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Step-by-step Solution

Integral of $\frac{6x}{\left(5+3x^2\right)^4}$ with respect to x

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Answer

$\frac{1}{-3\left(5+3x^2\right)^{3}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(\frac{6x}{\left(5+3x^2\right)^4}\right)dx$
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Taking the constant out of the integral

$6\int\frac{x}{\left(5+3x^2\right)^4}dx$
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Solve the integral $\int\frac{x}{\left(5+3x^2\right)^4}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=5+3x^2 \\ du=6xdx\end{matrix}$

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Answer

$\frac{1}{-3\left(5+3x^2\right)^{3}}+C_0$