What is the integral of e^{15x}(15) ?

The integral of e^{15x}(15) is e^{15x}+C

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integral of e^{15x}(15)

\int e^{15 x} (15) d x

e^{15 x} + C

Solution steps

\int e^{15 x} \cdot 15 d x

Take the constant out:

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

= 15 \cdot \int e^{15 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{15} d u

= 15 \cdot \int e^{u} \frac{1}{15} d u

Take the constant out:

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

= 15 \cdot \frac{1}{15} \cdot \int e^{u} d u

Use the common integral:

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

= 15 \cdot \frac{1}{15} e^{u}

Substitute back

u = 15 x

= 15 \cdot \frac{1}{15} e^{15 x}

Simplify

15 \cdot \frac{1}{15} e^{15 x} : e^{15 x}

= e^{15 x}

Add a constant to the solution

= e^{15 x} + C

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