Please answer all questions and show work:

8) The power series f(x) = ) (2x + 1)" is (2x + 1)2 1=0 O centered at r O 10 (2x + 1)"+1 Which of the following is the general term of the power series of / f(x)dx? n +1 (2x + 1 )"+1 2(n + 1) 9) Evaluate the indefinite integral sin (t ? ) at OF(-1) as an indefinite series. (2n)! OF n=0 (2n)! pin - 2 n=1 (2n - 1)! pin - 1 7= 1 (4n - 1) (2n - 1)! 10) Which of the following Taylor series for f (x) = In(1 + x) centered at x = 0? IM (-1)2-1 O n=0 n (-1)2- O n=1 n n (-1)2-1 O n- 1