What is the integral of (4+4e^{2t})/(e^{2t)} ?

The integral of (4+4e^{2t})/(e^{2t)} is -2e^{-2t}+4t+C

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integral of (4+4e^{2t})/(e^{2t)}

\int \frac{4 + 4 e ^{2 t}}{e ^{2 t}} d t

- 2 e^{- 2 t} + 4 t + C

Solution steps

\int \frac{4 + 4 e ^{2 t}}{e ^{2 t}} d t

Expand

\frac{4 + 4 e ^{2 t}}{e ^{2 t}} : \frac{4}{e ^{2 t}} + 4

= \int \frac{4}{e ^{2 t}} + 4 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 \frac{4}{e ^{2 t}} d t + \int 4 d t

\int \frac{4}{e ^{2 t}} d t = - 2 e^{- 2 t}

\int 4 d t = 4 t

= - 2 e^{- 2 t} + 4 t

Add a constant to the solution

= - 2 e^{- 2 t} + 4 t + C

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What is the integral of (4+4e^{2t})/(e^{2t)} ?
The integral of (4+4e^{2t})/(e^{2t)} is -2e^{-2t}+4t+C