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

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

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integral of 2^{x+2}

\int 2^{x + 2} d x

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

Solution steps

\int 2^{x + 2} d x

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

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

Take the constant out:

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

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

Simplify

= 4 \cdot \int 2^{x} d x

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

= 4 \cdot \frac{2 ^{x}}{ln ( 2 )}

Simplify

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

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

Add a constant to the solution

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

\int e^{- \frac{x}{2}} cos (\frac{x}{2}) d x

10 sin (3 t)

\int (x + π) sin (n x) d x

y^{'} = 0.0014 y (1700 - y)

4 cos^{2} (2 t)

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