What is the integral of-5e^{5t}+4 ?

The integral of-5e^{5t}+4 is -e^{5t}+4t+C

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integral of-5e^{5t}+4

\int - 5 e^{5 t} + 4 d t

- e^{5 t} + 4 t + C

Solution steps

\int - 5 e^{5 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 5 e^{5 t} d t + \int 4 d t

\int 5 e^{5 t} d t = e^{5 t}

\int 4 d t = 4 t

= - e^{5 t} + 4 t

Add a constant to the solution

= - e^{5 t} + 4 t + C

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