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

The integral of (3^{2x+3})/2 is (3^{3+2x})/(4ln(3))+C

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integral of (3^{2x+3})/2

\int \frac{3 ^{2 x + 3}}{2} d x

\frac{3 ^{3 + 2 x}}{4 ln ( 3 )} + C

Solution steps

\int \frac{3 ^{2 x + 3}}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int 3^{2 x + 3} d x

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

= \frac{1}{2} \cdot \int 3^{3} \cdot 3^{2 x} d x

Take the constant out:

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

= \frac{1}{2} \cdot 3^{3} \cdot \int 3^{2 x} d x

Simplify

= \frac{1}{2} \cdot 27 \cdot \int 3^{2 x} d x

Simplify

3^{2 x} : 9^{x}

= \frac{1}{2} \cdot 27 \cdot \int 9^{x} d x

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

= \frac{1}{2} \cdot 27 \cdot \frac{9 ^{x}}{ln ( 9 )}

Simplify

\frac{1}{2} \cdot 27 \cdot \frac{9 ^{x}}{ln ( 9 )} : \frac{3 ^{3 + 2 x}}{4 ln ( 3 )}

= \frac{3 ^{3 + 2 x}}{4 ln ( 3 )}

Add a constant to the solution

= \frac{3 ^{3 + 2 x}}{4 ln ( 3 )} + C

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What is the integral of (3^{2x+3})/2 ?
The integral of (3^{2x+3})/2 is (3^{3+2x})/(4ln(3))+C