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

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

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

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

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

Solution steps

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

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

\int 3 x d x = \frac{3 x ^{2}}{2}

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

Add a constant to the solution

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

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