What is the integral of 5^{x+3} ?

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

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integral of 5^{x+3}

\int 5^{x + 3} d x

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

Solution steps

\int 5^{x + 3} d x

Simplify

5^{x + 3} : 5^{x} \cdot 5^{3}

= \int 5^{x} \cdot 5^{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5^{3} \cdot \int 5^{x} d x

Simplify

= 125 \cdot \int 5^{x} d x

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

= 125 \cdot \frac{5 ^{x}}{ln ( 5 )}

Simplify

125 \cdot \frac{5 ^{x}}{ln ( 5 )} : \frac{5 ^{x + 3}}{ln ( 5 )}

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

Add a constant to the solution

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

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