What is the integral of e^{-x}*(2-x) ?

The integral of e^{-x}*(2-x) is e^{-x}x-e^{-x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-x}*(2-x)

\int e^{- x} \cdot (2 - x) d x

e^{- x} x - e^{- x} + C

Solution steps

\int e^{- x} (2 - x) d x

Apply Integration By Parts

: - e^{- x} (2 - x) - \int e^{- x} d x

= - e^{- x} (2 - x) - \int e^{- x} d x

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

= - e^{- x} (2 - x) - (- e^{- x})

Simplify

- e^{- x} (2 - x) - (- e^{- x}) : e^{- x} x - e^{- x}

= e^{- x} x - e^{- x}

Add a constant to the solution

= e^{- x} x - e^{- x} + C

y = \frac{1}{x}, y = \frac{3}{x}, y = x, y = 2 x

\frac{d ^{2}}{d y d x} (sin (x^{2} + y^{2}))

\int \frac{e ^{x} e ^{x} + 2}{e ^{x} + 6} d x

\frac{d}{d x} (ln (e^{5 x}))

\int sin^{5} (\frac{x}{7}) cos (\frac{x}{7}) d x

What is the integral of e^{-x}*(2-x) ?
The integral of e^{-x}*(2-x) is e^{-x}x-e^{-x}+C