 # Practice Problems for Module 5

Section 7.3

Directions. The following are review problems. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. You can also follow the link for the full video page to find related videos.
Evaluate the following integrals.
1. $$\displaystyle \int \! \frac{x^2}{\left(4-9x^2\right)^{3/2}}\, dx$$

$$\displaystyle \int \! \frac{x^2}{\left(4-9x^2\right)^{3/2}}\, dx = \frac{1}{27} \left[ \frac{3x}{\sqrt{4-9x^2}} -\arcsin \left(\frac{3x}{2}\right)\right] + C$$

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2. $$\displaystyle \int \! \frac{\sqrt{4x^2-25}}{x^4}\, dx$$​

$$\displaystyle \int \! \frac{\sqrt{4x^2-25}}{x^4}\, dx = \frac{8}{75} \left[ \frac{\sqrt{4x^2-25}}{5}\right]^3 + C$$

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3. $$\displaystyle \int \! \frac{1}{(x+3)^2\sqrt{x^2+6x+5}}\, dx$$

$$\displaystyle \int \! \frac{1}{(x+3)^2\sqrt{x^2+6x+5}}\, dx = \frac{1}{4}\cdot \frac{\sqrt{(x+3)^2-4}}{x+3}+C$$

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