Do not open this exam yet (1) fill in your name, id and section number (d01 or d02). (2) this exam is closed-book and closed-notes; no calculators, no phones. (3) please write legibly to receive credit. Out of fairness to others, please stop working and close the exam as soon as the time is called. A signi cant number of points will be taken o your exam score if you continue working after the time is called. You will be given a two-minute warning before the end. 1: (20 points) compute the following inde nite integrals, r sin(2x + 3)dx xdx. 2 dx (x+1)(x+2)(x+3: r, r 1 x2 x2 dx. 3: (20 points) compute the following de nite integrals: 0 x (x + 1)dx: r 1. 5: (10 points) solve the di erential equation y = 1 xy , (10 points) determine if the improper integral r + diverges.