What is the integral of e^{2/3 x} ?

The integral of e^{2/3 x} is 3/2 e^{2/3 x}+C

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integral of e^{2/3 x}

\int e^{\frac{2}{3} x} d x

\frac{3}{2} e^{\frac{2}{3} x} + C

Solution steps

\int e^{\frac{2}{3} x} d x

Apply u-substitution

: \int e^{u} \frac{3}{2} d u

= \int e^{u} \frac{3}{2} d u

Take the constant out:

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

= \frac{3}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{3}{2} e^{u}

Substitute back

u = \frac{2}{3} x

= \frac{3}{2} e^{\frac{2}{3} x}

Add a constant to the solution

= \frac{3}{2} e^{\frac{2}{3} x} + C

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What is the integral of e^{2/3 x} ?
The integral of e^{2/3 x} is 3/2 e^{2/3 x}+C