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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. \( \displaystyle \int \! \frac{x^2}{\left(4-9x^2\right)^{3/2}}\, dx\)  

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

    To see the full video page and find related videos, click the following link.
    WIR 20B M152 V31.5


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

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

    To see the full video page and find related videos, click the following link.
    WIR 20B M152 V32


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

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

    To see the full video page and find related videos, click the following link.
    WIR 20B M152 V33