Show all work and include appropriate explanations when necessary. Answers unaccompa- nied by work may not receive credit. Please try to do all work in the space provided and circle your nal answers. The last page contains some useful formulas: (10pts) compute the following derivatives: (a) (5pts) dx(tan 1 (x2)) (b) (5pts) dx(x7x, (15pts) compute the following inde nite integrals: remember: +c! (a) (5pts) z. 4x + 3 dx (b) (5pts) z cos3 x dx (c) (5pts) z x2 ln x dx. 1: (5pts) a formula for the inverse of the function f (x) = ln (3x + 8, (10pts) use the rationalizing substitution x = tan t to nd the antiderivative. 1 (x2 + 1)3/2 dx: (10pts) find the antiderivative z x x2 3x + 2 dx. 2: (14pts) determine, by whatever method you wish, whether the following series are convergent or divergent. Circle c" if the series is convergent or d" if the series is divergent.
