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Math 108 Practice Mini Test #2

Evaluate the following integrals using the substitution techniques. Show all work.

1. ${\displaystyle \int {(x^2+3x+1)}^2(2x+3)dx}$ (Solution)

2. ${\displaystyle \int {(3x^2-2x+5)}^3(3x-1)dx}$ (Solution)

3. ${\displaystyle \int \frac{x}{{(x^2-2)}^3}dx}$ (Solution)

4. ${\displaystyle \int \frac{1}{{(3x+4)}^5}dx}$ (Solution)

5. ${\displaystyle \int \frac{1}{3x-5}dx}$ (Solution)

6. ${\displaystyle \int (2x+3)e^{x^2+3x-7}dx}$ (Solution)

7. ${\displaystyle \int e^{4x+3}dx}$ (Solution)

8. ${\displaystyle \int x\sqrt{x-3}dx}$ (Solution)

9. ${\displaystyle \int x^2\sqrt{x-3}dx}$ (Solution)

10. ${\displaystyle \int \frac{x}{x+1}dx}$ (Solution)

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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)

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