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juan21
Posts: 11
Joined: Thu Dec 03, 2015 12:20 am

problems compiling a document of latex

Postby juan21 » Wed Sep 21, 2016 1:24 am

Good afternoon , I am presenting problems to compile a latex document I can not compile either a set of equations
sending the attached document , the error is on page 37 of adobe, the syntax of the set of equations is the following thank you in advance Help
  1. \item[3c] Si $p=\infty$, entonces $q=1$ y se tiene lo siguiente
  2. \begin{align*}
  3. \int_{a}^{b}|s_4(x)|\,dx &= -\frac{1}{24}\int_{a}^{\frac{a+b}{2}} (x-a)^3\left(x-\frac{a+2b}{3}\right)\,dx - \frac{1}{24}\int_{\frac{a+b}{2}}^{b} (x-b)^3\left(x-\frac{2a+b}{3}\right)\,dx\\
  4. &=-\frac{1}{24}\left[\int_{a}^{\frac{a+b}{2}}(x^3-3ax^2+3a^2x-a^3)\left(x-\frac{a+2b}{3}\right)\,dx\right.\\
  5. &\left.+\int_{\frac{a+b}{2}}^{b}(x^3-3bx^2+3b^2x-b^3)\left(x-\frac{2a+b}{3}\right)\,dx\right]\\
  6. &=-\frac{1}{24}\left[\int_{a}^{\frac{a+b}{2}}\left[x^4-3ax^3+3a^2x^2-a^3x-x^3\left(\frac{a+2b}{3}\right)\right.\right.\\
  7. &\left.+ax^2(a+2b)-a^2x(a+2b)+\frac{a^3}{3}(a+2b)\right]\,dx\\
  8. +\left.\int_{\frac{a+b}{2}}^{b}\left[x^4-3bx^3+3b^2x^2-b^3x - \frac{x^3}{3}(2a+b)+bx^2(2a+b)-b^2x(2a+b)+\frac{b^3}{3}(2a+b)\right]\,dx\right]\\
  9. &=-\frac{1}{24}\left[\frac{x^5}{5}-\frac{3}{4}ax^4+a^2x^3-\frac{a^3x^2}{2}-\frac{x^4}{12}(a+2b)+\frac{ax^3}{3}(a+2b)-\frac{a^2x^2}{2}\right.\\
  10. &\left.\left.+\frac{a^3}{3}(a+2b)x\right]\right|_a^{\frac{a+b}{2}}-\frac{1}{24}\left[\frac{x^5}{5}-\frac{3}{4}bx^4+b^2x^3-\frac{b^3x^2}{2}-\frac{x^4}{12}(2a+b)\right.\\
  11. &\left.\left.+\frac{bx^3}{3}(2a+b)-\frac{b^2x^2}{2}+\frac{b^3}{3}(2a+b)x\right]\right|_{\frac{a+b}{2}}^{b}\\
  12. &=-\frac{1}{24}\left[\frac{1}{5}\left(\frac{a+b}{2}\right)^5-\frac{3a}{4}\left(\frac{a+b}{2}\right)^4+a^2\left(\frac{a+b}{2}\right)^3-\frac{a^3}{2}\left(\frac{a+b}{2}\right)^2\right.\\
  13. &-\frac{1}{12}\left(\frac{a+b}{2}\right)^4(a+2b)+\frac{a}{3}\left(\frac{a+b}{2}\right)^3(a+2b)-\frac{a^2}{2}\left(\frac{a+b}{2}\right)^2(a+2b)\\
  14. &+\frac{a^3}{3}(a+2b)\left(\frac{a+b}{2}\right)-\frac{a^5}{5}+\frac{3}{4}a^5-a^5+\frac{a^5}{2}+\frac{a^4}{12}(a+2b)-\frac{a^4}{3}(a+2b)\\
  15. &+\frac{a^4}{2}(a+2b)-\frac{a^4}{3}(a+2b)\\
  16. &+\frac{b^5}{5}-\frac{3}{4}b^5+b^5-\frac{b^5}{2}^-\frac{b^4}{12}(2a+b)+\frac{b^4}{3}(2a+b)-\frac{b^4}{2}(2a+b)+\frac{b^4}{3}(2a+b)\\
  17. &-\frac{1}{5}\left(\frac{a+b}{2}\right)^5+\frac{3b}{4}\left(\frac{a+b}{2}\right)^4-b^2\left(\frac{a+b}{2}\right)^3+\frac{b^3}{2}\left(\frac{a+b}{2}\right)^2\\
  18. &\left.+\frac{1}{12}\left(\frac{a+b}{2}\right)^4(2a+b)-\frac{b}{3}\left(\frac{a+b}{2}\right)^3(2a+b)+\frac{b^2}{2}\left(\frac{a+b}{2}\right)^2(2a+b)-\frac{b^3}{3}(2a+b)\left(\frac{a+b}{2}\right)\right]\\
  19. &=-\frac{1}{24}\left[\frac{b^5-a^5}{20}+\frac{1}{12}(b^5-a^5+2ab^4-2ba^4)+2\left(\frac{a+b}{2}\right)^4(b-a)\right.\\
  20. &\left.+\frac{4}{3}(a^2-b^2)\left(\frac{a+b}{2}\right)^3+\left(\frac{a+b}{2}\right)^2[b^3-a^3+b^2a-a^2b]+\left(\frac{a+b}{2}\right)\left(\frac{a^3}{3}(a+2b)-\frac{b^3}{3}(2a+b)\right)\right]\\
  21. \end{align*}
Attachments
Maestro.pdf
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Johannes_B
Site Moderator
Posts: 4044
Joined: Thu Nov 01, 2012 4:08 pm

Postby Johannes_B » Wed Sep 21, 2016 8:31 am

This can't compile, documentclass and the document-environment are missing. Possibly also math packages.
The smart way: Calm down and take a deep breath, read posts and provided links attentively, try to understand and ask if necessary.

juan21
Posts: 11
Joined: Thu Dec 03, 2015 12:20 am

Postby juan21 » Thu Sep 22, 2016 9:33 pm

good afternoon had already posted this earlier post Menten , but I miss some things . I am compiling a document and I latex document as shown in the attachment .¿me could help with equations ? The sintexix is as follows


  1. \documentclass[12pt,oneside,letterpaper]{report}
  2. \usepackage{amssymb,amsthm}
  3. \usepackage[spanish,english]{babel}
  4. \usepackage{amssymb,amsfonts}
  5. \usepackage{amsmath}
  6. \usepackage{amscd}
  7. \usepackage[letterpaper,left=35mm,right=23mm]{geometry}
  8. \usepackage{fancyhdr}
  9. \usepackage{fancyhdr,endnotes}
  10. \usepackage{multicol}
  11. \usepackage{cite}
  12. %\usepackage[sort&compress]{natbib}
  13. \usepackage{}
  14. %\usepackage[dvips]{graphicx}
  15.  
  16.  
  17. \pagestyle{fancy}
  18.  
  19. \usepackage{algorithm}
  20. %\usepackage{algorithmic}
  21. %\usepackage{epsf,graphicx}
  22. \usepackage{graphics,graphicx,psfrag}
  23. \usepackage[ansinew]{inputenc}
  24. \usepackage{float}
  25. \usepackage{subfigure}
  26. \floatplacement{figure}{ht}
  27. \usepackage{color}
  28. \usepackage{amssymb,amsthm}
  29. \usepackage[spanish,english]{babel}
  30. \usepackage{amssymb,amsfonts}
  31. \usepackage{amsmath}
  32. \usepackage{amscd}
  33. \usepackage[letterpaper,left=35mm,right=23mm]{geometry}
  34. \usepackage{fancyhdr}
  35. \usepackage{fancyhdr,endnotes}
  36. \usepackage{multicol}
  37. \usepackage{cite}
  38. %\usepackage[sort&compress]{natbib}
  39. \usepackage{}
  40. %\usepackage[dvips]{graphicx}
  41.  
  42.  
  43. \pagestyle{fancy}
  44.  
  45. \usepackage{algorithm}
  46. %\usepackage{algorithmic}
  47. %\usepackage{epsf,graphicx}
  48. \usepackage{graphics,graphicx,psfrag}
  49. \usepackage[ansinew]{inputenc}
  50. \usepackage{float}
  51. \usepackage{subfigure}
  52. \floatplacement{figure}{ht}
  53. \usepackage{color}
  54. \usepackage{amssymb,amsthm}
  55. \usepackage[spanish,english]{babel}
  56. \usepackage{amssymb,amsfonts}
  57. \usepackage{amsmath}
  58. \usepackage{amscd}
  59. \usepackage[letterpaper,left=35mm,right=23mm]{geometry}
  60. \usepackage{fancyhdr}
  61. \usepackage{fancyhdr,endnotes}
  62. \usepackage{multicol}
  63. \usepackage{cite}
  64. %\usepackage[sort&compress]{natbib}
  65. \usepackage{}
  66. %\usepackage[dvips]{graphicx}
  67.  
  68.  
  69. \pagestyle{fancy}
  70.  
  71. \usepackage{algorithm}
  72. %\usepackage{algorithmic}
  73. %\usepackage{epsf,graphicx}
  74. \usepackage{graphics,graphicx,psfrag}
  75. \usepackage[ansinew]{inputenc}
  76. \usepackage{float}
  77. \usepackage{subfigure}
  78. \floatplacement{figure}{ht}
  79. \usepackage{color}
  80. \begin{document}
  81. \begin{align*}
  82. \int_{a}^{b}|s_4(x)|\,dx &= -\frac{1}{24}\int_{a}^{\frac{a+b}{2}} (x-a)^3\left(x-\frac{a+2b}{3}\right)\,dx - \frac{1}{24}\int_{\frac{a+b}{2}}^{b} (x-b)^3\left(x-\frac{2a+b}{3}\right)\,dx\\
  83. &=-\frac{1}{24}\left[\int_{a}^{\frac{a+b}{2}}(x^3-3ax^2+3a^2x-a^3)\left(x-\frac{a+2b}{3}\right)\,dx\right.\\
  84. &\left.+\int_{\frac{a+b}{2}}^{b}(x^3-3bx^2+3b^2x-b^3)\left(x-\frac{2a+b}{3}\right)\,dx\right]\\
  85. &=-\frac{1}{24}\left[\int_{a}^{\frac{a+b}{2}}\left[x^4-3ax^3+3a^2x^2-a^3x-x^3\left(\frac{a+2b}{3}\right)\right.\right.\\
  86. &\left.+ax^2(a+2b)-a^2x(a+2b)+\frac{a^3}{3}(a+2b)\right]\,dx\\
  87. +\left.\int_{\frac{a+b}{2}}^{b}\left[x^4-3bx^3+3b^2x^2-b^3x - \frac{x^3}{3}(2a+b)+bx^2(2a+b)-b^2x(2a+b)+\frac{b^3}{3}(2a+b)\right]\,dx\right]\\
  88. &=-\frac{1}{24}\left[\frac{x^5}{5}-\frac{3}{4}ax^4+a^2x^3-\frac{a^3x^2}{2}-\frac{x^4}{12}(a+2b)+\frac{ax^3}{3}(a+2b)-\frac{a^2x^2}{2}\right.\\
  89. &\left.\left.+\frac{a^3}{3}(a+2b)x\right]\right|_a^{\frac{a+b}{2}}-\frac{1}{24}\left[\frac{x^5}{5}-\frac{3}{4}bx^4+b^2x^3-\frac{b^3x^2}{2}-\frac{x^4}{12}(2a+b)\right.\\
  90. &\left.\left.+\frac{bx^3}{3}(2a+b)-\frac{b^2x^2}{2}+\frac{b^3}{3}(2a+b)x\right]\right|_{\frac{a+b}{2}}^{b}\\
  91. &=-\frac{1}{24}\left[\frac{1}{5}\left(\frac{a+b}{2}\right)^5-\frac{3a}{4}\left(\frac{a+b}{2}\right)^4+a^2\left(\frac{a+b}{2}\right)^3-\frac{a^3}{2}\left(\frac{a+b}{2}\right)^2\right.\\
  92. &-\frac{1}{12}\left(\frac{a+b}{2}\right)^4(a+2b)+\frac{a}{3}\left(\frac{a+b}{2}\right)^3(a+2b)-\frac{a^2}{2}\left(\frac{a+b}{2}\right)^2(a+2b)\\
  93. &+\frac{a^3}{3}(a+2b)\left(\frac{a+b}{2}\right)-\frac{a^5}{5}+\frac{3}{4}a^5-a^5+\frac{a^5}{2}+\frac{a^4}{12}(a+2b)-\frac{a^4}{3}(a+2b)\\
  94. &+\frac{a^4}{2}(a+2b)-\frac{a^4}{3}(a+2b)\\
  95. &+\frac{b^5}{5}-\frac{3}{4}b^5+b^5-\frac{b^5}{2}^-\frac{b^4}{12}(2a+b)+\frac{b^4}{3}(2a+b)-\frac{b^4}{2}(2a+b)+\frac{b^4}{3}(2a+b)\\
  96. &-\frac{1}{5}\left(\frac{a+b}{2}\right)^5+\frac{3b}{4}\left(\frac{a+b}{2}\right)^4-b^2\left(\frac{a+b}{2}\right)^3+\frac{b^3}{2}\left(\frac{a+b}{2}\right)^2\\
  97. &\left.+\frac{1}{12}\left(\frac{a+b}{2}\right)^4(2a+b)-\frac{b}{3}\left(\frac{a+b}{2}\right)^3(2a+b)+\frac{b^2}{2}\left(\frac{a+b}{2}\right)^2(2a+b)-\frac{b^3}{3}(2a+b)\left(\frac{a+b}{2}\right)\right]\\
  98. &=-\frac{1}{24}\left[\frac{b^5-a^5}{20}+\frac{1}{12}(b^5-a^5+2ab^4-2ba^4)+2\left(\frac{a+b}{2}\right)^4(b-a)\right.\\
  99. &\left.+\frac{4}{3}(a^2-b^2)\left(\frac{a+b}{2}\right)^3+\left(\frac{a+b}{2}\right)^2[b^3-a^3+b^2a-a^2b]+\left(\frac{a+b}{2}\right)\left(\frac{a^3}{3}(a+2b)-\frac{b^3}{3}(2a+b)\right)\right]\\
  100. \end{align*}
  101.  
  102.  
  103. \end{document}
Attachments
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Johannes_B
Site Moderator
Posts: 4044
Joined: Thu Nov 01, 2012 4:08 pm

Postby Johannes_B » Fri Sep 23, 2016 8:48 am

You can use allowdisplaybreaks[1] to allow displaybreaks. The other thing is, your equations are just too long to fit the page.

  1. \documentclass[12pt,oneside,letterpaper]{report}
  2. \usepackage{amssymb,amsthm}
  3. \usepackage[spanish,english]{babel}
  4. \usepackage{amssymb,amsfonts}
  5. \usepackage{amsmath}
  6. \usepackage{amscd}
  7. \usepackage[letterpaper,left=35mm,right=23mm]{geometry}
  8. \usepackage{fancyhdr}
  9. \usepackage{fancyhdr,endnotes}
  10. \usepackage{multicol}
  11. \usepackage{cite}
  12. %\usepackage[sort&compress]{natbib}
  13. \usepackage{}
  14. %\usepackage[dvips]{graphicx}
  15.  
  16.  
  17. \pagestyle{fancy}
  18. \setlength{\headheight}{14.5pt}
  19.  
  20. \usepackage{algorithm}
  21. %\usepackage{algorithmic}
  22. %\usepackage{epsf,graphicx}
  23. \usepackage{graphics,graphicx,psfrag}
  24. \usepackage[ansinew]{inputenc}
  25. \usepackage{float}
  26. %\usepackage{subfigure}% Deprecated for a decade
  27. \floatplacement{figure}{ht}
  28. \usepackage{color}
  29. \usepackage{amssymb,amsthm}
  30. \usepackage[spanish,english]{babel}
  31. \usepackage{amssymb,amsfonts}
  32. \usepackage{amsmath}
  33. \usepackage{amscd}
  34. \usepackage[letterpaper,left=35mm,right=23mm]{geometry}
  35. \usepackage{fancyhdr}
  36. \usepackage{fancyhdr,endnotes}
  37. \usepackage{multicol}
  38. \usepackage{cite}
  39. %\usepackage[sort&compress]{natbib}
  40. %\usepackage[dvips]{graphicx}
  41.  
  42.  
  43. \pagestyle{fancy}
  44.  
  45. \usepackage{algorithm}
  46. %\usepackage{algorithmic}
  47. %\usepackage{epsf,graphicx}
  48. \usepackage{graphics,graphicx,psfrag}
  49. \usepackage[ansinew]{inputenc}
  50. \usepackage{float}
  51. \usepackage{subfigure}
  52. \floatplacement{figure}{ht}
  53. \usepackage{color}
  54. \usepackage{amssymb,amsthm}
  55. \usepackage[spanish,english]{babel}
  56. \usepackage{amssymb,amsfonts}
  57. \usepackage{amsmath}
  58. \usepackage{amscd}
  59. \usepackage[letterpaper,left=35mm,right=23mm]{geometry}
  60. \usepackage{fancyhdr}
  61. \usepackage{fancyhdr,endnotes}
  62. \usepackage{multicol}
  63. \usepackage{cite}
  64. %\usepackage[sort&compress]{natbib}
  65. \usepackage{}
  66. %\usepackage[dvips]{graphicx}
  67.  
  68.  
  69. \pagestyle{fancy}
  70.  
  71. \usepackage{algorithm}
  72. %\usepackage{algorithmic}
  73. %\usepackage{epsf,graphicx}
  74. \usepackage{graphics,graphicx,psfrag}
  75. \usepackage[ansinew]{inputenc}
  76. \usepackage{float}
  77. %\usepackage{subfigure}
  78. \floatplacement{figure}{ht}
  79. \usepackage{color}
  80. \begin{document}
  81. \allowdisplaybreaks[1]
  82. \begin{align*}
  83. \int_{a}^{b}|s_4(x)|\,dx &= -\frac{1}{24}\int_{a}^{\frac{a+b}{2}} (x-a)^3\left(x-\frac{a+2b}{3}\right)\,dx - \frac{1}{24}\int_{\frac{a+b}{2}}^{b} (x-b)^3\left(x-\frac{2a+b}{3}\right)\,dx\\
  84. &=-\frac{1}{24}\left[\int_{a}^{\frac{a+b}{2}}(x^3-3ax^2+3a^2x-a^3)\left(x-\frac{a+2b}{3}\right)\,dx\right.\\
  85. &\left.+\int_{\frac{a+b}{2}}^{b}(x^3-3bx^2+3b^2x-b^3)\left(x-\frac{2a+b}{3}\right)\,dx\right]\\
  86. &=-\frac{1}{24}\left[\int_{a}^{\frac{a+b}{2}}\left[x^4-3ax^3+3a^2x^2-a^3x-x^3\left(\frac{a+2b}{3}\right)\right.\right.\\
  87. &\left.+ax^2(a+2b)-a^2x(a+2b)+\frac{a^3}{3}(a+2b)\right]\,dx\\
  88. &+\left.\int_{\frac{a+b}{2}}^{b}\left[x^4-3bx^3+3b^2x^2-b^3x - \frac{x^3}{3}(2a+b)+bx^2(2a+b)-b^2x(2a+b)+\frac{b^3}{3}(2a+b)\right]\,dx\right]\\
  89. &=-\frac{1}{24}\left[\frac{x^5}{5}-\frac{3}{4}ax^4+a^2x^3-\frac{a^3x^2}{2}-\frac{x^4}{12}(a+2b)+\frac{ax^3}{3}(a+2b)-\frac{a^2x^2}{2}\right.\\
  90. &\left.\left.+\frac{a^3}{3}(a+2b)x\right]\right|_a^{\frac{a+b}{2}}-\frac{1}{24}\left[\frac{x^5}{5}-\frac{3}{4}bx^4+b^2x^3-\frac{b^3x^2}{2}-\frac{x^4}{12}(2a+b)\right.\\
  91. &\left.\left.+\frac{bx^3}{3}(2a+b)-\frac{b^2x^2}{2}+\frac{b^3}{3}(2a+b)x\right]\right|_{\frac{a+b}{2}}^{b}\\
  92. &=-\frac{1}{24}\left[\frac{1}{5}\left(\frac{a+b}{2}\right)^5-\frac{3a}{4}\left(\frac{a+b}{2}\right)^4+a^2\left(\frac{a+b}{2}\right)^3-\frac{a^3}{2}\left(\frac{a+b}{2}\right)^2\right.\\
  93. &-\frac{1}{12}\left(\frac{a+b}{2}\right)^4(a+2b)+\frac{a}{3}\left(\frac{a+b}{2}\right)^3(a+2b)-\frac{a^2}{2}\left(\frac{a+b}{2}\right)^2(a+2b)\\
  94. &+\frac{a^3}{3}(a+2b)\left(\frac{a+b}{2}\right)-\frac{a^5}{5}+\frac{3}{4}a^5-a^5+\frac{a^5}{2}+\frac{a^4}{12}(a+2b)-\frac{a^4}{3}(a+2b)\\
  95. &+\frac{a^4}{2}(a+2b)-\frac{a^4}{3}(a+2b)\\
  96. &+\frac{b^5}{5}-\frac{3}{4}b^5+b^5-\frac{b^5}{2}^-\frac{b^4}{12}(2a+b)+\frac{b^4}{3}(2a+b)-\frac{b^4}{2}(2a+b)+\frac{b^4}{3}(2a+b)\\
  97. &-\frac{1}{5}\left(\frac{a+b}{2}\right)^5+\frac{3b}{4}\left(\frac{a+b}{2}\right)^4-b^2\left(\frac{a+b}{2}\right)^3+\frac{b^3}{2}\left(\frac{a+b}{2}\right)^2\\
  98. &\left.+\frac{1}{12}\left(\frac{a+b}{2}\right)^4(2a+b)-\frac{b}{3}\left(\frac{a+b}{2}\right)^3(2a+b)+\frac{b^2}{2}\left(\frac{a+b}{2}\right)^2(2a+b)-\frac{b^3}{3}(2a+b)\left(\frac{a+b}{2}\right)\right]\\
  99. &=-\frac{1}{24}\left[\frac{b^5-a^5}{20}+\frac{1}{12}(b^5-a^5+2ab^4-2ba^4)+2\left(\frac{a+b}{2}\right)^4(b-a)\right.\\
  100. &\left.+\frac{4}{3}(a^2-b^2)\left(\frac{a+b}{2}\right)^3+\left(\frac{a+b}{2}\right)^2[b^3-a^3+b^2a-a^2b]+\left(\frac{a+b}{2}\right)\left(\frac{a^3}{3}(a+2b)-\frac{b^3}{3}(2a+b)\right)\right]\\
  101. \end{align*}
  102.  
  103.  
  104. \end{document}
  105.  
  106.  
  107.  
  108.  
  109.  
  110.  
  111.  
  112.  
  113.  
  114.  
  115.  
  116.  
  117.  
  118.  
  119.  
  120.  
  121. \documentclass[]{article}
  122. \usepackage{mathtools}
  123. \allowdisplaybreaks[1]
  124. \begin{document}
  125. % \item[3c] Si $p=\infty$, entonces $q=1$ y se tiene lo siguiente
  126. \begin{align*}
  127. \int_{a}^{b}|s_4(x)|\,dx &= -\frac{1}{24}\int_{a}^{\frac{a+b}{2}} (x-a)^3\left(x-\frac{a+2b}{3}\right)\,dx - \frac{1}{24}\int_{\frac{a+b}{2}}^{b} (x-b)^3\left(x-\frac{2a+b}{3}\right)\,dx\\
  128. &=-\frac{1}{24}\left[\int_{a}^{\frac{a+b}{2}}(x^3-3ax^2+3a^2x-a^3)\left(x-\frac{a+2b}{3}\right)\,dx\right.\\
  129. &\left.+\int_{\frac{a+b}{2}}^{b}(x^3-3bx^2+3b^2x-b^3)\left(x-\frac{2a+b}{3}\right)\,dx\right]\\
  130. &=-\frac{1}{24}\left[\int_{a}^{\frac{a+b}{2}}\left[x^4-3ax^3+3a^2x^2-a^3x-x^3\left(\frac{a+2b}{3}\right)\right.\right.\\
  131. &\left.+ax^2(a+2b)-a^2x(a+2b)+\frac{a^3}{3}(a+2b)\right]\,dx\\
  132. &+\left.\int_{\frac{a+b}{2}}^{b}\left[x^4-3bx^3+3b^2x^2-b^3x - \frac{x^3}{3}(2a+b)+bx^2(2a+b)-b^2x(2a+b)+\frac{b^3}{3}(2a+b)\right]\,dx\right]\\
  133. &=-\frac{1}{24}\left[\frac{x^5}{5}-\frac{3}{4}ax^4+a^2x^3-\frac{a^3x^2}{2}-\frac{x^4}{12}(a+2b)+\frac{ax^3}{3}(a+2b)-\frac{a^2x^2}{2}\right.\\
  134. &\left.\left.+\frac{a^3}{3}(a+2b)x\right]\right|_a^{\frac{a+b}{2}}-\frac{1}{24}\left[\frac{x^5}{5}-\frac{3}{4}bx^4+b^2x^3-\frac{b^3x^2}{2}-\frac{x^4}{12}(2a+b)\right.\\
  135. &\left.\left.+\frac{bx^3}{3}(2a+b)-\frac{b^2x^2}{2}+\frac{b^3}{3}(2a+b)x\right]\right|_{\frac{a+b}{2}}^{b}\\
  136. &=-\frac{1}{24}\left[\frac{1}{5}\left(\frac{a+b}{2}\right)^5-\frac{3a}{4}\left(\frac{a+b}{2}\right)^4+a^2\left(\frac{a+b}{2}\right)^3-\frac{a^3}{2}\left(\frac{a+b}{2}\right)^2\right.\\
  137. &-\frac{1}{12}\left(\frac{a+b}{2}\right)^4(a+2b)+\frac{a}{3}\left(\frac{a+b}{2}\right)^3(a+2b)-\frac{a^2}{2}\left(\frac{a+b}{2}\right)^2(a+2b)\\
  138. &+\frac{a^3}{3}(a+2b)\left(\frac{a+b}{2}\right)-\frac{a^5}{5}+\frac{3}{4}a^5-a^5+\frac{a^5}{2}+\frac{a^4}{12}(a+2b)-\frac{a^4}{3}(a+2b)\\
  139. &+\frac{a^4}{2}(a+2b)-\frac{a^4}{3}(a+2b)\\
  140. &+\frac{b^5}{5}-\frac{3}{4}b^5+b^5-\frac{b^5}{2}^-\frac{b^4}{12}(2a+b)+\frac{b^4}{3}(2a+b)-\frac{b^4}{2}(2a+b)+\frac{b^4}{3}(2a+b)\\
  141. &-\frac{1}{5}\left(\frac{a+b}{2}\right)^5+\frac{3b}{4}\left(\frac{a+b}{2}\right)^4-b^2\left(\frac{a+b}{2}\right)^3+\frac{b^3}{2}\left(\frac{a+b}{2}\right)^2\\
  142. &\left.+\frac{1}{12}\left(\frac{a+b}{2}\right)^4(2a+b)-\frac{b}{3}\left(\frac{a+b}{2}\right)^3(2a+b)+\frac{b^2}{2}\left(\frac{a+b}{2}\right)^2(2a+b)-\frac{b^3}{3}(2a+b)\left(\frac{a+b}{2}\right)\right]\\
  143. &=-\frac{1}{24}\left[\frac{b^5-a^5}{20}+\frac{1}{12}(b^5-a^5+2ab^4-2ba^4)+2\left(\frac{a+b}{2}\right)^4(b-a)\right.\\
  144. &\left.+\frac{4}{3}(a^2-b^2)\left(\frac{a+b}{2}\right)^3+\left(\frac{a+b}{2}\right)^2[b^3-a^3+b^2a-a^2b]+\left(\frac{a+b}{2}\right)\left(\frac{a^3}{3}(a+2b)-\frac{b^3}{3}(2a+b)\right)\right]\\
  145. \end{align*}
  146. \end{document}
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