What is the integral of 4sin(3t)+1.2e^{-6t} ?

The integral of 4sin(3t)+1.2e^{-6t} is -1.33333…cos(3t)-0.2e^{-6t}+C

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integral of 4sin(3t)+1.2e^{-6t}

\int 4 sin (3 t) + 1.2 e^{- 6 t} d t

- 1.33333 \dots cos (3 t) - 0.2 e^{- 6 t} + C

Solution steps

\int 4 sin (3 t) + 1.2 e^{- 6 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 4 sin (3 t) d t + \int 1.2 e^{- 6 t} d t

\int 4 sin (3 t) d t = - \frac{4}{3} cos (3 t)

\int 1.2 e^{- 6 t} d t = - 0.2 e^{- 6 t}

= - \frac{4}{3} cos (3 t) - 0.2 e^{- 6 t}

Simplify

= - 1.33333 \dots cos (3 t) - 0.2 e^{- 6 t}

Add a constant to the solution

= - 1.33333 \dots cos (3 t) - 0.2 e^{- 6 t} + C

What is the integral of 4sin(3t)+1.2e^{-6t} ?
The integral of 4sin(3t)+1.2e^{-6t} is -1.33333…cos(3t)-0.2e^{-6t}+C