What is the integral of e^{-2x}+1 ?

The integral of e^{-2x}+1 is -1/2 e^{-2x}+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^{-2x}+1

\int e^{- 2 x} + 1 d x

- \frac{1}{2} e^{- 2 x} + x + C

Solution steps

\int e^{- 2 x} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{- 2 x} d x + \int 1 d x

\int e^{- 2 x} d x = - \frac{1}{2} e^{- 2 x}

\int 1 d x = x

= - \frac{1}{2} e^{- 2 x} + x

Add a constant to the solution

= - \frac{1}{2} e^{- 2 x} + x + C

\int \frac{x}{( 3 x ^{2} - 4 )} d x

\int (x + 3) (x - 1) d x

\int \frac{6 x ^{2} - 20 x - 5}{x ^{3} + 2 x ^{2} + x} d x

\int \frac{( \frac{x}{3} + \frac{1}{3} )}{( x ^{2} + x + 1 ) ^{2}} d x

\int x^{3} 1 + (3 x^{2})^{2} d x

What is the integral of e^{-2x}+1 ?
The integral of e^{-2x}+1 is -1/2 e^{-2x}+x+C