MAT 127 Final: S06finalsol

• School: University of Maine
• Department: Mathematics and Statistics
• Course: MAT 127
• Professor: All

Document Summary

Part i: (12 pts) compute the following integral: Let u = ln x, du = dx x . 3 (ln x)3/2 + c: (14 pts) compute the following integral: Z x2 + x 1 x2 x dx. The degree of the numerator is not smaller than that of the denominator, so we rst need to divide: x2 + x 1 goes into x2 x one time with a remainder of 2x 1. 2x 1 x2 x dx = x +z 2x 1 x2 x dx. The easiest is to let u = x2 x, so du = (2x 1)dx. This easily gives the answer x + ln|x2 x| + c. Another (more di cult) solution is to use partial fractions: = 2x 1 = a(x 1) + bx = (a + b)x a. Comparing coe cients, we see that a = 1 and hence b = 1.