What is the integral of (e^{-3t}+cos(2t)) ?

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

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integral of (e^{-3t}+cos(2t))

\int (e^{- 3 t} + cos (2 t)) d t

- \frac{1}{3} e^{- 3 t} + \frac{1}{2} sin (2 t) + C

Solution steps

\int e^{- 3 t} + cos (2 t) 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 e^{- 3 t} d t + \int cos (2 t) d t

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

\int cos (2 t) d t = \frac{1}{2} sin (2 t)

= - \frac{1}{3} e^{- 3 t} + \frac{1}{2} sin (2 t)

Add a constant to the solution

= - \frac{1}{3} e^{- 3 t} + \frac{1}{2} sin (2 t) + C

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