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Step-by-step Solution

Integral of (-48x)/((x^2-16)^2)

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Answer

$\frac{24}{x^2-16}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{-48x}{\left(x^2-16\right)^2}dx$
1

Taking the constant out of the integral

$-48\int\frac{x}{\left(x^2-16\right)^2}dx$
2

Solve the integral $\int\frac{x}{\left(x^2-16\right)^2}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x^2-16 \\ du=2xdx\end{matrix}$

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Answer

$\frac{24}{x^2-16}+C_0$
$\int\frac{-48x}{\left(x^2-16\right)^2}dx$

Main topic:

Integration by substitution

Used formulas:

4. See formulas

Time to solve it:

~ 1.68 seconds