What is the integral of e^{-5x}+2^x ?

The integral of e^{-5x}+2^x is -1/5 e^{-5x}+(2^x)/(ln(2))+C

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integral of e^{-5x}+2^x

\int e^{- 5 x} + 2^{x} d x

- \frac{1}{5} e^{- 5 x} + \frac{2 ^{x}}{ln ( 2 )} + C

Solution steps

\int e^{- 5 x} + 2^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{- 5 x} d x + \int 2^{x} d x

\int e^{- 5 x} d x = - \frac{1}{5} e^{- 5 x}

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

= - \frac{1}{5} e^{- 5 x} + \frac{2 ^{x}}{ln ( 2 )}

Add a constant to the solution

= - \frac{1}{5} e^{- 5 x} + \frac{2 ^{x}}{ln ( 2 )} + C

What is the integral of e^{-5x}+2^x ?
The integral of e^{-5x}+2^x is -1/5 e^{-5x}+(2^x)/(ln(2))+C