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Basic Integrals Calculator

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1

Here, we show you a step-by-step solved example of basic integrals. This solution was automatically generated by our smart calculator:

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

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

$\int x^{\frac{-1+2\cdot 2}{2}}dx$

Multiply $2$ times $2$

$\int x^{\frac{-1+4}{2}}dx$

Subtract the values $4$ and $-1$

$\int\sqrt{x^{3}}dx$
2

Simplify the expression

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

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 $\frac{3}{2}$

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

Simplify the addition $\frac{3}{2}+1$

$\frac{x^{\frac{3+1\cdot 2}{2}}}{\frac{3}{2}+1}$

Any expression multiplied by $1$ is equal to itself

$\frac{x^{\frac{3+2}{2}}}{\frac{3}{2}+1}$

Add the values $3$ and $2$

$\frac{\sqrt{x^{5}}}{\frac{3}{2}+1}$

Simplify the addition $\frac{3}{2}+1$

$\frac{\sqrt{x^{5}}}{\frac{3+1\cdot 2}{2}}$

Any expression multiplied by $1$ is equal to itself

$\frac{\sqrt{x^{5}}}{\frac{3+2}{2}}$

Add the values $3$ and $2$

$\frac{\sqrt{x^{5}}}{\frac{5}{2}}$
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 $\frac{3}{2}$

$\frac{\sqrt{x^{5}}}{\frac{5}{2}}$
4

Divide fractions $\frac{\sqrt{x^{5}}}{\frac{5}{2}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$

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

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

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

Final answer to the problem

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

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