Chapter 4.6, Problem 41E

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

Evaluate ${\displaystyle \int x\sqrt{5x+1}dx}$ by letting $u=5x+1\text{ and }du=5dx\left(\text{so that }dx=\frac{1}{5}du\right)$ and observing that $x=\frac{u-1}{5}$. Compare your answer to that found in Exercises 3 of this section. Are they the same? (Hint: Simplify both forms of the answer into a common third form.)