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A few practice problems:

There will be no practice exam for the final, and this document should in no way be considered a comprehensive list of practice problems.

As I mentioned in class, one thing you absolutely postively need to able to do is take the derivative of any function. If you have any doubts about your ability to do so, you should review the following problems:

Also here are some practice integrals. Some can be done with substitution and some can be done with integration by parts; the fun part is figuring out which method to use.

  1. $\displaystyle{\int \frac{1}{x \ln(x)} dx}$
  2. $\displaystyle{\int \frac{e^x}{1+e^x} dx}$
  3. $\displaystyle{\int xe^{2x} dx}$
  4. $\displaystyle{\int \frac{\arcsin(x)}{\sqrt{1-x^2}} dx}$
  5. $\displaystyle{\int \sqrt{x} \ln(x) dx}$
  6. $\displaystyle{\int \sin^2(x) dx}$
  7. $\displaystyle{\int \cos(x) \cos(\sin(x)) dx}$
  8. $\displaystyle{\int \cos(\ln(x)) dx}$
  9. $\displaystyle{\int x \sin(4x) dx}$
  10. $\displaystyle{\int \frac{e^x}{1+e^{2x}} dx}$
  11. $\displaystyle{\int (x^2+1)e^{-x} dx}$
  12. $\displaystyle{\int \cot(x) dx}$
  13. $\displaystyle{\int \frac{e^{1/x}}{x^2} dx}$
  14. $\displaystyle{\int \arccos(x) dx}$
  15. $\displaystyle{\int \sin^3(x) dx}$
  16. $\displaystyle{\int (\ln(x))^2 dx}$
  17. $\displaystyle{\int \frac{1+4x}{\sqrt{1+x+2x^2}} dx}$
  18. $\displaystyle{\int \sqrt{\tan(x)} \sec^2(x) dx}$

Math 3 Winter 2001 2001-03-22