Math 132: Calculus for the Physical & Life Sciences 2 Problem Set 4 – Answers

1. a.

\frac{1}{2} ln |\sqrt{9 + 4x^{2}} + 2x| + C

c.

sin^{−1} (\frac{x + 1}{2}) + C.

2. b.

\frac{x^{3}}{3} − 4x + 8 tan^{−1}(x/2) + C.

d.

ln |x| + \frac{2}{x + 1} + C.

3. a.

\frac{x}{2}\sqrt{x^{2} + 25} − \frac{25}{2} ln |x + \sqrt{25 + x^{2}}| + C.

c.

sec^{−1}(e^{x}) + C.

e.

tan^{−1}(tan(x) + 1) + C.