What is the integral of 2^{x+3} ?

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

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integral of 2^{x+3}

\int 2^{x + 3} d x

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

Solution steps

\int 2^{x + 3} d x

2^{x + 3} = 2^{3} \cdot 2^{x}

= \int 2^{3} \cdot 2^{x} d x

Take the constant out:

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

= 2^{3} \cdot \int 2^{x} d x

Simplify

= 8 \cdot \int 2^{x} d x

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

= 8 \cdot \frac{2 ^{x}}{ln ( 2 )}

Simplify

8 \cdot \frac{2 ^{x}}{ln ( 2 )} : \frac{2 ^{x + 3}}{ln ( 2 )}

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

Add a constant to the solution

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

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