Integral of x3\sqrt[3]{x}

The calculator will find the integral/antiderivative of x3\sqrt[3]{x}, with steps shown.

Related calculator: Definite and Improper Integral Calculator

Please write without any differentials such as dxdx, dydy etc.
Leave empty for autodetection.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Your Input

Find x3dx\int \sqrt[3]{x}\, dx.

Solution

Apply the power rule xndx=xn+1n+1\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1} (n1)\left(n \neq -1 \right) with n=13n=\frac{1}{3}:

x3dx=x13dx=x13+113+1=(3x434){\color{red}{\int{\sqrt[3]{x} d x}}}={\color{red}{\int{x^{\frac{1}{3}} d x}}}={\color{red}{\frac{x^{\frac{1}{3} + 1}}{\frac{1}{3} + 1}}}={\color{red}{\left(\frac{3 x^{\frac{4}{3}}}{4}\right)}}

Therefore,

x3dx=3x434\int{\sqrt[3]{x} d x} = \frac{3 x^{\frac{4}{3}}}{4}

Add the constant of integration:

x3dx=3x434+C\int{\sqrt[3]{x} d x} = \frac{3 x^{\frac{4}{3}}}{4}+C

Answer: x3dx=3x434+C\int{\sqrt[3]{x} d x}=\frac{3 x^{\frac{4}{3}}}{4}+C