What is the integral of-(e^{4x})/x ?

The integral of-(e^{4x})/x is -\Ei(4x)+C

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integral of-(e^{4x})/x

\int - \frac{e ^{4 x}}{x} d x

- Ei (4 x) + C

Solution steps

\int - \frac{e ^{4 x}}{x} d x

Take the constant out:

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

= - \int \frac{e ^{4 x}}{x} d x

Apply u-substitution

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

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

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= - Ei (u)

Substitute back

u = 4 x

= - Ei (4 x)

Add a constant to the solution

= - Ei (4 x) + C

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