What is the integral of (e^x+a^x) ?

The integral of (e^x+a^x) is e^x+(a^x)/(ln(a))+C

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integral of (e^x+a^x)

\int (e^{x} + a^{x}) d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

What is the integral of (e^x+a^x) ?
The integral of (e^x+a^x) is e^x+(a^x)/(ln(a))+C