What is the integral of (5/(sqrt(t))+4e^t) ?

The integral of (5/(sqrt(t))+4e^t) is 10sqrt(t)+4e^t+C

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integral of (5/(sqrt(t))+4e^t)

\int (\frac{5}{t} + 4 e^{t}) d t

10 t + 4 e^{t} + C

Solution steps

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

\int \frac{5}{t} d t = 10 t

\int 4 e^{t} d t = 4 e^{t}

= 10 t + 4 e^{t}

Add a constant to the solution

= 10 t + 4 e^{t} + C

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What is the integral of (5/(sqrt(t))+4e^t) ?
The integral of (5/(sqrt(t))+4e^t) is 10sqrt(t)+4e^t+C