# Step-by-step Solution

## Integrate $10x\left(x^2+3\right)^3$ with respect to x

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### Videos

$\frac{5}{4}\left(x^2+3\right)^{4}+C_0$

## Step-by-step explanation

Problem to solve:

$\int10x\left(x^2+3\right)^3dx$
1

Take the constant out of the integral

$10\int x\left(x^2+3\right)^3dx$
2

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

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

$\frac{5}{4}\left(x^2+3\right)^{4}+C_0$
$\int10x\left(x^2+3\right)^3dx$

### Main topic:

Integration by substitution

~ 0.82 seconds