Question

Section 3: Full Solutions Answer each of the questions below by writing the full solution process in the space provided. (Work required!) Write your final answer in the box provided. Do not approximate any of your answers! Problem 1 Integrate: 3х dx .22 - 2 - 2 (Show all details.)

Answer 1

34 dy 118-4 72_X-2 Take the constant out = 3] dx Take the partial fraction of 42_x-2 A atl + B x-2 (x+1)(x-2) X = ACX-2) + BCx+1) for the knominator root - :: A = 13 for the denominater root .2 B = 213 1/3 2/3 TI + Xt1 x-2 1 2 + 3(x+1) 3(2-2) =3 J J 3aHD + dhe 34+1) 3(2-2) Apply the son rule 2 (J3c4+1) det 3(x-2) dx) find, J 3640 dx Take the constant out

= J xt dhe Apply unsubstitution U=XtI du dr :) => dr=du a . back uaxti Š J to do 3 lnlul substo tute = $ In wi+1 and, J2 22 de 2 / 3 J 27-2 da 2 In 18-21

= 3 C3 Inlxtil +3 16 1x-21) Inlx+1)+2 11x-2) Add a constant to the solution . 101x+11+2 In 14-21+ c Thank you.