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Integration by substitution Calculator

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1

Solved example of Integration by substitution

$\int\sqrt{5x-3}dx$
2

Solve the integral $\int\sqrt{5x-3}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=5x-3 \\ du=5dx\end{matrix}$
3

Isolate $dx$ in the previous equation

$\frac{du}{5}=dx$
4

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

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

Take the constant out of the integral

$\frac{1}{5}\int\sqrt{u}du$
6

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

$\frac{2}{15}\sqrt{u^{3}}$
7

Substitute $u$ back for it's value, $5x-3$

$\frac{2}{15}\sqrt{\left(5x-3\right)^{3}}$
8

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

$\frac{2}{15}\sqrt{\left(5x-3\right)^{3}}+C_0$

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