Please only solve 9,12 by partial fraction 27. +4r d6:08 ao OO X all 66%iView embedIMG_5800.pngSECTION 7.4 Integration of Rational Functions by Partial Fractions5017.4 EXERCISES1-6 Write out the form of the partial fraction decomposition ofthe function (as in Example 7). Do not determine the numericalvalues of the coefficients.31. - ds32. (' ds-dx*+ 4+ 134(1+ 2x)(3 - a)x'+ 2x+4+ 334. j(b)33. Ari"dx*' +1+ +1J+ S'+ St dxs+7+x + 22. (a) 6(b) + +635.36.x'+1(a'+ 2x' + 3x - 2(x + 2x + 2)3. (a)(b)x'- 3+ 2xx- 3r + 737.38.(x' - 4x + 6)x -1(b)+ +- 21'+ + 2x -14. (a)- 2r +139-52 Make a substitution to express the integrand as a rationalfunction and then evaluate the integral.5. (a)(b)(x -x+ IK + 2)-4drdr39.40.* +1(b) ( - x(x + 2x + 1)2a + 3 +x6. (a)d41. s42.xp.7-38 Evaluate the integral.3 -7. de8.43.dx44.I+1Sx +19. 124 + 14 - 1) ds10. 7(v + 4)(2y - 1)45.dx Hint: Substitute -(' de11. 1 +ir+12. ' -4dxSr + 6VI + va-dx46.13. - bs14. i(x+ alix + b)sin x47.+ je +2 dx48.cosx - 3 cos A15. ("- 41 +IJ-x' + 4x' + x - |dx16.sect49.drtan'r + 3 tanI+250. -le - 2)(e + 1)dx17. ('y - 7y - 12dy3 + 6x + 218.18.-dxcosh rvi v + 2Kv - 3)51.52.+ e + 2sinh'r + sinh tar(3 - 5)19. + u + 2) *20.de(Ar- IM - d53-54 Use integration by parts, together with the techniques ofthis section, to evaluate the integral.21. u*+ 9x + x +2dxdr22.53. j mtx" - * + 2) dk54. x tan a dax +91023. K24. jx-x+6dxx'+ 3x(- )(x + 9)E 55. Use a graph of f(x) - 1/(x - 2x - 3) to decide whether) dx is positive or negative. Use the graph to give arough estimate of the value of the integral and then use partialfractions to find the exact value.++I25. ++ x+1-dx26.'+4x +3dx*+ S+ 4x' + 6x - 227.28.56. Evaluate-dax'- 2r + 2x - 5dx+ 4+1x+ 429.x* + 2x + 5-dx30.by considering several cases for the constant k.D sCne tea R d May ddく

Question

Please only solve 9,12 by partial fraction 27. +4r d6:08 ao OO X all 66%iView embedIMG_5800.pngSECTION 7.4 Integration of Rational Functions by Partial Fractions5017.4 EXERCISES1-6 Write out the form of the partial fraction decomposition ofthe function (as in Example 7). Do not determine the numericalvalues of the coefficients.31. - ds32. (' ds-dx*+ 4+ 134(1+ 2x)(3 - a)x'+ 2x+4+ 334. j(b)33. Ari&#34;dx*' +1+ +1J+ S'+ St dxs+7+x + 22. (a) 6(b) + +635.36.x'+1(a'+ 2x' + 3x - 2(x + 2x + 2)3. (a)(b)x'- 3+ 2xx- 3r + 737.38.(x' - 4x + 6)x -1(b)+ +- 21'+ + 2x -14. (a)- 2r +139-52 Make a substitution to express the integrand as a rationalfunction and then evaluate the integral.5. (a)(b)(x -x+ IK + 2)-4drdr39.40.* +1(b) ( - x(x + 2x + 1)2a + 3 +x6. (a)d41. s42.xp.7-38 Evaluate the integral.3 -7. de8.43.dx44.I+1Sx +19. 124 + 14 - 1) ds10. 7(v + 4)(2y - 1)45.dx Hint: Substitute -(' de11. 1 +ir+12. ' -4dxSr + 6VI + va-dx46.13. - bs14. i(x+ alix + b)sin x47.+ je +2 dx48.cosx - 3 cos A15. (&#34;- 41 +IJ-x' + 4x' + x - |dx16.sect49.drtan'r + 3 tanI+250. -le - 2)(e + 1)dx17. ('y - 7y - 12dy3 + 6x + 218.18.-dxcosh rvi v + 2Kv - 3)51.52.+ e + 2sinh'r + sinh tar(3 - 5)19. + u + 2) *20.de(Ar- IM - d53-54 Use integration by parts, together with the techniques ofthis section, to evaluate the integral.21. u*+ 9x + x +2dxdr22.53. j mtx&#34; - * + 2) dk54. x tan a dax +91023. K24. jx-x+6dxx'+ 3x(- )(x + 9)E 55. Use a graph of f(x) - 1/(x - 2x - 3) to decide whether) dx is positive or negative. Use the graph to give arough estimate of the value of the integral and then use partialfractions to find the exact value.++I25. ++ x+1-dx26.'+4x +3dx*+ S+ 4x' + 6x - 227.28.56. Evaluate-dax'- 2r + 2x - 5dx+ 4+1x+ 429.x* + 2x + 5-dx30.by considering several cases for the constant k.D sCne tea R d May ddく

Accepted Answer

We need to solve integrals by using partial fraction method.