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Basic Integrals Calculator

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1

Solved example of basic integrals

$\int\frac{x^2}{\sqrt{x}}$
2

Simplify the fraction $\frac{x^2}{\sqrt{x}}$ by $x$

$\int\sqrt{x^{3}}dx$
3

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $\frac{3}{2}$

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

Add the values $\frac{3}{2}$ and $1$

$x^{\left(\frac{3}{2}+1\right)}\frac{1}{\frac{5}{2}}$
5

Divide $1$ by $\frac{5}{2}$

$\frac{2}{5}x^{\left(\frac{3}{2}+1\right)}$
6

Add the values $\frac{3}{2}$ and $1$

$\frac{2}{5}\sqrt{x^{5}}$
7

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

$\frac{2}{5}\sqrt{x^{5}}+C_0$

Final Answer

$\frac{2}{5}\sqrt{x^{5}}+C_0$

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