What is the integral of (2^x+3^x) ?

The integral of (2^x+3^x) is (2^x)/(ln(2))+(3^x)/(ln(3))+C

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integral of (2^x+3^x)

\int (2^{x} + 3^{x}) d x

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

Solution steps

\int 2^{x} + 3^{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 2^{x} d x + \int 3^{x} d x

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

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

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

Add a constant to the solution

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

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