I NEED HELP

6. (1.5 pts each) Write out the partial fraction decomposition FORM for each of the following rational functions. You do NOT need to solve for the coefficients. x2 + 1 a) x2 (x + 1)3 b) (x - 1) (22 + 1)27. (4 pts) Write out the partial fraction decomposition of the following rational function. For this problem, you must calculate all the coefficients and cannot just leave them as A, B, etc. 3x (x - 2) (2x - 1)9. (3 pts) Find a bound for the error Er when using the trapezoidal rule in the previous problem. Simplify your answer. 10. (4 pts each) Evaluate four of the following five integrals. a) dx (Trig substitution with x = sin 0) x2 V1 - x2 b) (x2 + 1) sin a dx (Integration by parts with u = (2 + 1), du = sinr dx) c) 325VI+ 13 dr (Substitution with u = 1 + 23 ) d) sin? x cos' x da (Trig integral with u = sina) 1 1 + 2x e) + 1 + x2 dx (Break into simpler pieces and evaluate separately) 3 - x1. (1 pt each) For each of the following integrals, state which integration technique should be applied first to solve it. (You should not evaluate the integral.) The possible techniques are "u substitution," "integration by parts," "trigonometric integral," "trigonometric sub- stitution," "partial fraction decomposition," or "no special technique needed." Vx2 - 4 a) dx b ) ( x2 + 1 ) (x + 1)2 d. c) cos( 2x)etz dx d) cost r dx e) 3 - ex dx f ) ( 1 + x ) ( 32 2 - 4) dx g ) arctan x dx 7-3 2. (1 pt) In one sentence, describe what you would do first when trying to solve 1 + x + x2 dx. (Hint: it is not any of the techniques mentioned in problem 1.)8. (3 pts) Approximate the integral , In a da using the trapezoidal rule with n = 3. (You do not need to simplify your answer. )5. (1.5 pts each) The following integrals require trigonometric substitution. State what is the correct substitution to use for each of these. For example, a substitution might be written as 3x = sin 0. a) V4x2 - 1 dx b ) V 9 + 1 2 dx\f