What is the integral of e^{3ax} ?

The integral of e^{3ax} is 1/(3a)e^{3ax}+C

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integral of e^{3ax}

\int e^{3 a x} d x

\frac{1}{3 a} e^{3 a x} + C

Solution steps

\int e^{3 a x} d x

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 3 a x

= \frac{1}{3 a} e^{3 a x}

Add a constant to the solution

= \frac{1}{3 a} e^{3 a x} + C