Show all work and include appropriate explanations when necessary. The last page contains some useful identities: (15pts) compute the following derivatives: (a) (5pts) dx(log5 x) (b) (5pts) dx(3x2 (c) (5pts) dx((2x)3x, (15pts) compute the following inde nite integrals: remember: +c! (a) (5pts) z. 1 x2 dx (b) (5pts) z x2px3 + 4 dx (c) (5pts) z x cos x dx. 1 x2 x2 + 4 dx by making the rationalizing substitution x = 2 tan t: (10pts) use partial fractions to nd the antiderivative z. 2: (12pts) 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. )4: (12pts) use either the integral test or the comparison test to determine whether the series. Note: you can assume that this series satis es the hypotheses of both tests; you do not need to check this. 3: (10pts) use the fact that dx( 1.
