Problem Evaluate $\displaystyle \int \sqrt{ax + b} ~ dx$.
Solution
$= \displaystyle \dfrac{1}{a}\int (ax + b)^{1/2} \, (a \, dx)$
$= \dfrac{1}{a} \, \dfrac{(ax + b)^{3/2}}{3/2}$
$= \dfrac{2}{3a} (ax + b)^{3/2}$ answer
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