What is the integral of e^{0.4x} ?

The integral of e^{0.4x} is 2.5e^{0.4x}+C

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integral of e^{0.4x}

\int e^{0.4 x} d x

2.5 e^{0.4 x} + C

Solution steps

\int e^{0.4 x} d x

Apply u-substitution

= \int e^{u} \frac{1}{0.4} d u

Take the constant out:

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

= \frac{1}{0.4} \cdot \int e^{u} d u

Simplify

= 2.5 \cdot \int e^{u} d u

Use the common integral:

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

= 2.5 e^{u}

Substitute back

u = 0.4 x

= 2.5 e^{0.4 x}

Add a constant to the solution

= 2.5 e^{0.4 x} + C