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Answer 1 · 2017-09-19T00:06:25

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

We have: $\int (3^{x - 3}) d x$ $int(3^(x - 3)) dx$

Using the laws of exponents:

$= \int (3^{x} \cdot 3^{- 3}) d x$ $= int(3^(x) cdot 3^(- 3)) dx$

Let's take the constant out of the integrand:

$= 3^{- 3} \cdot \int (3^{x}) d x$ $= 3^(- 3) cdot int(3^(x)) dx$

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

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