What is the integral of (e^{\sqrt[3]{x}})/(3\sqrt[3]{x^2)} ?

The integral of (e^{\sqrt[3]{x}})/(3\sqrt[3]{x^2)} is e^{\sqrt[3]{x}}+C

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integral of (e^{\sqrt[3]{x}})/(3\sqrt[3]{x^2)}

Solution steps

Take the constant out:

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

assuming

x \geq 0

Apply u-substitution

: \int 3 e^{u} d u

= \frac{1}{3} \cdot \int 3 e^{u} d u

Take the constant out:

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

= \frac{1}{3} \cdot 3 \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{3} \cdot 3 e^{u}

Substitute back

Simplify

Add a constant to the solution

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\int \frac{( 3 x - 7 x ^{2} )}{x} d x

\int (\frac{2}{x + x ^{3} - 5 x}) d x

\int \frac{1}{sec ( x ) - tan ( x )} d x

What is the integral of (e^{\sqrt[3]{x}})/(3\sqrt[3]{x^2)} ?
The integral of (e^{\sqrt[3]{x}})/(3\sqrt[3]{x^2)} is e^{\sqrt[3]{x}}+C