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

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

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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 \frac{- x}{x ^{2} + 4} d x

x \to 1 lim (2 x - 1)

f (x) = 3 x - 2 x^{2}

\frac{d y}{d x} - y = e^{x}

n = 0 \sum \infty 9 (\frac{2}{3})^{n}

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