What is the integral of (9^x)/(3^{x+2)} ?

The integral of (9^x)/(3^{x+2)} is (3^{x-2})/(ln(3))+C

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integral of (9^x)/(3^{x+2)}

\int \frac{9 ^{x}}{3 ^{x + 2}} d x

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

Solution steps

\int \frac{9 ^{x}}{3 ^{x + 2}} d x

\frac{9 ^{x}}{3 ^{x + 2}} = \frac{1}{3 ^{2}} \frac{9 ^{x}}{3 ^{x}}

= \int \frac{1}{3 ^{2}} \cdot \frac{9 ^{x}}{3 ^{x}} d x

Take the constant out:

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

= \frac{1}{3 ^{2}} \cdot \int \frac{9 ^{x}}{3 ^{x}} d x

Simplify

= \frac{1}{9} \cdot \int \frac{9 ^{x}}{3 ^{x}} d x

Simplify

\frac{9 ^{x}}{3 ^{x}} : 3^{x}

= \frac{1}{9} \cdot \int 3^{x} d x

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

= \frac{1}{9} \cdot \frac{3 ^{x}}{ln ( 3 )}

Simplify

\frac{1}{9} \cdot \frac{3 ^{x}}{ln ( 3 )} : \frac{3 ^{x - 2}}{ln ( 3 )}

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

Add a constant to the solution

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

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What is the integral of (9^x)/(3^{x+2)} ?
The integral of (9^x)/(3^{x+2)} is (3^{x-2})/(ln(3))+C