# Integration by substitution Calculator

## Get detailed solutions to your math problems with our Integration by substitution step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.

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### Difficult Problems

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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