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1. Use integration by parts to find the following indefinite integrals. a. fx' In(x) dx with u = In(x) and du = x'dx. b. [ arctan(2x) dx with u = arctan(2x) and du = dx. 2. Use integration by parts to find the following indefinite integrals. Then check your answer using differentiation. In(x) a. J -dx b. [x3ex dx c. 3x sec2 (x) dx d. fxsec(x) tan(x) dx e. [ arccos(x) dx f. fx3 (Inx)2dx g. Jex cos(2x) dx. (Hint: Let / = fe* cos(2x) dx and solve for I after applying integration by parts twice.) 3. Use integration by parts to find J 8x sin(7x) dx. Give the exact answer in terms of II. 4. Find a function f such that J f (x) sin(x) dx = -f(x) cos(x) + J x3 cos(x) dx