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Step-by-step Solution

Integral of (7x^3)/((x^4-2)^4)

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Answer

$\frac{-\frac{7}{12}}{\left(x^4-2\right)^{3}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{7x^3}{\left(x^4-2\right)^4}dx$
1

Taking the constant out of the integral

$7\int\frac{x^3}{\left(x^4-2\right)^4}dx$
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Solve the integral $\int\frac{x^3}{\left(x^4-2\right)^4}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x^4-2 \\ du=4x^{3}dx\end{matrix}$

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Answer

$\frac{-\frac{7}{12}}{\left(x^4-2\right)^{3}}+C_0$
$\int\frac{7x^3}{\left(x^4-2\right)^4}dx$

Main topic:

Integration by substitution

Time to solve it:

~ 4.49 seconds

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