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Answer 1 · 2017-09-19T00:06:25

#frac(3^(x - 3))(ln(3)) + C#

We have: #int(3^(x - 3)) dx#

Using the laws of exponents:

#= int(3^(x) cdot 3^(- 3)) dx#

Let's take the constant out of the integrand:

#= 3^(- 3) cdot int(3^(x)) dx#

#=3^(- 3) cdot frac(3^(x))(ln(3)) + C#

#= frac(3^(x - 3))(ln(3)) + C#