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Step-by-step Solution

Integrate 3x*(x^2-2)^(1/3)

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Answer

$\frac{9}{8}\sqrt[3]{\left(x^2-2\right)^{4}}+C_0$

Step-by-step explanation

Problem to solve:

$\int3x\:\sqrt[3]{x^2-2}dx$
1

Take the constant out of the integral

$3\int x\sqrt[3]{x^2-2}dx$
2

Solve the integral $\int x\sqrt[3]{x^2-2}dx$ applying u-substitution. Let $u$ and $du$ be

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

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Answer

$\frac{9}{8}\sqrt[3]{\left(x^2-2\right)^{4}}+C_0$
$\int3x\:\sqrt[3]{x^2-2}dx$

Main topic:

Integration by substitution

Used formulas:

4. See formulas

Time to solve it:

~ 0.87 seconds

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