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

The integral of (e^x)/(x^4) is -(e^x}{3x^3}+1/3 (-(e^x)/(2x^2)+1/2 (-\frac{e^x)/x+\Ei(x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (e^x)/(x^4)

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

- \frac{e ^{x}}{3 x ^{3}} + \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x))) + C

Solution steps

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

Apply Integration By Parts

= - \frac{e ^{x}}{3 x ^{3}} - \int - \frac{e ^{x}}{3 x ^{3}} d x

\int - \frac{e ^{x}}{3 x ^{3}} d x = - \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x)))

= - \frac{e ^{x}}{3 x ^{3}} - (- \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x))))

Simplify

= - \frac{e ^{x}}{3 x ^{3}} + \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x)))

Add a constant to the solution

= - \frac{e ^{x}}{3 x ^{3}} + \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x))) + C

What is the integral of (e^x)/(x^4) ?
The integral of (e^x)/(x^4) is -(e^x}{3x^3}+1/3 (-(e^x)/(2x^2)+1/2 (-\frac{e^x)/x+\Ei(x)))+C