What is the integral of 1/(e^{ax)} ?

The integral of 1/(e^{ax)} is x/(e^{ax)}-e^{-ax}x-(e^{-ax})/a+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(e^{ax)}

\int \frac{1}{e ^{a x}} d x

\frac{x}{e ^{a x}} - e^{- a x} x - \frac{e ^{- a x}}{a} + C

Solution steps

\int \frac{1}{e ^{a x}} d x

Apply Integration By Parts

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

\int - a e^{- a x} x d x = e^{- a x} x + \frac{e ^{- a x}}{a}

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

Simplify

= \frac{x}{e ^{a x}} - e^{- a x} x - \frac{e ^{- a x}}{a}

Add a constant to the solution

= \frac{x}{e ^{a x}} - e^{- a x} x - \frac{e ^{- a x}}{a} + C

What is the integral of 1/(e^{ax)} ?
The integral of 1/(e^{ax)} is x/(e^{ax)}-e^{-ax}x-(e^{-ax})/a+C