What is the integral of e^{1.5x} ?

The integral of e^{1.5x} is 0.66666…e^{1.5x}+C

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integral of e^{1.5x}

\int e^{1.5 x} d x

0.66666 \dots e^{1.5 x} + C

Solution steps

\int e^{1.5 x} d x

Apply u-substitution

= \int e^{u} \frac{1}{1.5} d u

Take the constant out:

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

= \frac{1}{1.5} \cdot \int e^{u} d u

Simplify

= 0.66666 \dots \cdot \int e^{u} d u

Use the common integral:

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

= 0.66666 \dots e^{u}

Substitute back

u = 1.5 x

= 0.66666 \dots e^{1.5 x}

Add a constant to the solution

= 0.66666 \dots e^{1.5 x} + C

What is the integral of e^{1.5x} ?
The integral of e^{1.5x} is 0.66666…e^{1.5x}+C