What is the integral of 5\sqrt[3]{x^4} ?

The integral of 5\sqrt[3]{x^4} is 15/7 x^{7/3}+C

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integral of 5\sqrt[3]{x^4}

\frac{15}{7} x^{\frac{7}{3}} + C

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

assuming

x \geq 0

= 5 \cdot \int x^{\frac{4}{3}} d x

Apply the Power Rule

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

= 5 \cdot \frac{3}{7} x^{\frac{7}{3}}

Simplify

5 \cdot \frac{3}{7} x^{\frac{7}{3}} : \frac{15}{7} x^{\frac{7}{3}}

= \frac{15}{7} x^{\frac{7}{3}}

Add a constant to the solution

= \frac{15}{7} x^{\frac{7}{3}} + C

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What is the integral of 5\sqrt[3]{x^4} ?
The integral of 5\sqrt[3]{x^4} is 15/7 x^{7/3}+C