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 $x$ ?

Answer

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Answer

3. Simplify: $\frac{1}{8} \int \frac{u^{3} d u}{\sqrt{u^{2} + 36}}$

Steps

Step 1 ：1. Let $u = 2 x$ then $\frac{d u}{d x} = 2$

Step 2 ：2. Replace x in the integral: $\int \frac{\frac{u^{3}}{8} d u}{\sqrt{u^{2} + 36}}$

Step 3 ：3. Simplify: $\frac{1}{8} \int \frac{u^{3} d u}{\sqrt{u^{2} + 36}}$