What is the integral of 4^{x+1/2} ?

The integral of 4^{x+1/2} is (4^x)/(ln(2))+C

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integral of 4^{x+1/2}

\int 4^{x + \frac{1}{2}} d x

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

Solution steps

\int 4^{x + \frac{1}{2}} d x

4^{x + \frac{1}{2}} = 4 4^{x}

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

Take the constant out:

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

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

4 = 2

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

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

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

Simplify

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

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

Add a constant to the solution

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

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What is the integral of 4^{x+1/2} ?
The integral of 4^{x+1/2} is (4^x)/(ln(2))+C