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Text File  |  1996-05-08  |  4.6 KB  |  121 lines  |  [TEXT/OMEG]
  1. (*^
  2.  
  3. ::[paletteColors = 128; 
  4.     fontset = title, "New York", 24, L3, center, bold, nohscroll;
  5.     fontset = subtitle, "New York", 18, L2, center, bold, nohscroll;
  6.     fontset = subsubtitle, "New York", 14, L2, center, bold, nohscroll;
  7.     fontset = section, "New York", 14, L2, bold, nohscroll, grayBox;
  8.     fontset = subsection, "New York", 12, L2, bold, nohscroll, blackBox;
  9.     fontset = subsubsection, "New York", 10, L2, bold, nohscroll, whiteBox;
  10.     fontset = text, "New York", 12, L2, nohscroll;
  11.     fontset = smalltext, "New York", 10, L2, nohscroll;
  12.     fontset = input, "Courier", 12, L2, bold, nowordwrap;
  13.     fontset = output, "Courier", 12, L2, nowordwrap;
  14.     fontset = message, "Courier", 12, L2, R65535, nowordwrap;
  15.     fontset = print, "Courier", 12, L2, nowordwrap;
  16.     fontset = info, "Courier", 12, L2, nowordwrap;
  17.     fontset = postscript, "Courier", 12, L2, nowordwrap;
  18.     fontset = name, "Geneva", 10, L2, italic, B65535, nowordwrap, nohscroll;
  19.     fontset = header, "Times", 10, L2;
  20.     fontset = footer, "Times", 12, L2, center;
  21.     fontset = help, "Geneva", 10, L2, nohscroll;
  22.     fontset = clipboard, "New York", 12, L2;
  23.     fontset = completions, "New York", 12, L2, nowordwrap;
  24.     fontset = network, "Courier", 10, L2, nowordwrap;
  25.     fontset = graphlabel, "Courier", 12, L2, nowordwrap;
  26.     fontset = special1, "New York", 12, L2, nowordwrap;
  27.     fontset = special2, "New York", 12, L2, center, nowordwrap;
  28.     fontset = special3, "New York", 12, L2, right, nowordwrap;
  29.     fontset = special4, "New York", 12, L2, nowordwrap;
  30.     fontset = special5, "New York", 12, L2, nowordwrap;]
  31. :[font = input; startGroup; ]
  32. Integrate[Sqrt[ t^2 + b t + c], {t, 0, x}]
  33. :[font = output; inactive; output; endGroup; ]
  34. (b^3*c^(1/2))/(16*(-b^2/4 + c)) - (b*c^(3/2))/(4*(-b^2/4 + c)) - 
  35.   (b^2*(b/2 + x)*(c + b*x + x^2)^(1/2))/(8*(-b^2/4 + c)) + 
  36.   (c*(b/2 + x)*(c + b*x + x^2)^(1/2))/(2*(-b^2/4 + c)) + 
  37.   (b^2*Log[b/2 + c^(1/2)])/8 - (c*Log[b/2 + c^(1/2)])/2 - 
  38.   (b^2*Log[b/2 + x + (c + b*x + x^2)^(1/2)])/8 + 
  39.   (c*Log[b/2 + x + (c + b*x + x^2)^(1/2)])/2
  40. ;[o]
  41.                               2  b                      2
  42.   3                 3/2      b  (- + x) Sqrt[c + b x + x ]
  43.  b  Sqrt[c]      b c             2
  44. ------------ - ----------- - ----------------------------- + 
  45.       2             2                      2
  46.     -b            -b                     -b
  47. 16 (--- + c)   4 (--- + c)            8 (--- + c)
  48.      4             4                      4
  49.  
  50.  
  51.      b                      2     2     b
  52.   c (- + x) Sqrt[c + b x + x ]   b  Log[- + Sqrt[c]]
  53.      2                                  2
  54.   ---------------------------- + ------------------- - 
  55.                2                          8
  56.              -b
  57.           2 (--- + c)
  58.               4
  59.  
  60.  
  61.         b               2     b                       2
  62.   c Log[- + Sqrt[c]]   b  Log[- + x + Sqrt[c + b x + x ]]
  63.         2                     2
  64.   ------------------ - ---------------------------------- + 
  65.           2                            8
  66.  
  67.  
  68.         b                       2
  69.   c Log[- + x + Sqrt[c + b x + x ]]
  70.         2
  71.   ---------------------------------
  72.                   2
  73.                   
  74.                   
  75. :[font = input; startGroup; ]
  76. Simplify[%]
  77. :[font = output; inactive; output; endGroup; ]
  78. -(2*b*c^(1/2) - 2*b*(c + b*x + x^2)^(1/2) - 
  79.      4*x*(c + b*x + x^2)^(1/2) - b^2*Log[b/2 + c^(1/2)] + 
  80.      4*c*Log[b/2 + c^(1/2)] + 
  81.      b^2*Log[b/2 + x + (c + b*x + x^2)^(1/2)] - 
  82.      4*c*Log[b/2 + x + (c + b*x + x^2)^(1/2)])/8
  83. ;[o]
  84.                                     2                        2
  85. -(2 b Sqrt[c] - 2 b Sqrt[c + b x + x ] - 4 x Sqrt[c + b x + x ] - 
  86.  
  87.       2     b                      b
  88.      b  Log[- + Sqrt[c]] + 4 c Log[- + Sqrt[c]] + 
  89.             2                      2
  90.  
  91.       2     b                       2
  92.      b  Log[- + x + Sqrt[c + b x + x ]] - 
  93.             2
  94.  
  95.              b                       2
  96.      4 c Log[- + x + Sqrt[c + b x + x ]]) / 8
  97.              2
  98. :[font = input; startGroup; ]
  99. Simplify[%]
  100. :[font = output; inactive; output; endGroup; ]
  101. -(2*b*c^(1/2) - 2*b*(c + b*x + x^2)^(1/2) - 
  102.      4*x*(c + b*x + x^2)^(1/2) - b^2*Log[b/2 + c^(1/2)] + 
  103.      4*c*Log[b/2 + c^(1/2)] + 
  104.      b^2*Log[b/2 + x + (c + b*x + x^2)^(1/2)] - 
  105.      4*c*Log[b/2 + x + (c + b*x + x^2)^(1/2)])/8
  106. ;[o]
  107.                                     2                        2
  108. -(2 b Sqrt[c] - 2 b Sqrt[c + b x + x ] - 4 x Sqrt[c + b x + x ] - 
  109.  
  110.       2     b                      b
  111.      b  Log[- + Sqrt[c]] + 4 c Log[- + Sqrt[c]] + 
  112.             2                      2
  113.  
  114.       2     b                       2
  115.      b  Log[- + x + Sqrt[c + b x + x ]] - 
  116.             2
  117.  
  118.              b                       2
  119.      4 c Log[- + x + Sqrt[c + b x + x ]]) / 8
  120.              2
  121. ^*)