Math 132: Calculus for the Physical & Life Sciences 2 Problem Set 4 Due Friday, February 15, 2008, at the beginning of class.

General Directions: You must show all work for credit on these problems.

1. Use trigonometric substitutions (possibly after completing the square) to evaluate each of the following integrals.

a. ∫ \frac{1}{\sqrt{9 + 4x^{2}}} dx

b. ∫ \frac{\sqrt{x^{2} − 1}}{x^{2}} dx

c. ∫ \frac{1}{\sqrt{3 − 2x − x^{2}}} dx

2. Integrate using the partial fraction technique (divide the denominator polynomial into the top first when necessary).

a. ∫ \frac{1}{x^{2} + x − 6} dx

b. ∫ \frac{x^{4}}{x^{2} + 4} dx

c. ∫ \frac{x + 10}{2x^{2} + 5x − 3} dx

d. ∫ \frac{x^{2} + 1}{x^{3} + 2x^{2} + x} dx

e. ∫ \frac{x + 4}{x^{3} + 4x} dx

3. Integrate using the table of integrals in Stewart, and preliminary substitutions or algebraic manipulation as necessary. In each case, state clearly the number of the table entry you are using.

a. ∫ \frac{x^{2}}{\sqrt{x^{2} + 25}} dx

b. ∫ \sqrt{2x − x^{2}} dx

c. ∫ \frac{dx}{\sqrt{e^{2x} − 1}}

d. ∫ \frac{cos(x)}{\sqrt{4 − sin^{2}(x)}} dx

e. ∫ \frac{sec^{2}(x)}{tan^{2}(x) + 2 tan(x) + 2} dx

f. ∫ e^{x}\sqrt{1 + e^{2x}} dx