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  1. command: Integrate[Tan[x]/Sqrt[1 + Sec[x]^3],x]
  2. Version 11.2 leaf size: 37353
  3. Version 9 leaf size: 296
  4. Ratio of version 11.2 leaf size to verion 9: 126
  5.  
  6. Integrate[Tan[x]/Sqrt[1+Sec[x]^3],x]
  7. (*output too large to post*)
  8.  
  9. Command used: Integrate[Tan[x]/Sqrt[1 + Sec[x]^3],x]
  10. Version 11.2 leaf size: 37353.
  11. Version 9 leaf size: 296.
  12. Ratio of version 11.2 leaf size to verion 9 leaf size: 126
  13.  
  14. Command used: Integrate[ArcTan[Sqrt[-1 + Sec[x]]]*Sin[x],x]
  15. Version 11.2 leaf size: 6968.
  16. Version 9 leaf size: 1043.
  17. Ratio of version 11.2 leaf size to verion 9 leaf size: 7
  18.  
  19. Command used: Integrate[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]
  20. Version 11.2 leaf size: 269.
  21. Version 9 leaf size: 36.
  22. Ratio of version 11.2 leaf size to verion 9 leaf size: 7
  23.  
  24. Command used: Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]
  25. Version 11.2 leaf size: 266.
  26. Version 9 leaf size: 40.
  27. Ratio of version 11.2 leaf size to verion 9 leaf size: 7
  28.  
  29. Command used: Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]
  30. Version 11.2 leaf size: 266.
  31. Version 9 leaf size: 40.
  32. Ratio of version 11.2 leaf size to verion 9 leaf size: 7
  33.  
  34.  
  35. Command used: Integrate[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]
  36. Version 11.2 leaf size: 269.
  37. Version 9 leaf size: 36.
  38. Ratio of version 11.2 leaf size to verion 9 leaf size: 7
  39.  
  40.  
  41. Command used: Integrate[(1 - x^2)/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]
  42. Version 11.2 leaf size: 567.
  43. Version 9 leaf size: 94.
  44. Ratio of version 11.2 leaf size to verion 9 leaf size: 6
  45.  
  46. Command used: Integrate[(Sqrt[Cos[x]*Sin[x]^3] - 2*Sin[2*x])/(-Sqrt[Cos[x]^3*Sin[x]] + Sqrt[Tan[x]]),x]
  47. Version 11.2 leaf size: 68457.
  48. Version 9 leaf size: 2051.
  49. Ratio of version 11.2 leaf size to verion 9 leaf size: 33
  50.  
  51. Command used: Integrate[(Cosh[x]*(-Cosh[2*x] + Tanh[x]))/(Sqrt[Sinh[2*x]]*(Sinh[x]^2 + Sinh[2*x])),x]
  52. Version 11.2 leaf size: 5173.
  53. Version 9 leaf size: 490.
  54. Ratio of version 11.2 leaf size to verion 9 leaf size: 11
  55.  
  56. Command used: Integrate[Sqrt[1 + p*x^2 - x^4]/(1 + x^4),x]
  57. Version 11.2 leaf size: 10200.
  58. Version 9 leaf size: 322.
  59. Ratio of version 11.2 leaf size to verion 9 leaf size: 32
  60.  
  61. Command used: Integrate[Sqrt[e + f*x^2]/((a + b*x^2)*(c + d*x^2)^(7/2)),x]
  62. Version 11.2 leaf size: 12924.
  63. Version 9 leaf size: 577.
  64. Ratio of version 11.2 leaf size to verion 9 leaf size: 22
  65.  
  66. Command used: Integrate[(Sqrt[c + d*x^2]*(e + f*x^2)^(3/2))/(a + b*x^2),x]
  67. Version 11.2 leaf size: 11662.
  68. Version 9 leaf size: 739.
  69. Ratio of version 11.2 leaf size to verion 9 leaf size: 16
  70.  
  71. Command used: Integrate[(Sqrt[2 + d*x^2]*Sqrt[3 + f*x^2])/(a + b*x^2),x]
  72. Version 11.2 leaf size: 7470.
  73. Version 9 leaf size: 134.
  74. Ratio of version 11.2 leaf size to verion 9 leaf size: 56
  75.  
  76. Command used: Integrate[(Sqrt[c + d*x^2]*Sqrt[e + f*x^2])/(a + b*x^2)^2,x]
  77. Version 11.2 leaf size: 3879.
  78. Version 9 leaf size: 401.
  79. Ratio of version 11.2 leaf size to verion 9 leaf size: 10
  80.  
  81. Command used: Integrate[1/((a + b*x^2)^2*Sqrt[c - d*x^2]*Sqrt[e + f*x^2]),x]
  82. Version 11.2 leaf size: 7216.
  83. Version 9 leaf size: 773.
  84. Ratio of version 11.2 leaf size to verion 9 leaf size: 9
  85.  
  86. Command used: Integrate[((e*x)^m*(a + b*x^n)^2*(A + B*x^n))/(c + d*x^n)^3,x]
  87. Version 11.2 leaf size: 1924.
  88. Version 9 leaf size: 345.
  89. Ratio of version 11.2 leaf size to verion 9 leaf size: 6
  90.  
  91. Command used: Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^(3/2),x]
  92. Version 11.2 leaf size: 5706.
  93. Version 9 leaf size: 1045.
  94. Ratio of version 11.2 leaf size to verion 9 leaf size: 5
  95.  
  96. Command used: Integrate[1/(x*(1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]
  97. Version 11.2 leaf size: 2539.
  98. Version 9 leaf size: 98.
  99. Ratio of version 11.2 leaf size to verion 9 leaf size: 26
  100.  
  101. Command used: Integrate[Sqrt[2 + 3*x^2 + x^4]/(7 + 5*x^2),x]
  102. Version 11.2 leaf size: 520.
  103. Version 9 leaf size: 90.
  104. Ratio of version 11.2 leaf size to verion 9 leaf size: 6
  105.  
  106. Command used: Integrate[1/((d + e*x^2)^2*Sqrt[a + b*x^2 - c*x^4]),x]
  107. Version 11.2 leaf size: 10996.
  108. Version 9 leaf size: 1341.
  109. Ratio of version 11.2 leaf size to verion 9 leaf size: 8
  110.  
  111. Command used: Integrate[Sqrt[a + b*x^2 + c*x^4]/(x^3*(d + e*x^2)),x]
  112. Version 11.2 leaf size: 10848.
  113. Version 9 leaf size: 244.
  114. Ratio of version 11.2 leaf size to verion 9 leaf size: 44
  115.  
  116. Command used: Integrate[Sqrt[1 + 2*x^2 + 2*x^4]/(x^4*(3 + 2*x^2)),x]
  117. Version 11.2 leaf size: 1546.
  118. Version 9 leaf size: 154.
  119. Ratio of version 11.2 leaf size to verion 9 leaf size: 10
  120.  
  121. Command used: Integrate[Sqrt[1 + 2*x^2 + 2*x^4]/(x^6*(3 + 2*x^2)),x]
  122. Version 11.2 leaf size: 1650.
  123. Version 9 leaf size: 224.
  124. Ratio of version 11.2 leaf size to verion 9 leaf size: 7
  125.  
  126. Command used: Integrate[(1 + 2*x^2 + 2*x^4)^(3/2)/(x^2*(3 - 2*x^2)),x]
  127. Version 11.2 leaf size: 1609.
  128. Version 9 leaf size: 213.
  129. Ratio of version 11.2 leaf size to verion 9 leaf size: 8
  130.  
  131. Command used: Integrate[1/(x*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]
  132. Version 11.2 leaf size: 3622.
  133. Version 9 leaf size: 174.
  134. Ratio of version 11.2 leaf size to verion 9 leaf size: 21
  135.  
  136. Command used: Integrate[x^2/((3 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4]),x]
  137. Version 11.2 leaf size: 1518.
  138. Version 9 leaf size: 99.
  139. Ratio of version 11.2 leaf size to verion 9 leaf size: 15
  140.  
  141. Command used: Integrate[x^2/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]
  142. Version 11.2 leaf size: 1636.
  143. Version 9 leaf size: 199.
  144. Ratio of version 11.2 leaf size to verion 9 leaf size: 8
  145.  
  146. Command used: Integrate[1/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]
  147. Version 11.2 leaf size: 1636.
  148. Version 9 leaf size: 199.
  149. Ratio of version 11.2 leaf size to verion 9 leaf size: 8
  150.  
  151. Command used: Integrate[Sqrt[1 - x^2]/(x^3*(a + b*x^2 + c*x^4)),x]
  152. Version 11.2 leaf size: 6953.
  153. Version 9 leaf size: 298.
  154. Ratio of version 11.2 leaf size to verion 9 leaf size: 23
  155.  
  156. Command used: Integrate[(d + e*x^n)*(a + b*x^n + c*x^(2*n))^(3/2),x]
  157. Version 11.2 leaf size: 8312.
  158. Version 9 leaf size: 690.
  159. Ratio of version 11.2 leaf size to verion 9 leaf size: 12
  160.  
  161. Command used: Integrate[(a - c*x^4)/(Sqrt[a + b*x^2 + c*x^4]*(a*d + a*e*x^2 + c*d*x^4)),x]
  162. Version 11.2 leaf size: 26953.
  163. Version 9 leaf size: 419.
  164. Ratio of version 11.2 leaf size to verion 9 leaf size: 64
  165.  
  166. Command used: Integrate[(a - c*x^4)/((a*e + c*d*x^2)*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]
  167. Version 11.2 leaf size: 15438.
  168. Version 9 leaf size: 383.
  169. Ratio of version 11.2 leaf size to verion 9 leaf size: 40
  170.  
  171. Command used: Integrate[Cos[c + d*x]^6*Sqrt[a + a*Sin[c + d*x]],x]
  172. Version 11.2 leaf size: 995.
  173. Version 9 leaf size: 99.
  174. Ratio of version 11.2 leaf size to verion 9 leaf size: 10
  175.  
  176. Command used: Integrate[1/((a + b*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^(3/2)),x]
  177. Version 11.2 leaf size: 6518.
  178. Version 9 leaf size: 1057.
  179. Ratio of version 11.2 leaf size to verion 9 leaf size: 6
  180.  
  181. Command used: Integrate[1/((a + b*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^(5/2)),x]
  182. Version 11.2 leaf size: 6780.
  183. Version 9 leaf size: 1319.
  184. Ratio of version 11.2 leaf size to verion 9 leaf size: 5
  185.  
  186. Command used: Integrate[(c + d*Sin[e + f*x])^(5/2)/(a + b*Sin[e + f*x])^3,x]
  187. Version 11.2 leaf size: 6610.
  188. Version 9 leaf size: 1149.
  189. Ratio of version 11.2 leaf size to verion 9 leaf size: 6
  190.  
  191. Command used: Integrate[Sqrt[c + d*Sin[e + f*x]]/(a + b*Sin[e + f*x])^3,x]
  192. Version 11.2 leaf size: 6499.
  193. Version 9 leaf size: 1038.
  194. Ratio of version 11.2 leaf size to verion 9 leaf size: 6
  195.  
  196. Command used: Integrate[1/((a + b*Sin[e + f*x])^3*(c + d*Sin[e + f*x])^(3/2)),x]
  197. Version 11.2 leaf size: 6779.
  198. Version 9 leaf size: 1318.
  199. Ratio of version 11.2 leaf size to verion 9 leaf size: 5
  200.  
  201. Command used: Integrate[Cos[c + d*x]*Sin[c + d*x]^n*(a + a*Sin[c + d*x])^4,x]
  202. Version 11.2 leaf size: 457.
  203. Version 9 leaf size: 80.
  204. Ratio of version 11.2 leaf size to verion 9 leaf size: 6
  205.  
  206. Command used: Integrate[Sqrt[g*Sin[e + f*x]]/(Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])),x]
  207. Version 11.2 leaf size: 58053.
  208. Version 9 leaf size: 232.
  209. Ratio of version 11.2 leaf size to verion 9 leaf size: 250
  210.  
  211. Command used: Integrate[1/(Sqrt[g*Sin[e + f*x]]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])),x]
  212. Version 11.2 leaf size: 58056.
  213. Version 9 leaf size: 234.
  214. Ratio of version 11.2 leaf size to verion 9 leaf size: 248
  215.  
  216. Command used: Integrate[1/(Sqrt[g*Sin[e + f*x]]*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])),x]
  217. Version 11.2 leaf size: 663005.
  218. Version 9 leaf size: 99997.
  219. Ratio of version 11.2 leaf size to verion 9 leaf size: 7
  220.  
  221. Command used: Integrate[Sqrt[3 + 4*Cos[c + d*x]]*Sec[c + d*x]^2,x]
  222. Version 11.2 leaf size: 987.
  223. Version 9 leaf size: 157.
  224. Ratio of version 11.2 leaf size to verion 9 leaf size: 6
  225.  
  226. Command used: Integrate[Cos[c + d*x]^(3/2)/(a + b*Cos[c + d*x]),x]
  227. Version 11.2 leaf size: 642.
  228. Version 9 leaf size: 84.
  229. Ratio of version 11.2 leaf size to verion 9 leaf size: 8
  230.  
  231. Command used: Integrate[Cos[c + d*x]^(3/2)/(a + b*Cos[c + d*x])^3,x]
  232. Version 11.2 leaf size: 1390.
  233. Version 9 leaf size: 276.
  234. Ratio of version 11.2 leaf size to verion 9 leaf size: 5
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