What is the integral of x^e+2^x ?

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

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integral of x^e+2^x

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

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

Solution steps

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

\int x^{e} d x = \frac{x ^{e + 1}}{e + 1}

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

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

Add a constant to the solution

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

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