What is the integral of \sqrt[3]{x^4} ?

The integral of \sqrt[3]{x^4} is 3/7 x^{7/3}+C

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integral of \sqrt[3]{x^4}

\int 3 x^{4} d x

\frac{3}{7} x^{\frac{7}{3}} + C

Solution steps

\int 3 x^{4} d x

3 x^{4} = x^{\frac{4}{3}},

assuming

x \geq 0

= \int x^{\frac{4}{3}} d x

Apply the Power Rule

: \frac{3}{7} x^{\frac{7}{3}}

= \frac{3}{7} x^{\frac{7}{3}}

Add a constant to the solution

= \frac{3}{7} x^{\frac{7}{3}} + C

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What is the integral of \sqrt[3]{x^4} ?
The integral of \sqrt[3]{x^4} is 3/7 x^{7/3}+C