Problem
Question 9 (4 points) When evaluating the integral \( \int \frac{x^{3} d x}{\sqrt{4 x^{2}+36}} \) which of the following would be the best substitution for \( \boldsymbol{x} \) ?
Solution
Step 1 ：1. Let \(u = 2x\) then \(\frac{du}{dx} = 2\)
Step 2 ：2. Replace x in the integral: \(\int \frac{\frac{u^3}{8} du}{\sqrt{u^{2}+36}}\)
Step 3 ：3. Simplify: \(\frac{1}{8} \int \frac{u^{3} du}{\sqrt{u^{2}+36}}\)
