Answer
$ \displaystyle \frac{(3x-5)^{4}}{12}+C$
Work Step by Step
see Substituiion RuIe, p.962:
1. Write $u$ a{\it s} a function of x.
2. Take the derivative $du/dx$ and solve for the quantity $dx$ in terms of $du$.
3. Use the expression you obtain in step 2 to substitute for $dx$ in the given integral and substitute $u$ for its defining expression.
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Given (1)$ \quad u=3x-5,$
(2)$ \displaystyle \quad du=3dx\ \ \Rightarrow\ \ dx=\frac{du}{3}$
$(3)$
$\displaystyle \int(3x-5)^{3}dx=\int u^{3}\cdot\frac{du}{3}$=
... constant multiple ...
$=\displaystyle \frac{1}{3}\int u^{3}du$= .... power rule ...
$=\displaystyle \frac{1}{3}\cdot\frac{u^{4}}{4}+C$ ... bring x back ...
$=\displaystyle \frac{(3x-5)^{4}}{12}+C$
