos resolver la integral $\int\frac{x}{\left(x^2+1\right)^3}dx$ aplicando un cambio de variable. Sean $u$ y $du$

$\begin{matrix}u=x^2+1 \\ du=2xdx\end{matrix}$
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Despejando $dx$ de la ecuación anterior

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

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Answer

$\frac{-\frac{1}{4}}{\left(x^2+1\right)^{2}}+C_0$
$\int\frac{x}{\left(x^2+1\right)^3}dx$

Main topic:

Integration by substitution

Time to solve it:

~ 5.31 seconds

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