What is the integral of (5^x-3^x) ?

The integral of (5^x-3^x) is (5^x)/(ln(5))-(3^x)/(ln(3))+C

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integral of (5^x-3^x)

\int (5^{x} - 3^{x}) d x

\frac{5 ^{x}}{ln ( 5 )} - \frac{3 ^{x}}{ln ( 3 )} + C

Solution steps

\int 5^{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 5^{x} d x - \int 3^{x} d x

\int 5^{x} d x = \frac{5 ^{x}}{ln ( 5 )}

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

= \frac{5 ^{x}}{ln ( 5 )} - \frac{3 ^{x}}{ln ( 3 )}

Add a constant to the solution

= \frac{5 ^{x}}{ln ( 5 )} - \frac{3 ^{x}}{ln ( 3 )} + C

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What is the integral of (5^x-3^x) ?
The integral of (5^x-3^x) is (5^x)/(ln(5))-(3^x)/(ln(3))+C