\fIntegration Involving Partial Fractions Evaluate the integrals 1. 2. 11x + 17 - dx x2 - 3x - 4 2x2 + 7x-4 dx 3. 2x2 - 9x - 9 4 X - 8 dx dx x3 - 9x x+3 5. 3x2 - 10 6. 2 dx dx x2 - 4x + 4 X 7. 2x2 + 3 8. 2x2 - 10x + 4 x(x - 1)2 7 dx ( + 1)(x - 3)2 . dx 9. 10. x- + 2x - 1 (x+ 1)2 ax 2x3 + 3x2 - 2x dx Answers : (1) = (In/x - 41 - In/x + 1[) + C (2) =In|2x - 1| + 3 In/x + 4| + C (3) Inlx| + 2 Inlx + 3| - Inlx - 3| + c (4) - - 3x + Inlx + 3|+ c (5) 3x + 12 Inlx - 21 -+ C (6) -2 Inx + Inlx - 1| + In|x + 1/ + c (7) 3Inx - In|x - 1/ - -+C (8) + In/x - 3| + In/x + 1| + C (9) x - 2 Inlx + 1/ - (10) -Inx + - In|2x - 1| - _ In 10 Inlx + 21 + C