What is the integral of 2e^{-2x}+4x+1 ?

The integral of 2e^{-2x}+4x+1 is -e^{-2x}+2x^2+x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2e^{-2x}+4x+1

\int 2 e^{- 2 x} + 4 x + 1 d x

- e^{- 2 x} + 2 x^{2} + x + C

Solution steps

\int 2 e^{- 2 x} + 4 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 2 e^{- 2 x} d x + \int 4 x d x + \int 1 d x

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

\int 4 x d x = 2 x^{2}

\int 1 d x = x

= - e^{- 2 x} + 2 x^{2} + x

Add a constant to the solution

= - e^{- 2 x} + 2 x^{2} + x + C

\int + x e^{x^{2}} sin (x^{2}) d x

\int \frac{( ln ( x ) ) ^{2}}{2 x ^{6}} d x

\int \frac{1 + x}{x} d x

\int \frac{1}{100 + t} d t

\int \frac{1}{9 y ^{2} + 64} d y

What is the integral of 2e^{-2x}+4x+1 ?
The integral of 2e^{-2x}+4x+1 is -e^{-2x}+2x^2+x+C