What is the integral of e^{0.03x} ?

The integral of e^{0.03x} is 33.33333…e^{0.03x}+C

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integral of e^{0.03x}

\int e^{0.03 x} d x

33.33333 \dots e^{0.03 x} + C

Solution steps

\int e^{0.03 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{0.03} d u

= \int e^{u} \frac{1}{0.03} d u

Take the constant out:

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

= \frac{1}{0.03} \cdot \int e^{u} d u

Simplify

= 33.33333 \dots \cdot \int e^{u} d u

Use the common integral:

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

= 33.33333 \dots e^{u}

Substitute back

u = 0.03 x

= 33.33333 \dots e^{0.03 x}

Add a constant to the solution

= 33.33333 \dots e^{0.03 x} + C

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What is the integral of e^{0.03x} ?
The integral of e^{0.03x} is 33.33333…e^{0.03x}+C