What is the integral of 20+75e^{-x/(50)} ?

The integral of 20+75e^{-x/(50)} is 20x-3750e^{-x/(50)}+C

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integral of 20+75e^{-x/(50)}

\int 20 + 75 e^{- \frac{x}{50}} d x

20 x - 3750 e^{- \frac{x}{50}} + C

Solution steps

\int 20 + 75 e^{- \frac{x}{50}} 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 20 d x + \int 75 e^{- \frac{x}{50}} d x

\int 20 d x = 20 x

\int 75 e^{- \frac{x}{50}} d x = - 3750 e^{- \frac{x}{50}}

= 20 x - 3750 e^{- \frac{x}{50}}

Add a constant to the solution

= 20 x - 3750 e^{- \frac{x}{50}} + C

5 x^{2}

n = 1 \sum \infty (- 3)^{3 n - 1}

\frac{d}{d x} (ln (\frac{x ^{3} + 1}{x ^{2} + 1}))

\int 3 e^{3 t} d t

\frac{x}{x + 1}

What is the integral of 20+75e^{-x/(50)} ?
The integral of 20+75e^{-x/(50)} is 20x-3750e^{-x/(50)}+C