MATH 181 Study Guide - Final Guide: Ibm System P, Trigonometric Substitution, Absolute Convergence

• School: UIC
• Department: Mathematics
• Course: MATH 181
• Professor: All

Document Summary

Problem 1 solution: compute the following inde nite integrals: (a) z x2 ln x dx (d) z arctan x dx. Solution: dx x (b) z x2 + x 6 (e) z ex cos x dx (c) z x cos x dx (a) we evaluate the integral using integration by parts. Let u = ln x and v = x2. Z uv dx = uv z u v dx x3 dx. Z x2 ln x dx = (ln x)(cid:18) 1. 9 x3 + c (b) we compute this integral using partial fraction decomposition. Factoring the denom- inator and decomposing we get: x x2 + x 6 x (x + 3)(x 2) Multiplying the equation by (x + 3)(x 2) we get: x = a(x 2) + b(x + 3) Next we plug in two di erent values of x to get a system of two equations in two unknowns (a, b).