solve this

8. Evaluate the integral using the fact that (23 + 1) = (x + 1)(23 - x +1) - (x + 1) [(x - 1)3 +1] In |z + 1| - - In(x2 - x + 1) + 1 tan-1 (15 1) +c (B) = In |x + 1/ + = In (23 - x + 1) +t 1 tan 1 ( 2x - 1) (C) : Inlz + 1/ - In (x2 - x+1) - 1 tan 1 (2x - 1) (D) - In |z + 1/ - 2In (22 - x + 1) + 1 tan 1 (" - 1) 40 (E) = In jz + 1/ - - In (23 - x + 1) + 1 tan-1 (2x - 1) 9. Using an appropriate inverse substitution find V9 + aidz a Haggmvoos (8) (A) cos(9 + z?) + C (B) In | sec 0 - tan e| + C (C) V9 + 12 (D) In(x + v9+2?) + C. 7 (C) absolutely convergent (D) is conditionally convergent (E) diverges if n $ 7 17. To use the comparison test for the series _ 2 20 41 We can compare to the series (B) E- (C) all the series in the other options can in fact be used. (D)YL (E) +Z 18. The root test would tell us that E (")" (hint: recall that e - lim (1 + 1)") (A) converges to = (B) converges to e. (C) diverges. (D) converges. (E) is conditionally convergent