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Step-by-step Solution

Integral of $8x\left(x^2-3\right)^3$

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Answer

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

Step-by-step explanation

Problem to solve:

$\int8x\left(x^2-3\right)^3dx$
1

Take the constant out of the integral

$8\int x\left(x^2-3\right)^3dx$
2

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

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

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Answer

$\left(x^2-3\right)^{4}+C_0$
$\int8x\left(x^2-3\right)^3dx$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 0.84 seconds