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Indefinite integrals Calculator

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1

Solved example of indefinite integrals

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

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

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

Isolate $dx$ in the previous equation

$\frac{du}{2x}=dx$
4

Substituting $u$ and $dx$ in the integral and simplify

$\int\frac{u}{2}du$
5

Take the constant out of the integral

$\frac{1}{2}\int udu$
6

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$\frac{1}{4}u^2$
7

Substitute $u$ back for it's value, $x^2-3$

$\frac{1}{4}\left(x^2-3\right)^2$
8

As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$\frac{1}{4}\left(x^2-3\right)^2+C_0$

Answer

$\frac{1}{4}\left(x^2-3\right)^2+C_0$

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