What is the integral of (2^t+e^pi) ?

The integral of (2^t+e^pi) is (2^t)/(ln(2))+e^pit+C

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integral of (2^t+e^pi)

\int (2^{t} + e^{π}) d t

\frac{2 ^{t}}{ln ( 2 )} + e^{π} t + C

Solution steps

\int 2^{t} + e^{π} 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 2^{t} d t + \int e^{π} d t

\int 2^{t} d t = \frac{2 ^{t}}{ln ( 2 )}

\int e^{π} d t = e^{π} t

= \frac{2 ^{t}}{ln ( 2 )} + e^{π} t

Add a constant to the solution

= \frac{2 ^{t}}{ln ( 2 )} + e^{π} t + C

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What is the integral of (2^t+e^pi) ?
The integral of (2^t+e^pi) is (2^t)/(ln(2))+e^pit+C