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

The integral of-(e^{4x})/(4x) is -1/4 \Ei(4x)+C

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

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

- \frac{1}{4} Ei (4 x) + C

Solution steps

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

Take the constant out:

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

= - \frac{1}{4} \cdot \int \frac{e ^{4 x}}{x} d x

Apply u-substitution

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

= - \frac{1}{4} \cdot \int \frac{e ^{u}}{u} d u

Use the nonelementary integral:

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

= - \frac{1}{4} Ei (u)

Substitute back

u = 4 x

= - \frac{1}{4} Ei (4 x)

Add a constant to the solution

= - \frac{1}{4} Ei (4 x) + C

\int \frac{cos ( 4 x )}{2 + sin ( 4 x )} d x

f (x) = x sin (2 x^{2})

\frac{e ^{x}}{5 + e ^{x}}

\int_{- 2}^{3} ∣ x ∣ d x

\frac{d}{d x} (cos (x) + 2 x)

What is the integral of-(e^{4x})/(4x) ?
The integral of-(e^{4x})/(4x) is -1/4 \Ei(4x)+C