Chapter 4.6, Problem 42E

In Exercises 43-44, evaluate the given indefinite interval using substitution. Refer to Example 9 in section 4.5 to review the technique.

Consider ${\displaystyle \int \frac{x}{\sqrt{x-3}}dx}$.

a. Evaluate this integral using integration by parts.

b. Evaluate this integral using the substitution $u=x-3$ and observing that $x=u+3$.

c. Show algebraically that the answer from parts (a) and (b) are equivalent.