KEEP WRITING A. Integration by Partial Fraction a . show that 2x3+ 3 x - 1. = 2x + 2 + 5x - 1 using long division 20 2 - 1 2 x3 + 3x -1 = 2x3 - 5x2 +2x2- 28+5x-1 Wrong !! x 2_ x x 2 - x This is improper funchon, convert = 2x( 2)- 2)+ 2(x2- 24) + (5 x-1 ) it to proper 32 - x ustong tong 2x + 2 + 5x -1 division . b. Hence, evaluate ( 2x3+ 3x -1 dx by first expressing the integrand as a sum of partial x2 - x fractions [ax+2 4 5x-1 dx : Jazdx + S2dx + 5x-' x 2 -2 5x - 1 5 x - 1 +B X - 1 5x- 1 = A (x- 1) + 8xx X = 1/ B : 4 :. 5 xe - 1 + x (2-1) x - 1 = [ 2 x dx + ( 2 d x + S ( 2 . + 4 ) da + 4 In (x - 13 + c CS Scanned ed with CamScanner where C constantA. Integration by Partial Fraction a) Show that 2x3 +3x -1 = 2x + 2+ 5x -1 x2 - X X- - X b) Hence, evaluate 2x +3x -1 dx by first expressing the integrand as a sum of partial X- - X fractions. [8 marks]