What is the integral of (e^{4x})/(x^2) ?

The integral of (e^{4x})/(x^2) is -(e^{4x})/x+4\Ei(4x)+C

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integral of (e^{4x})/(x^2)

\int \frac{e ^{4 x}}{x ^{2}} d x

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

Solution steps

\int \frac{e ^{4 x}}{x ^{2}} d x

Apply Integration By Parts

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

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

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

= - \frac{e ^{4 x}}{x} - (- 4 Ei (4 x))

Simplify

= - \frac{e ^{4 x}}{x} + 4 Ei (4 x)

Add a constant to the solution

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

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What is the integral of (e^{4x})/(x^2) ?
The integral of (e^{4x})/(x^2) is -(e^{4x})/x+4\Ei(4x)+C