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

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

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integral of e\sqrt[3]{x}

\int e 3 x d x

e \frac{3}{4} x^{\frac{4}{3}} + C

Solution steps

\int e 3 x d x

Take the constant out:

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

= e \cdot \int 3 x d x

Apply the Power Rule

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

Add a constant to the solution

= e \frac{3}{4} x^{\frac{4}{3}} + C

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