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

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

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

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

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

Solution steps

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

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

\int 20 d t = 20 t

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

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

Add a constant to the solution

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

t \cdot cos (π \cdot t)

y^{^{'}} + 2 y = 3 sin (e^{2 x})

n = 1 \sum \infty \frac{( 2 ^{2 n} n ! )}{2 n + 1}

e^{- 3 t} \cdot sin (t)

x \to 3 + lim (\frac{2}{x + 3})

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