What is the integral of e^{18x}(18) ?

The integral of e^{18x}(18) is e^{18x}+C

integral of e^{18x}(18)

\int e^{18 x} (18) d x

e^{18 x} + C

Solution steps

\int e^{18 x} \cdot 18 d x

Take the constant out:

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

= 18 \cdot \int e^{18 x} d x

Apply u-substitution

= 18 \cdot \int e^{u} \frac{1}{18} d u

Take the constant out:

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

= 18 \cdot \frac{1}{18} \cdot \int e^{u} d u

Use the common integral:

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

= 18 \cdot \frac{1}{18} e^{u}

Substitute back

u = 18 x

= 18 \cdot \frac{1}{18} e^{18 x}

Simplify

18 \cdot \frac{1}{18} e^{18 x} : e^{18 x}

= e^{18 x}

Add a constant to the solution

= e^{18 x} + C

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