What is the integral of (e^x+4^{(x+2)}) ?

The integral of (e^x+4^{(x+2)}) is e^x+(2^{2x+3})/(ln(2))+C

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integral of (e^x+4^{(x+2)})

\int (e^{x} + 4^{(x + 2)}) d x

e^{x} + \frac{2 ^{2 x + 3}}{ln ( 2 )} + C

Solution steps

\int e^{x} + 4^{x + 2} 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^{x} d x + \int 4^{x + 2} d x

\int e^{x} d x = e^{x}

\int 4^{x + 2} d x = \frac{2 ^{2 x + 3}}{ln ( 2 )}

= e^{x} + \frac{2 ^{2 x + 3}}{ln ( 2 )}

Add a constant to the solution

= e^{x} + \frac{2 ^{2 x + 3}}{ln ( 2 )} + C

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What is the integral of (e^x+4^{(x+2)}) ?
The integral of (e^x+4^{(x+2)}) is e^x+(2^{2x+3})/(ln(2))+C