Pre-Calc Homework Solutions 348

Pre-Calc Homework Solutions 348 - 348 17. (x 2 Section 8.4...

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Unformatted text preview: 348 17. (x 2 Section 8.4 1)2 1 1)2 (x A x 1 1)2(x B (x 1)2 C 1)2 x 1 (x D 1)2 21. x 3 x2 x3 1 2x 1 (x 2 1)(x 2 A x 1 x Bx x2 1) C x 1 (x 2 1 A(x 1)(x D(x 1)2 1)2 x x2 ( A 2B C 1) x B(x 1)2 C(x 1)2(x 1) x2 2x 2 A(x 2 (A x B)x 2 1) (A (Bx B C)(x C)x 1) (A C) A(x 3 x2 C(x 3 B(x 2 1) B C 2x D(x 2 D)x (A 2 1) 2x 1) Equating coefficients of like terms gives A B 1, A B C 2, and A C 2. (A C)x ( A 3 Solving the system simultaneously yields C D) A x 2 2D)x B 1, B 2x x3 1 2 2, C dx 1. x 1 dx 1 2x 1 dx x2 x 1 Equating coefficients of like terms gives A A C 2B 0, A C B 2D C D 0, B C D 1 ln x 22. x 3 x 2 1 x Bx x2 ln (x 2 1) C x 1 x 1) C 0, and A 1 4x x3 1 (x 4 1)(x 2 A x 1 Solving the system simultaneously yields 1 1 A ,B ,C 4 4 dx (x 2 1)2 1/4 dx x 1 1 ln x 1 4 1 ,D 4 1 . 4 x2 4x 4 A(x 2 (A x B)x 2 1) (Bx B C)(x C)x 1) (A C) ( A 1/4 1/4 1/4 dx dx dx (x 1)2 x 1 (x 1)2 1 1 1 ln x 1 C 4 4(x 1) 4(x 1) Equating coefficients of like terms gives A B 1, A B C 4, and A C 4. 18. x 2 x x2 5x 6 (x A x 6 6)(x B x 1) 1 Solving the system simultaneously yields A x2 x3 4 5x 6 3, B 4x 1 4 2, C dx 1. 3 x 1 x 4 A(x (A 1) B)x B(x ( A 6) 6B) 23. dx 1 Cx (x 2 x2 2x 1 dx x 1 3 ln x 3x 2 2x 12 (x 2 4)2 Ax x2 B 4 ln (x 2 D 4)2 x 1) C Equating coefficients of like terms gives A B 1 and A 6B 4. 3x 2 2x 12 (Ax Ax 3 B)(x 2 Bx 2 4) (4A (Cx C)x D) 4B D Solving the system simultaneously yields 2 5 A ,B . 7 7 x 4 dx x 2 5x 6 Equating coefficients of like terms gives 2/7 dx x 6 2 ln x 7 5/7 dx x 1 5 ln x 1 7 A C 0, B 3, 4A C 2, and 4B D 12 6 Solving the system simultaneously yields A 3x 2 19. Complete the square in the denominator. r2 r 2 0, B 2x (x 2 3, C 12 4)2 2, D 3 x2 4 0. dx 2x dx (x 2 4)2 1 C x2 4 2r 2 dr 2r 2 2 r2 2r 2 dr (r 1)2 1 1 1 (r 2 tan 1 1)2 (r 1 1) C dx 3 x tan 1 2 2 20. Complete the square in the denominator. r2 r2 The first integral was evaluated by using Formula 16 from the Brief Table of Integrals. 1 2) C 4r 3 dr 4r 5 5 r2 (r 4r 3 dr 2)2 4 1 1 (r 3 tan 1 2)2 (r ...
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