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

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

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

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

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

Solution steps

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

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

\int \frac{1}{2} d x = \frac{1}{2} x

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

Add a constant to the solution

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

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