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Basic Integrals Calculator

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1

Solved example of basic integrals

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

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int x^2x^{-\frac{1}{2}}dx$
3

When multiplying exponents with same base we can add the exponents

$\int\sqrt{x^{3}}dx$
4

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

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

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

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

Final Answer

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

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