Integrand size = 128, antiderivative size = 19 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625 x^{16} \left (3+\log \left (\frac {x^2}{4}\right )\right )^8}{4722366482869645213696} \]
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Leaf count is larger than twice the leaf count of optimal. \(142\) vs. \(2(19)=38\).
Time = 0.57 (sec) , antiderivative size = 142, normalized size of antiderivative = 7.47, number of steps used = 38, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {12, 2341, 2342} \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {43095327221832275390625 x^{16}}{4722366482869645213696}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {19705225067138671875 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {413809726409912109375 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {1241429179229736328125 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {18621437688446044921875 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{2361183241434822606848}+\frac {11172862613067626953125 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {33518587839202880859375 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {14365109073944091796875 x^{16} \log \left (\frac {x^2}{4}\right )}{590295810358705651712} \]
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Rule 12
Rule 2341
Rule 2342
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )\right ) \, dx}{295147905179352825856} \\ & = \frac {14365109073944091796875 x^{16}}{1180591620717411303424}+\frac {6568408355712890625 \int x^{15} \log ^8\left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856}+\frac {164210208892822265625 \int x^{15} \log ^7\left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856}+\frac {1793175481109619140625 \int x^{15} \log ^6\left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856}+\frac {11172862613067626953125 \int x^{15} \log ^5\left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856}+\frac {43450021273040771484375 \int x^{15} \log ^4\left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856}+\frac {108004338592987060546875 \int x^{15} \log ^3\left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856}+\frac {148439460430755615234375 \int x^{15} \log \left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856}+\frac {167592939196014404296875 \int x^{15} \log ^2\left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856} \\ & = \frac {311244029935455322265625 x^{16}}{37778931862957161709568}+\frac {148439460430755615234375 x^{16} \log \left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {167592939196014404296875 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {108004338592987060546875 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {43450021273040771484375 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {11172862613067626953125 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {1793175481109619140625 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {164210208892822265625 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696}-\frac {6568408355712890625 \int x^{15} \log ^7\left (\frac {x^2}{4}\right ) \, dx}{295147905179352825856}-\frac {1149471462249755859375 \int x^{15} \log ^6\left (\frac {x^2}{4}\right ) \, dx}{2361183241434822606848}-\frac {5379526443328857421875 \int x^{15} \log ^5\left (\frac {x^2}{4}\right ) \, dx}{1180591620717411303424}-\frac {55864313065338134765625 \int x^{15} \log ^4\left (\frac {x^2}{4}\right ) \, dx}{2361183241434822606848}-\frac {43450021273040771484375 \int x^{15} \log ^3\left (\frac {x^2}{4}\right ) \, dx}{590295810358705651712}-\frac {324013015778961181640625 \int x^{15} \log ^2\left (\frac {x^2}{4}\right ) \, dx}{2361183241434822606848}-\frac {167592939196014404296875 \int x^{15} \log \left (\frac {x^2}{4}\right ) \, dx}{1180591620717411303424} \\ & = \frac {1412569058937835693359375 x^{16}}{151115727451828646838272}+\frac {426164902527008056640625 x^{16} \log \left (\frac {x^2}{4}\right )}{18889465931478580854784}+\frac {1016730497789154052734375 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{37778931862957161709568}+\frac {172558655912933349609375 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{9444732965739290427392}+\frac {291735857118988037109375 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{37778931862957161709568}+\frac {39311924008941650390625 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{18889465931478580854784}+\frac {13195932386627197265625 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{37778931862957161709568}+\frac {19705225067138671875 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {45978858489990234375 \int x^{15} \log ^6\left (\frac {x^2}{4}\right ) \, dx}{2361183241434822606848}+\frac {3448414386749267578125 \int x^{15} \log ^5\left (\frac {x^2}{4}\right ) \, dx}{9444732965739290427392}+\frac {26897632216644287109375 \int x^{15} \log ^4\left (\frac {x^2}{4}\right ) \, dx}{9444732965739290427392}+\frac {55864313065338134765625 \int x^{15} \log ^3\left (\frac {x^2}{4}\right ) \, dx}{4722366482869645213696}+\frac {130350063819122314453125 \int x^{15} \log ^2\left (\frac {x^2}{4}\right ) \, dx}{4722366482869645213696}+\frac {324013015778961181640625 \int x^{15} \log \left (\frac {x^2}{4}\right ) \, dx}{9444732965739290427392} \\ & = \frac {10976539455723724365234375 x^{16}}{1208925819614629174706176}+\frac {3733332235995025634765625 x^{16} \log \left (\frac {x^2}{4}\right )}{151115727451828646838272}+\frac {2163811059397430419921875 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{75557863725914323419136}+\frac {1436333560368804931640625 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{75557863725914323419136}+\frac {1193841060692596435546875 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{151115727451828646838272}+\frac {317943806458282470703125 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{151115727451828646838272}+\frac {413809726409912109375 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {19705225067138671875 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696}-\frac {137936575469970703125 \int x^{15} \log ^5\left (\frac {x^2}{4}\right ) \, dx}{9444732965739290427392}-\frac {17242071933746337890625 \int x^{15} \log ^4\left (\frac {x^2}{4}\right ) \, dx}{75557863725914323419136}-\frac {26897632216644287109375 \int x^{15} \log ^3\left (\frac {x^2}{4}\right ) \, dx}{18889465931478580854784}-\frac {167592939196014404296875 \int x^{15} \log ^2\left (\frac {x^2}{4}\right ) \, dx}{37778931862957161709568}-\frac {130350063819122314453125 \int x^{15} \log \left (\frac {x^2}{4}\right ) \, dx}{18889465931478580854784} \\ & = \frac {22083428975266571044921875 x^{16}}{2417851639229258349412352}+\frac {7336314408170928955078125 x^{16} \log \left (\frac {x^2}{4}\right )}{302231454903657293676544}+\frac {17142895535983428955078125 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{604462909807314587353088}+\frac {5718436609258575439453125 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{302231454903657293676544}+\frac {9533486413607025146484375 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{1208925819614629174706176}+\frac {1241429179229736328125 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {413809726409912109375 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {19705225067138671875 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {689682877349853515625 \int x^{15} \log ^4\left (\frac {x^2}{4}\right ) \, dx}{75557863725914323419136}+\frac {17242071933746337890625 \int x^{15} \log ^3\left (\frac {x^2}{4}\right ) \, dx}{151115727451828646838272}+\frac {80692896649932861328125 \int x^{15} \log ^2\left (\frac {x^2}{4}\right ) \, dx}{151115727451828646838272}+\frac {167592939196014404296875 \int x^{15} \log \left (\frac {x^2}{4}\right ) \, dx}{151115727451828646838272} \\ & = \frac {176499838862936553955078125 x^{16}}{19342813113834066795298816}+\frac {58858108204563446044921875 x^{16} \log \left (\frac {x^2}{4}\right )}{2417851639229258349412352}+\frac {68652275040583648681640625 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{2417851639229258349412352}+\frac {45764734946002349853515625 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{2417851639229258349412352}+\frac {18621437688446044921875 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{2361183241434822606848}+\frac {1241429179229736328125 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {413809726409912109375 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {19705225067138671875 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696}-\frac {689682877349853515625 \int x^{15} \log ^3\left (\frac {x^2}{4}\right ) \, dx}{151115727451828646838272}-\frac {51726215801239013671875 \int x^{15} \log ^2\left (\frac {x^2}{4}\right ) \, dx}{1208925819614629174706176}-\frac {80692896649932861328125 \int x^{15} \log \left (\frac {x^2}{4}\right ) \, dx}{604462909807314587353088} \\ & = \frac {706080048348396148681640625 x^{16}}{77371252455336267181195264}+\frac {235351739921603851318359375 x^{16} \log \left (\frac {x^2}{4}\right )}{9671406556917033397649408}+\frac {549166474108867950439453125 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{19342813113834066795298816}+\frac {11172862613067626953125 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {18621437688446044921875 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{2361183241434822606848}+\frac {1241429179229736328125 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {413809726409912109375 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {19705225067138671875 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696}+\frac {2069048632049560546875 \int x^{15} \log ^2\left (\frac {x^2}{4}\right ) \, dx}{1208925819614629174706176}+\frac {51726215801239013671875 \int x^{15} \log \left (\frac {x^2}{4}\right ) \, dx}{4835703278458516698824704} \\ & = \frac {5648588660571367950439453125 x^{16}}{618970019642690137449562112}+\frac {1882865645588632049560546875 x^{16} \log \left (\frac {x^2}{4}\right )}{77371252455336267181195264}+\frac {33518587839202880859375 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {11172862613067626953125 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {18621437688446044921875 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{2361183241434822606848}+\frac {1241429179229736328125 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {413809726409912109375 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {19705225067138671875 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696}-\frac {2069048632049560546875 \int x^{15} \log \left (\frac {x^2}{4}\right ) \, dx}{4835703278458516698824704} \\ & = \frac {43095327221832275390625 x^{16}}{4722366482869645213696}+\frac {14365109073944091796875 x^{16} \log \left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {33518587839202880859375 x^{16} \log ^2\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {11172862613067626953125 x^{16} \log ^3\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {18621437688446044921875 x^{16} \log ^4\left (\frac {x^2}{4}\right )}{2361183241434822606848}+\frac {1241429179229736328125 x^{16} \log ^5\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {413809726409912109375 x^{16} \log ^6\left (\frac {x^2}{4}\right )}{1180591620717411303424}+\frac {19705225067138671875 x^{16} \log ^7\left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {6568408355712890625 x^{16} \log ^8\left (\frac {x^2}{4}\right )}{4722366482869645213696} \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625 x^{16} \left (3+\log \left (\frac {x^2}{4}\right )\right )^8}{4722366482869645213696} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(108\) vs. \(2(15)=30\).
Time = 0.11 (sec) , antiderivative size = 109, normalized size of antiderivative = 5.74
method | result | size |
risch | \(\frac {6568408355712890625 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{8}}{4722366482869645213696}+\frac {19705225067138671875 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{7}}{590295810358705651712}+\frac {413809726409912109375 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{6}}{1180591620717411303424}+\frac {1241429179229736328125 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{5}}{590295810358705651712}+\frac {18621437688446044921875 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{4}}{2361183241434822606848}+\frac {11172862613067626953125 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{3}}{590295810358705651712}+\frac {33518587839202880859375 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{2}}{1180591620717411303424}+\frac {14365109073944091796875 x^{16} \ln \left (\frac {x^{2}}{4}\right )}{590295810358705651712}+\frac {43095327221832275390625 x^{16}}{4722366482869645213696}\) | \(109\) |
parallelrisch | \(\frac {6568408355712890625 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{8}}{4722366482869645213696}+\frac {19705225067138671875 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{7}}{590295810358705651712}+\frac {413809726409912109375 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{6}}{1180591620717411303424}+\frac {1241429179229736328125 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{5}}{590295810358705651712}+\frac {18621437688446044921875 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{4}}{2361183241434822606848}+\frac {11172862613067626953125 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{3}}{590295810358705651712}+\frac {33518587839202880859375 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{2}}{1180591620717411303424}+\frac {14365109073944091796875 x^{16} \ln \left (\frac {x^{2}}{4}\right )}{590295810358705651712}+\frac {43095327221832275390625 x^{16}}{4722366482869645213696}\) | \(109\) |
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Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (15) = 30\).
Time = 0.25 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.68 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625}{4722366482869645213696} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{8} + \frac {19705225067138671875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{7} + \frac {413809726409912109375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{6} + \frac {1241429179229736328125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{5} + \frac {18621437688446044921875}{2361183241434822606848} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{4} + \frac {11172862613067626953125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{3} + \frac {33518587839202880859375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{2} + \frac {14365109073944091796875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right ) + \frac {43095327221832275390625}{4722366482869645213696} \, x^{16} \]
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Leaf count of result is larger than twice the leaf count of optimal. 126 vs. \(2 (15) = 30\).
Time = 0.18 (sec) , antiderivative size = 126, normalized size of antiderivative = 6.63 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{8}}{4722366482869645213696} + \frac {19705225067138671875 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{7}}{590295810358705651712} + \frac {413809726409912109375 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{6}}{1180591620717411303424} + \frac {1241429179229736328125 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{5}}{590295810358705651712} + \frac {18621437688446044921875 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{4}}{2361183241434822606848} + \frac {11172862613067626953125 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{3}}{590295810358705651712} + \frac {33518587839202880859375 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{2}}{1180591620717411303424} + \frac {14365109073944091796875 x^{16} \log {\left (\frac {x^{2}}{4} \right )}}{590295810358705651712} + \frac {43095327221832275390625 x^{16}}{4722366482869645213696} \]
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Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (15) = 30\).
Time = 0.19 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.68 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625}{4722366482869645213696} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{8} + \frac {19705225067138671875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{7} + \frac {413809726409912109375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{6} + \frac {1241429179229736328125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{5} + \frac {18621437688446044921875}{2361183241434822606848} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{4} + \frac {11172862613067626953125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{3} + \frac {33518587839202880859375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{2} + \frac {14365109073944091796875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right ) + \frac {43095327221832275390625}{4722366482869645213696} \, x^{16} \]
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Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (15) = 30\).
Time = 0.26 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.68 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625}{4722366482869645213696} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{8} + \frac {19705225067138671875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{7} + \frac {413809726409912109375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{6} + \frac {1241429179229736328125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{5} + \frac {18621437688446044921875}{2361183241434822606848} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{4} + \frac {11172862613067626953125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{3} + \frac {33518587839202880859375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{2} + \frac {14365109073944091796875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right ) + \frac {43095327221832275390625}{4722366482869645213696} \, x^{16} \]
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Time = 8.89 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.68 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^8}{4722366482869645213696}+\frac {19705225067138671875\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^7}{590295810358705651712}+\frac {413809726409912109375\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^6}{1180591620717411303424}+\frac {1241429179229736328125\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^5}{590295810358705651712}+\frac {18621437688446044921875\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^4}{2361183241434822606848}+\frac {11172862613067626953125\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^3}{590295810358705651712}+\frac {33518587839202880859375\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^2}{1180591620717411303424}+\frac {14365109073944091796875\,x^{16}\,\ln \left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {43095327221832275390625\,x^{16}}{4722366482869645213696} \]
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