I just learned calculus, so I want to be able to figure out how to solve each step. If it is a paper answer hope to be able to clear the word, I am afraid that I will not understand the font, grateful.

21.1 Homework Practice Exercise 21.1: Integrate the following using partial fractions: 3x +1 a ) dx x-+2x -3 3x +10 b) dx x2 - 4 2x2 +9x +11 C) (x + 1)(x+2)(x+3) dx 7x d) -dx 3x- +5x-2 1-3 e) - dx x - x x2 + 3x-1 dx x2 - 4 x2 + 5 g) dx (x - 2) (x+1)2 h) (3x5 -10x2 -9x + 27 dx x* - 6x +9x- 1 i) dx -x j) x - 2x - x -2 dx x*-1 k) -x-2 dx x'txtx 3x-2 1) dx x' - 121.1 Homework Practice Answers Exercise 21.1: a) In x -1 + 2In x+3+C b) 4Inx - 2+ In x+2+ C c) 2In x+1-Inx+2+ Inx+3+c In 3x -1+ 2In/x+2| + c e) -+x+Inx-1+c fx+-In x -2+~In/x+2+C 4 2 g) - In| x- 2+ C x+1 h) 1 3 x-3 x + 2 In/x -3/+ In/x/ + C i) 1 2.x2 _+ In x-1 - In|x|+C x (x+ 1) (x2 + 1 ) 1/2 D) In + C x-1 k) xtxtc x 2 1) In (x2 + x+1) (x-1) +cUnit 21: Special Methods 2 - Partial Fractions Partial fractions- Non-repeating Linear Factors Two conditions must be met in order to resolve a rational function into partial fractions: . The degree of numerator must be less than degree of denominator. If this is not the case, long division will produce a polynomial and remainder in the proper form. Denominator must be factorable into linear or quadratic factors Examples Example 1: Integrate the following: a) x+3 -dx x +7x+10 x+2 x2 + 7x+10 x-1 A B (x + 5) (x+2) x+5 x+2 x-1 A(x+2) +B(x+5) (x +5)(x+2) (x +5) (x+2) x-1 = A(x+2)+B(x+5) Let x = -2: -2-1=B(-2+5)=-3=3B= B=-1 Let x = -5: -5-1=A(-5+2)=-6=-34= A=2 x+2 A B 2 x' +7x+10 x+5 x+2 x+5 x+2 x+2 -dx = - dx = 26 - dx - dx x2 + 7x+10 x+5 x+2 x+5 x+2 = 2In x +5-In x+2+ C