What is the integral of e^{-3x}+2x ?

The integral of e^{-3x}+2x is -1/3 e^{-3x}+x^2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{-3x}+2x

\int e^{- 3 x} + 2 x d x

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

Solution steps

\int e^{- 3 x} + 2 x 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^{- 3 x} d x + \int 2 x d x

\int e^{- 3 x} d x = - \frac{1}{3} e^{- 3 x}

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

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

Add a constant to the solution

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

\int cos (t - x) d x

d er i v a t i v e f (x) = 7 x - 5

\frac{d}{d x} (\frac{1}{ln ( 2 )})

d er i v a t i v e f (x) = 1100 (x^{2} - 0.2 x)

t an g e n t y = - 2 sin (x), at x = \frac{3}{4} π

What is the integral of e^{-3x}+2x ?
The integral of e^{-3x}+2x is -1/3 e^{-3x}+x^2+C