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  1. The closed form of the main integral
  2.  
  3. 1/48 (73 \[Pi]^3 -
  4. I \[Pi]^2 (Log[1/2 - I/2] - Log[1/2 + I/2] - 14 Log[1 - I] +
  5. 14 Log[1 + I] - 168 Log[2] + Log[2 - 2 I] - Log[2 + 2 I] -
  6. 96 Log[2/((1 - I) + Sqrt[2])] -
  7. 24 Log[(2 Sqrt[2] Sin[\[Pi]/8])/(
  8. 3 Cos[\[Pi]/8] + Sin[\[Pi]/8])] + 48 Log[-I + Tan[\[Pi]/8]] +
  9. 48 Log[I + Tan[\[Pi]/8]] +
  10. 96 Log[1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])]) +
  11. 12 \[Pi] (6 Log[1 - I]^2 + 6 Log[1 + I]^2 + 7 Log[2]^2 +
  12. Log[1 + I] Log[16] + Log[1 - I] (-8 Log[1 + I] + Log[16]) +
  13. 6 Log[1 + (-1)^(1/4)]^2 + 6 Log[1 + (1 - I)/Sqrt[2]]^2 +
  14. 2 Log[2] Log[(2 Sqrt[2] Sin[\[Pi]/8])/(
  15. 3 Cos[\[Pi]/8] + Sin[\[Pi]/8])] +
  16. 8 Log[2/((1 - I) + Sqrt[2])] Log[1 - Tan[\[Pi]/8]] +
  17. 8 Log[2/((1 - I) + Sqrt[2])] Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] +
  18. 16 Log[1/(1 + (-1)^(1/4))] Log[1/2 (1 + I Tan[\[Pi]/8])] -
  19. 16 Log[2/((1 - I) + Sqrt[2])] Log[1/2 (1 + I Tan[\[Pi]/8])] -
  20. 16 Log[1/(1 + (-1)^(1/4))] Log[1 + I Tan[\[Pi]/8]] +
  21. 8 Log[2/((1 - I) + Sqrt[2])] Log[Tan[\[Pi]/8]] -
  22. 2 Log[4] Log[-I + Tan[\[Pi]/8]] -
  23. 16 Log[1/(1 + (-1)^(1/4))] Log[-I + Tan[\[Pi]/8]] +
  24. 4 Log[-I + Tan[\[Pi]/8]]^2 +
  25. 16 Log[1/(1 + (-1)^(1/4))] Log[(1 + I) (-I + Tan[\[Pi]/8])] -
  26. 2 Log[4] Log[I + Tan[\[Pi]/8]] -
  27. 16 Log[2/((1 - I) + Sqrt[2])] Log[I + Tan[\[Pi]/8]] +
  28. 16 Log[1/2 (1 + I Tan[\[Pi]/8])] Log[I + Tan[\[Pi]/8]] +
  29. 4 Log[I + Tan[\[Pi]/8]]^2 +
  30. 16 Log[1/
  31. 2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[(1/2 - I/2) (1 +
  32. Tan[\[Pi]/8])] -
  33. 16 Log[(1 - I)/(
  34. 1 + (-1)^(1/4))] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  35. 16 Log[2/((1 - I) + Sqrt[
  36. 2])] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  37. 16 Log[(1 - I)/(1 + (-1)^(1/4))] Log[1 + Tan[\[Pi]/8]] -
  38. 8 Log[2/((1 - I) + Sqrt[2])] Log[1 + Tan[\[Pi]/8]] -
  39. 16 Log[1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[
  40. 1 + Tan[\[Pi]/8]] -
  41. 8 Log[1 - Tan[\[Pi]/8]] Log[
  42. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] -
  43. 8 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[
  44. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] -
  45. 8 Log[Tan[\[Pi]/8]] Log[1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] +
  46. 16 Log[-I + Tan[\[Pi]/8]] Log[
  47. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] -
  48. 16 Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])] Log[
  49. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] +
  50. 8 Log[1 + Tan[\[Pi]/8]] Log[
  51. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])]) +
  52. 48 (Catalan (Log[1/2 - I/2] + Log[1/2 + I/2] + Log[2 - 2 I] +
  53. Log[2 + 2 I]) +
  54. I (Log[1/2 + I/2] Log[1 - I]^2 - Log[1/2 - I/2] Log[1 + I]^2 +
  55. 4 Log[2] Log[-(1/(-1 + (-1)^(1/4)))] Log[1/(
  56. 1 + (-1)^(1/4))] - 2 Log[2] Log[1/(1 + (-1)^(1/4))]^2 -
  57. 2 Log[1/(1 + (-1)^(1/4))] Log[1 + (-1)^(1/4)]^2 +
  58. 2 Log[(1/2 + I/2) (1 + (-1)^(1/4))] Log[
  59. 1 + (1 - I)/Sqrt[2]]^2 -
  60. 2 Log[(1 + I)/((1 + I) - Sqrt[2])]^2 Log[-((
  61. 1 - I)/((-1 + I) + Sqrt[2]))] +
  62. 2 Log[(1 + I)/((1 + I) - Sqrt[2])] Log[-((
  63. 1 - I)/((-1 + I) + Sqrt[2]))]^2 -
  64. 2 Log[-((1 - I)/((-1 + I) + Sqrt[2]))]^2 Log[
  65. 2/((1 - I) + Sqrt[2])] -
  66. 2 Log[(2 + 2 I)/((1 + I) - Sqrt[2])] Log[((1 + I) + Sqrt[
  67. 2])/((-1 - I) + Sqrt[2])]^2 +
  68. 2 Log[4/((1 - I) + Sqrt[2])] Log[((1 + I) + Sqrt[
  69. 2])/((-1 - I) + Sqrt[2])]^2 +
  70. 2 Log[2/(1 + (-1)^(1/4))] Log[1/2 (1 - I Cot[\[Pi]/8])]^2 +
  71. 2 Log[-(1/(-1 + (-1)^(1/4)))]^2 Log[1 - I Cot[\[Pi]/8]] -
  72. 2 Log[1/2 (1 - I Cot[\[Pi]/8])]^2 Log[1 + I Cot[\[Pi]/8]] -
  73. 2 Log[-(1/(-1 + (-1)^(1/4)))]^2 Log[-2 I Cot[\[Pi]/8]] +
  74. 2 Log[1/2 (1 - I Cot[\[Pi]/8])]^2 Log[2 I Cot[\[Pi]/8]] -
  75. 2 Log[1 + (-1)^(1/4)]^2 Log[(1 + I)/(I - Tan[\[Pi]/8])] -
  76. 2 Log[((1 + I) + Sqrt[2])/((-1 - I) + Sqrt[2])]^2 Log[
  77. 1 - Tan[\[Pi]/8]] -
  78. 2 Log[2/((1 - I) + Sqrt[2])] Log[1 - Tan[\[Pi]/8]] Log[
  79. Cot[\[Pi]/8] - Tan[\[Pi]/8]] +
  80. 2 Log[1 + (1 - I)/Sqrt[2]]^2 Log[1/2 (1 + I Tan[\[Pi]/8])] +
  81. 4 Log[1/(1 + (-1)^(1/4))] Log[(
  82. 1 + I)/((1 + I) - Sqrt[2])] Log[
  83. 1/2 (1 + I Tan[\[Pi]/8])] -
  84. 4 Log[1/(
  85. 1 + (-1)^(1/4))] Log[-((1 - I)/((-1 + I) + Sqrt[2]))] Log[
  86. 1/2 (1 + I Tan[\[Pi]/8])] +
  87. 4 Log[-((1 - I)/((-1 + I) + Sqrt[2]))] Log[
  88. 2/((1 - I) + Sqrt[2])] Log[1/2 (1 + I Tan[\[Pi]/8])] -
  89. 4 Log[2] Log[1/2 (1 - I Cot[\[Pi]/8])] Log[
  90. 1/2 (1 + I Tan[\[Pi]/8])] -
  91. 4 Log[1/(1 + (-1)^(1/4))] Log[1 - Tan[\[Pi]/8]] Log[
  92. 1/2 (1 + I Tan[\[Pi]/8])] +
  93. 4 Log[2/((1 - I) + Sqrt[2])] Log[1 - Tan[\[Pi]/8]] Log[
  94. 1/2 (1 + I Tan[\[Pi]/8])] +
  95. 2 Log[2] Log[1/2 (1 + I Tan[\[Pi]/8])]^2 +
  96. 2 Log[1/(1 + (-1)^(1/4))] Log[1/2 (1 + I Tan[\[Pi]/8])]^2 -
  97. 2 Log[2/((1 - I) + Sqrt[2])] Log[
  98. 1/2 (1 + I Tan[\[Pi]/8])]^2 -
  99. 2 Log[-(1/(-1 + (-1)^(1/4)))]^2 Log[1 + I Tan[\[Pi]/8]] -
  100. 2 Log[1/(1 + (-1)^(1/4))]^2 Log[1 + I Tan[\[Pi]/8]] +
  101. 4 Log[1/(1 + (-1)^(1/4))] Log[1 - Tan[\[Pi]/8]] Log[
  102. 1 + I Tan[\[Pi]/8]] +
  103. 2 Log[(1 + I)/((1 + I) - Sqrt[2])]^2 Log[-((
  104. 1 + I)/(-1 + Tan[\[Pi]/8]))] -
  105. 2 Log[-((1 - I)/((-1 + I) + Sqrt[2]))]^2 Log[-((
  106. 1 - I)/(-1 + Tan[\[Pi]/8]))] +
  107. 4 Log[2] Log[1/(1 + (-1)^(1/4))] Log[Tan[\[Pi]/8]] +
  108. 2 Log[2/(1 + (-1)^(1/4))] Log[1 - Tan[\[Pi]/8]] Log[
  109. Tan[\[Pi]/8]] -
  110. 2 Log[2/((1 - I) + Sqrt[2])] Log[1 - Tan[\[Pi]/8]] Log[
  111. Tan[\[Pi]/8]] -
  112. 2 Log[2/(1 + (-1)^(1/4))] Log[
  113. Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[Tan[\[Pi]/8]] -
  114. 4 Log[2] Log[1/2 (1 + I Tan[\[Pi]/8])] Log[Tan[\[Pi]/8]] -
  115. 2 Log[1 - Tan[\[Pi]/8]] Log[1 + I Tan[\[Pi]/8]] Log[
  116. Tan[\[Pi]/8]] +
  117. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[
  118. 1 + I Tan[\[Pi]/8]] Log[Tan[\[Pi]/8]] +
  119. 4 Log[1/(1 + (-1)^(1/4))] Log[
  120. Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[-I + Tan[\[Pi]/8]] +
  121. 4 Log[1 + I Tan[\[Pi]/8]] Log[
  122. Tan[\[Pi]/8]] Log[-I + Tan[\[Pi]/8]] +
  123. 2 Log[1 - Tan[\[Pi]/8]] Log[-I + Tan[\[Pi]/8]]^2 -
  124. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[-I +
  125. Tan[\[Pi]/8]]^2 -
  126. 2 Log[(-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] Log[-I +
  127. Tan[\[Pi]/8]]^2 +
  128. 2 Log[1/(
  129. 1 + (-1)^(1/4))]^2 Log[(1 + I) (-I + Tan[\[Pi]/8])] -
  130. 4 Log[1/(1 + (-1)^(1/4))] Log[
  131. 1 - Tan[\[Pi]/8]] Log[(1 + I) (-I + Tan[\[Pi]/8])] +
  132. 4 Log[2/((1 - I) + Sqrt[2])] Log[1 - Tan[\[Pi]/8]] Log[
  133. I + Tan[\[Pi]/8]] -
  134. 4 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[
  135. 1/2 (1 + I Tan[\[Pi]/8])] Log[I + Tan[\[Pi]/8]] -
  136. 4 Log[2/(1 + (-1)^(1/4))] Log[Tan[\[Pi]/8]] Log[
  137. I + Tan[\[Pi]/8]] -
  138. 2 Log[1 - Tan[\[Pi]/8]] Log[I + Tan[\[Pi]/8]]^2 +
  139. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[I + Tan[\[Pi]/8]]^2 +
  140. 2 Log[(-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] Log[
  141. I + Tan[\[Pi]/8]]^2 -
  142. 4 Log[1 - Tan[\[Pi]/8]] Log[
  143. 1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[(1/2 - I/2) (1 +
  144. Tan[\[Pi]/8])] +
  145. 4 Log[1 + (1 - I)/Sqrt[
  146. 2]] Log[(1 + I) - (1 - I) Tan[\[Pi]/8]] Log[(1/2 - I/
  147. 2) (1 + Tan[\[Pi]/8])] -
  148. 4 Log[1 + (1 - I)/Sqrt[2]] Log[
  149. 1 + I Tan[\[Pi]/8]] Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])] -
  150. 2 Log[-I +
  151. Tan[\[Pi]/8]]^2 Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])] +
  152. 4 Log[(1 + I) - (1 - I) Tan[\[Pi]/8]] Log[
  153. I + Tan[\[Pi]/8]] Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])] -
  154. 4 Log[1 + I Tan[\[Pi]/8]] Log[
  155. I + Tan[\[Pi]/8]] Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])] +
  156. 2 Log[
  157. 1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[(1/2 - I/2) (1 +
  158. Tan[\[Pi]/8])]^2 -
  159. 2 Log[(1 + I) - (1 - I) Tan[\[Pi]/8]] Log[(1/2 - I/2) (1 +
  160. Tan[\[Pi]/8])]^2 +
  161. 2 Log[1 +
  162. I Tan[\[Pi]/8]] Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])]^2 +
  163. 4 Log[2/(1 + (-1)^(1/4))] Log[
  164. 1 + (-1)^(1/4)] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] -
  165. 4 Log[(2 - 2 I)/(1 + (-1)^(1/4))] Log[
  166. 1 + (-1)^(1/4)] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  167. 4 Log[(1 - I)/(
  168. 1 + (-1)^(1/4))] Log[((1 + I) + Sqrt[2])/((-1 - I) + Sqrt[
  169. 2])] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] -
  170. 4 Log[2/((1 - I) + Sqrt[2])] Log[((1 + I) + Sqrt[
  171. 2])/((-1 - I) + Sqrt[
  172. 2])] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  173. 4 Log[(1 - I)/(1 + (-1)^(1/4))] Log[
  174. 1 - Tan[\[Pi]/8]] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] -
  175. 4 Log[2/((1 - I) + Sqrt[2])] Log[
  176. 1 - Tan[\[Pi]/8]] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  177. 4 Log[2/(
  178. 1 + (-1)^(1/4))] Log[-I +
  179. Tan[\[Pi]/8]] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] -
  180. 4 Log[(2 - 2 I)/(
  181. 1 + (-1)^(1/4))] Log[-I +
  182. Tan[\[Pi]/8]] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  183. 2 Log[I +
  184. Tan[\[Pi]/8]]^2 Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])] -
  185. 2 Log[(1 - I)/(
  186. 1 + (-1)^(1/4))] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])]^2 -
  187. 2 Log[2/(
  188. 1 + (-1)^(1/4))] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])]^2 +
  189. 2 Log[(2 - 2 I)/(
  190. 1 + (-1)^(1/4))] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])]^2 +
  191. 2 Log[2/((1 - I) + Sqrt[
  192. 2])] Log[(1/2 + I/2) (1 + Tan[\[Pi]/8])]^2 -
  193. 2 Log[(1 - I)/(1 + (-1)^(1/4))] Log[1 - Tan[\[Pi]/8]] Log[
  194. 1 + Tan[\[Pi]/8]] +
  195. 2 Log[2/((1 - I) + Sqrt[2])] Log[1 - Tan[\[Pi]/8]] Log[
  196. 1 + Tan[\[Pi]/8]] -
  197. 2 Log[(1 - I)/(1 + (-1)^(1/4))] Log[
  198. Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[1 + Tan[\[Pi]/8]] +
  199. 2 Log[1 - Tan[\[Pi]/8]] Log[
  200. 1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[
  201. 1 + Tan[\[Pi]/8]] +
  202. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[
  203. 1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[
  204. 1 + Tan[\[Pi]/8]] -
  205. 2 Log[(1 - I)/(1 + (-1)^(1/4))] Log[Tan[\[Pi]/8]] Log[
  206. 1 + Tan[\[Pi]/8]] +
  207. 2 Log[2/(1 + (-1)^(1/4))] Log[Tan[\[Pi]/8]] Log[
  208. 1 + Tan[\[Pi]/8]] +
  209. 2 Log[1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[
  210. Tan[\[Pi]/8]] Log[1 + Tan[\[Pi]/8]] -
  211. 2 Log[1 + I Tan[\[Pi]/8]] Log[Tan[\[Pi]/8]] Log[
  212. 1 + Tan[\[Pi]/8]] -
  213. 4 Log[1/(1 + (-1)^(1/4))] Log[-I + Tan[\[Pi]/8]] Log[
  214. 1 + Tan[\[Pi]/8]] +
  215. 4 Log[(1 - I)/(1 + (-1)^(1/4))] Log[-I + Tan[\[Pi]/8]] Log[
  216. 1 + Tan[\[Pi]/8]] -
  217. 4 Log[1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[-I +
  218. Tan[\[Pi]/8]] Log[1 + Tan[\[Pi]/8]] +
  219. 2 Log[-I + Tan[\[Pi]/8]]^2 Log[1 + Tan[\[Pi]/8]] +
  220. 4 Log[(1 - I)/(1 + (-1)^(1/4))] Log[I + Tan[\[Pi]/8]] Log[
  221. 1 + Tan[\[Pi]/8]] -
  222. 4 Log[1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[
  223. I + Tan[\[Pi]/8]] Log[1 + Tan[\[Pi]/8]] +
  224. 4 Log[1/2 (1 + I Tan[\[Pi]/8])] Log[I + Tan[\[Pi]/8]] Log[
  225. 1 + Tan[\[Pi]/8]] -
  226. 2 Log[I + Tan[\[Pi]/8]]^2 Log[1 + Tan[\[Pi]/8]] -
  227. 4 Log[1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] Log[(1/2 - I/
  228. 2) (1 + Tan[\[Pi]/8])] Log[(
  229. I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])] +
  230. 2 Log[-((2 - 2 I)/((-1 + I) + Sqrt[2]))] Log[(
  231. I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])]^2 -
  232. 2 Log[-(2/(-1 + Tan[\[Pi]/8]))] Log[(
  233. I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])]^2 -
  234. 4 Log[1/(1 + (-1)^(1/4))] Log[(
  235. 1 + I)/((1 + I) - Sqrt[2])] Log[
  236. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] +
  237. 2 Log[(1 + I)/((1 + I) - Sqrt[2])]^2 Log[
  238. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] +
  239. 2 Log[1 - Tan[\[Pi]/8]] Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] Log[
  240. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] +
  241. 2 Log[1 - Tan[\[Pi]/8]] Log[Tan[\[Pi]/8]] Log[
  242. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] -
  243. 4 Log[1 - Tan[\[Pi]/8]] Log[-I + Tan[\[Pi]/8]] Log[
  244. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] +
  245. 4 Log[1 -
  246. Tan[\[Pi]/8]] Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])] Log[
  247. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] -
  248. 2 Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])]^2 Log[
  249. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] -
  250. 2 Log[1 - Tan[\[Pi]/8]] Log[1 + Tan[\[Pi]/8]] Log[
  251. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] +
  252. 4 Log[(1/2 - I/2) (1 + Tan[\[Pi]/8])] Log[(
  253. I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])] Log[
  254. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] -
  255. 2 Log[(I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])]^2 Log[
  256. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] -
  257. 3 Log[1 - I] PolyLog[2, 1 - I] +
  258. Log[1 + I] PolyLog[2, 1 - I] -
  259. Log[1 - I] PolyLog[2, 1 + I] +
  260. 3 Log[1 + I] PolyLog[2, 1 + I] +
  261. 4 Log[-(1/(-1 + (-1)^(1/4)))] PolyLog[
  262. 2, -(1/(-1 + (-1)^(1/4)))] -
  263. 4 Log[-(1/(-1 + (-1)^(1/4)))] PolyLog[2, 1/(
  264. 1 + (-1)^(1/4))] -
  265. 4 Log[1 + (1 - I)/Sqrt[2]] PolyLog[2, 1/(1 + (-1)^(1/4))] +
  266. 4 Log[(1 + I)/((1 + I) - Sqrt[2])] PolyLog[2, 1/(
  267. 1 + (-1)^(1/4))] +
  268. 4 Log[1 - Tan[\[Pi]/8]] PolyLog[2, 1/(1 + (-1)^(1/4))] -
  269. 4 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] PolyLog[2, 1/(
  270. 1 + (-1)^(1/4))] -
  271. 4 Log[Tan[\[Pi]/8]] PolyLog[2, 1/(1 + (-1)^(1/4))] +
  272. 4 Log[1 + Tan[\[Pi]/8]] PolyLog[2, 1/(1 + (-1)^(1/4))] +
  273. 4 Log[I + Tan[\[Pi]/8]] PolyLog[2, (1 - I)/(
  274. 1 + (-1)^(1/4))] -
  275. 4 Log[I + Tan[\[Pi]/8]] PolyLog[2, 2/(1 + (-1)^(1/4))] +
  276. 4 Log[1 + (-1)^(1/4)] PolyLog[2, 1 + (-1)^(1/4)] -
  277. 4 Log[1 + (1 - I)/Sqrt[2]] PolyLog[2, 1 + (1 - I)/Sqrt[2]] -
  278. 4 Log[(1 + I)/((1 + I) - Sqrt[2])] PolyLog[2, (
  279. 1 + I)/((1 + I) - Sqrt[2])] +
  280. 4 Log[(1 + I)/((1 + I) - Sqrt[2])] PolyLog[
  281. 2, -(2/((-1 - I) + Sqrt[2]))] +
  282. 4 Log[-((1 - I)/((-1 + I) + Sqrt[2]))] PolyLog[2, Sqrt[
  283. 2]/((-1 - I) + Sqrt[2])] -
  284. 4 Log[-((1 - I)/((-1 + I) + Sqrt[2]))] PolyLog[
  285. 2, ((1 + I) Sqrt[2])/((-1 - I) + Sqrt[2])] +
  286. 4 Log[I + Tan[\[Pi]/8]] PolyLog[2, 2/((1 - I) + Sqrt[2])] +
  287. 4 Log[1 + (1 - I)/Sqrt[2]] PolyLog[
  288. 2, -(1/2) I ((1 + I) + Sqrt[2])] -
  289. 4 Log[((1 + I) + Sqrt[2])/((-1 - I) + Sqrt[2])] PolyLog[
  290. 2, ((1 + I) + Sqrt[2])/((-1 - I) + Sqrt[2])] -
  291. 4 Log[1/2 (1 - I Cot[\[Pi]/8])] PolyLog[2,
  292. 1/2 (1 - I Cot[\[Pi]/8])] +
  293. 4 Log[1/2 (1 - I Cot[\[Pi]/8])] PolyLog[2,
  294. 1 - I Cot[\[Pi]/8]] -
  295. 4 Log[-(1/(-1 + (-1)^(1/4)))] PolyLog[2,
  296. 1 + I Cot[\[Pi]/8]] -
  297. 4 Log[-I + Tan[\[Pi]/8]] PolyLog[2,
  298. 1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] +
  299. 4 Log[1 + (-1)^(1/4)] PolyLog[2, 1/2 (1 + I Tan[\[Pi]/8])] -
  300. 4 Log[-((1 - I)/((-1 + I) + Sqrt[2]))] PolyLog[2,
  301. 1/2 (1 + I Tan[\[Pi]/8])] +
  302. 4 Log[1/2 (1 - I Cot[\[Pi]/8])] PolyLog[2,
  303. 1/2 (1 + I Tan[\[Pi]/8])] -
  304. 4 Log[1 - Tan[\[Pi]/8]] PolyLog[2,
  305. 1/2 (1 + I Tan[\[Pi]/8])] +
  306. 4 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] PolyLog[2,
  307. 1/2 (1 + I Tan[\[Pi]/8])] +
  308. 4 Log[Tan[\[Pi]/8]] PolyLog[2, 1/2 (1 + I Tan[\[Pi]/8])] -
  309. 4 Log[1 + Tan[\[Pi]/8]] PolyLog[2,
  310. 1/2 (1 + I Tan[\[Pi]/8])] +
  311. 4 Log[-I + Tan[\[Pi]/8]] PolyLog[2, 1 + I Tan[\[Pi]/8]] -
  312. 4 Log[(1 + I)/((1 + I) - Sqrt[2])] PolyLog[
  313. 2, (-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] -
  314. 2 Log[1 - Tan[\[Pi]/8]] PolyLog[
  315. 2, (-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] +
  316. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] PolyLog[
  317. 2, (-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] +
  318. 2 Log[Tan[\[Pi]/8]] PolyLog[
  319. 2, (-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] -
  320. 4 Log[-I + Tan[\[Pi]/8]] PolyLog[
  321. 2, (-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] -
  322. 2 Log[1 + Tan[\[Pi]/8]] PolyLog[
  323. 2, (-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] +
  324. 4 Log[(I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])] PolyLog[
  325. 2, (-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] +
  326. 4 Log[-((1 - I)/((-1 + I) + Sqrt[2]))] PolyLog[
  327. 2, (-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] -
  328. 4 Log[((1 + I) + Sqrt[2])/((-1 - I) + Sqrt[2])] PolyLog[
  329. 2, (-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] +
  330. 2 Log[1 - Tan[\[Pi]/8]] PolyLog[
  331. 2, (-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] -
  332. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] PolyLog[
  333. 2, (-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] -
  334. 2 Log[Tan[\[Pi]/8]] PolyLog[
  335. 2, (-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] +
  336. 4 Log[I + Tan[\[Pi]/8]] PolyLog[
  337. 2, (-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] +
  338. 2 Log[1 + Tan[\[Pi]/8]] PolyLog[
  339. 2, (-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] +
  340. 4 Log[1 + I Cot[\[Pi]/8]] PolyLog[2, -I Tan[\[Pi]/8]] -
  341. 2 Log[1 - Tan[\[Pi]/8]] PolyLog[2, -I Tan[\[Pi]/8]] +
  342. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] PolyLog[
  343. 2, -I Tan[\[Pi]/8]] +
  344. 2 Log[Tan[\[Pi]/8]] PolyLog[2, -I Tan[\[Pi]/8]] +
  345. 4 Log[-I + Tan[\[Pi]/8]] PolyLog[2, -I Tan[\[Pi]/8]] +
  346. 4 Log[I + Tan[\[Pi]/8]] PolyLog[2, -I Tan[\[Pi]/8]] -
  347. 4 Log[2 (I + Tan[\[Pi]/8])] PolyLog[2, -I Tan[\[Pi]/8]] -
  348. 2 Log[1 + Tan[\[Pi]/8]] PolyLog[2, -I Tan[\[Pi]/8]] -
  349. 4 Log[1 - I Cot[\[Pi]/8]] PolyLog[2, I Tan[\[Pi]/8]] +
  350. 2 Log[1 - Tan[\[Pi]/8]] PolyLog[2, I Tan[\[Pi]/8]] -
  351. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] PolyLog[2,
  352. I Tan[\[Pi]/8]] -
  353. 2 Log[Tan[\[Pi]/8]] PolyLog[2, I Tan[\[Pi]/8]] -
  354. 4 Log[-I + Tan[\[Pi]/8]] PolyLog[2, I Tan[\[Pi]/8]] +
  355. 4 Log[2 (-I + Tan[\[Pi]/8])] PolyLog[2, I Tan[\[Pi]/8]] -
  356. 4 Log[I + Tan[\[Pi]/8]] PolyLog[2, I Tan[\[Pi]/8]] +
  357. 2 Log[1 + Tan[\[Pi]/8]] PolyLog[2, I Tan[\[Pi]/8]] +
  358. 4 Log[1 + (1 - I)/Sqrt[2]] PolyLog[
  359. 2, (1/2 - I/2) (1 + Tan[\[Pi]/8])] -
  360. 2 Log[1 - Tan[\[Pi]/8]] PolyLog[
  361. 2, (1/2 - I/2) (1 + Tan[\[Pi]/8])] +
  362. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] PolyLog[
  363. 2, (1/2 - I/2) (1 + Tan[\[Pi]/8])] +
  364. 2 Log[Tan[\[Pi]/8]] PolyLog[
  365. 2, (1/2 - I/2) (1 + Tan[\[Pi]/8])] -
  366. 4 Log[-I + Tan[\[Pi]/8]] PolyLog[
  367. 2, (1/2 - I/2) (1 + Tan[\[Pi]/8])] -
  368. 2 Log[1 + Tan[\[Pi]/8]] PolyLog[
  369. 2, (1/2 - I/2) (1 + Tan[\[Pi]/8])] -
  370. 4 Log[(I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])] PolyLog[
  371. 2, (1/2 - I/2) (1 + Tan[\[Pi]/8])] -
  372. 4 Log[1 + (-1)^(1/4)] PolyLog[
  373. 2, (1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  374. 4 Log[((1 + I) + Sqrt[2])/((-1 - I) + Sqrt[2])] PolyLog[
  375. 2, (1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  376. 2 Log[1 - Tan[\[Pi]/8]] PolyLog[
  377. 2, (1/2 + I/2) (1 + Tan[\[Pi]/8])] -
  378. 2 Log[Cot[\[Pi]/8] - Tan[\[Pi]/8]] PolyLog[
  379. 2, (1/2 + I/2) (1 + Tan[\[Pi]/8])] -
  380. 2 Log[Tan[\[Pi]/8]] PolyLog[
  381. 2, (1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  382. 4 Log[I + Tan[\[Pi]/8]] PolyLog[
  383. 2, (1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  384. 2 Log[1 + Tan[\[Pi]/8]] PolyLog[
  385. 2, (1/2 + I/2) (1 + Tan[\[Pi]/8])] +
  386. 4 Log[(I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])] PolyLog[2,
  387. (I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])] +
  388. 4 Log[((1 + I) + Sqrt[2])/((-1 - I) + Sqrt[2])] PolyLog[2, (
  389. 1 + Tan[\[Pi]/8])/(-1 + Tan[\[Pi]/8])] -
  390. 4 Log[(I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])] PolyLog[
  391. 2, (1 + Tan[\[Pi]/8])/(-1 + Tan[\[Pi]/8])] -
  392. 4 Log[1 + (-1)^(1/4)] PolyLog[2, (
  393. 1 + Tan[\[Pi]/8])/(-I + Tan[\[Pi]/8])] -
  394. 4 Log[-I + Tan[\[Pi]/8]] PolyLog[2,
  395. 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])] + 2 PolyLog[3, -I] -
  396. 2 PolyLog[3, I] - 2 PolyLog[3, 1/2 - I/2] +
  397. 2 PolyLog[3, 1/2 + I/2] + 2 PolyLog[3, 1 - I] -
  398. 2 PolyLog[3, 1 + I] - 4 PolyLog[3, -(1/(-1 + (-1)^(1/4)))] -
  399. 4 PolyLog[3, 1/(1 + (-1)^(1/4))] -
  400. 4 PolyLog[3, (1 - I)/(1 + (-1)^(1/4))] +
  401. 4 PolyLog[3, 2/(1 + (-1)^(1/4))] -
  402. 4 PolyLog[3, 1 + (-1)^(1/4)] +
  403. 4 PolyLog[3, 1 + (1 - I)/Sqrt[2]] +
  404. 4 PolyLog[3, (1 + I)/((1 + I) - Sqrt[2])] -
  405. 4 PolyLog[3, -(2/((-1 - I) + Sqrt[2]))] -
  406. 4 PolyLog[3, Sqrt[2]/((-1 - I) + Sqrt[2])] +
  407. 4 PolyLog[3, ((1 + I) Sqrt[2])/((-1 - I) + Sqrt[2])] -
  408. 4 PolyLog[3, 2/((1 - I) + Sqrt[2])] -
  409. 4 PolyLog[3, -(1/2) I ((1 + I) + Sqrt[2])] +
  410. 4 PolyLog[3, ((1 + I) + Sqrt[2])/((-1 - I) + Sqrt[2])] +
  411. 4 PolyLog[3, 1/2 (1 - I Cot[\[Pi]/8])] -
  412. 4 PolyLog[3, 1 - I Cot[\[Pi]/8]] +
  413. 4 PolyLog[3, 1 + I Cot[\[Pi]/8]] +
  414. 4 PolyLog[3, 1/2 ((1 + I) - (1 - I) Tan[\[Pi]/8])] +
  415. 4 PolyLog[3, 1/2 (1 + I Tan[\[Pi]/8])] -
  416. 4 PolyLog[3, 1 + I Tan[\[Pi]/8]] +
  417. 4 PolyLog[3, (-(1/2) - I/2) (-1 + Tan[\[Pi]/8])] -
  418. 4 PolyLog[3, (-(1/2) + I/2) (-1 + Tan[\[Pi]/8])] +
  419. 4 PolyLog[3, (1/2 - I/2) (1 + Tan[\[Pi]/8])] -
  420. 4 PolyLog[3, (1/2 + I/2) (1 + Tan[\[Pi]/8])] -
  421. 4 PolyLog[3, (I (1 + Tan[\[Pi]/8]))/(-1 + Tan[\[Pi]/8])] +
  422. 4 PolyLog[3, (1 + Tan[\[Pi]/8])/(-I + Tan[\[Pi]/8])] +
  423. 4 PolyLog[3, 1/2 ((1 - I) + (1 + I) Tan[\[Pi]/8])])))
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