What is the integral of-6e^t+3e^{3t} ?

The integral of-6e^t+3e^{3t} is -6e^t+e^{3t}+C

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integral of-6e^t+3e^{3t}

\int - 6 e^{t} + 3 e^{3 t} d t

- 6 e^{t} + e^{3 t} + C

Solution steps

\int - 6 e^{t} + 3 e^{3 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 6 e^{t} d t + \int 3 e^{3 t} d t

\int 6 e^{t} d t = 6 e^{t}

\int 3 e^{3 t} d t = e^{3 t}

= - 6 e^{t} + e^{3 t}

Add a constant to the solution

= - 6 e^{t} + e^{3 t} + C

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What is the integral of-6e^t+3e^{3t} ?
The integral of-6e^t+3e^{3t} is -6e^t+e^{3t}+C