Integrand size = 23, antiderivative size = 638 \[ \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx =\text {Too large to display} \]
1/1840124479200000000*(37358055634422583-14024622879097678*x)/(x^2-2*x+3)^ (19/2)+1/104273720488000000000*(476849951294984711-125181871472148210*x)/( x^2-2*x+3)^(17/2)+1/15641058073200000000000*(7851758375483333511+194216499 6204584234*x)/(x^2-2*x+3)^(15/2)-11/406667509903200000000000*(750232510630 8201089-7813986379726516886*x)/(x^2-2*x+3)^(13/2)-3/1147010925368000000000 000*(69053268515296359011-44840736195018286006*x)/(x^2-2*x+3)^(11/2)+1/938 4634843920000000000000*(-838519439380295335657+466189390555853643870*x)/(x ^2-2*x+3)^(9/2)+1/31282116146400000000000000*(-1117646664729238460189+5688 39749685437871554*x)/(x^2-2*x+3)^(7/2)+1/521368602440000000000000000*(-655 1405511565449301689+3127298559983309301910*x)/(x^2-2*x+3)^(5/2)+1/10427372 04880000000000000000*(-4179039782398459850819+1886993445589652402694*x)/(x ^2-2*x+3)^(3/2)+1/630*(-1+10*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^9+1/88200*( 887+2218*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^8+1/1080450*(14453+29371*x)/(x^ 2-2*x+3)^(19/2)/(2*x^2+x+1)^7+1/605052000*(8837931+17459234*x)/(x^2-2*x+3) ^(19/2)/(2*x^2+x+1)^6+1/26471025000*(447940041+813432205*x)/(x^2-2*x+3)^(1 9/2)/(2*x^2+x+1)^5+1/29647548000000*(592729157441+911061463974*x)/(x^2-2*x +3)^(19/2)/(2*x^2+x+1)^4+1/12353145000000*(277010166219+310705340015*x)/(x ^2-2*x+3)^(19/2)/(2*x^2+x+1)^3+1/276710448000000*(5488221294349+1384103301 166*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^2+1/2421216420000000*(-3785719779211 7-146548895467025*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)+1/10427372048800000...
Result contains complex when optimal does not.
Time = 21.66 (sec) , antiderivative size = 1431, normalized size of antiderivative = 2.24 \[ \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx =\text {Too large to display} \]
Sqrt[3 - 2*x + x^2]*((1 - x)/(11875000000*(3 - 2*x + x^2)^10) + (265 - 113 *x)/(403750000000*(3 - 2*x + x^2)^9) + (82361 - 4841*x)/(60562500000000*(3 - 2*x + x^2)^8) + (1062937 + 1642511*x)/(1574625000000000*(3 - 2*x + x^2) ^7) + (7*(-678331 + 833371*x))/(2220625000000000*(3 - 2*x + x^2)^6) + (7*( -73161291 + 43964675*x))/(90843750000000000*(3 - 2*x + x^2)^5) + (-1340879 383 + 430593031*x)/(181687500000000000*(3 - 2*x + x^2)^4) - (11*(162612572 3 + 112950205*x))/(3028125000000000000*(3 - 2*x + x^2)^3) - (11*(331157064 7 + 15286717673*x))/(36337500000000000000*(3 - 2*x + x^2)^2) - (11*(-41152 1923277 + 484788625685*x))/(363375000000000000000*(3 - 2*x + x^2)) + (2519 43 + 221770*x)/(6300000000000*(1 + x + 2*x^2)^9) - (73*(-888423 + 1604678* x))/(882000000000000*(1 + x + 2*x^2)^8) + (-2596903794 - 4965311863*x)/(10 804500000000000*(1 + x + 2*x^2)^7) + (-539608494637 - 334647150510*x)/(121 0104000000000000*(1 + x + 2*x^2)^6) + (-40800462989458 + 56711874696335*x) /(264710250000000000000*(1 + x + 2*x^2)^5) + (42018358198215561 + 12919659 7088670934*x)/(296475480000000000000000*(1 + x + 2*x^2)^4) + (628195598643 14747 + 169630389653846945*x)/(370594350000000000000000*(1 + x + 2*x^2)^3) + (1082422109196374795 + 4797048907791526114*x)/(830131344000000000000000 0*(1 + x + 2*x^2)^2) + (65571203144429922747 + 367152793968978953465*x)/(3 63182463000000000000000000*(1 + x + 2*x^2))) + ((232442807954946745795*I + 21634177831191924841*Sqrt[7])*ArcTan[(-1350637388604350168995865589487...
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {1}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^{10}} \, dx\) |
| \(\Big \downarrow \) 1305 |
| \(\displaystyle -\frac {\int -\frac {20 \left (90 x^2-153 x+148\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^9}dx}{3150}-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \int \frac {90 x^2-153 x+148}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^9}dx-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {\int \frac {5 \left (75412 x^2-86509 x+80661\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^8}dx}{2800}+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \int \frac {75412 x^2-86509 x+80661}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^8}dx+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {\int \frac {50 \left (3759488 x^2-3790178 x+3715561\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^7}dx}{2450}+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \int \frac {3759488 x^2-3790178 x+3715561}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^7}dx+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {\int \frac {15 \left (523777020 x^2-494230435 x+458962907\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^6}dx}{2100}+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \int \frac {523777020 x^2-494230435 x+458962907}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^6}dx+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {\int \frac {10 \left (91104406960 x^2-76561243634 x+63390281609\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^5}dx}{1750}+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \int \frac {91104406960 x^2-76561243634 x+63390281609}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^5}dx+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {\int \frac {15 \left (7895866021108 x^2-5294487996061 x+3622330118837\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^4}dx}{1400}+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \int \frac {7895866021108 x^2-5294487996061 x+3622330118837}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^4}dx+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {\int \frac {1050 \left (5965542528288 x^2-2041006971986 x+660555973049\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^3}dx}{1050}+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\int \frac {5965542528288 x^2-2041006971986 x+660555973049}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^3}dx+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{700} \int -\frac {25 \left (-30450272625652 x^2-90242403939711 x+57003619484663\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^2}dx+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (-\frac {1}{28} \int \frac {-30450272625652 x^2-90242403939711 x+57003619484663}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )^2}dx+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (-\frac {1}{350} \int -\frac {10 \left (-11723911637362000 x^2+9423200395626322 x+2186320722336583\right )}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )}dx-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \int \frac {-11723911637362000 x^2+9423200395626322 x+2186320722336583}{\left (x^2-2 x+3\right )^{21/2} \left (2 x^2+x+1\right )}dx-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {\int -\frac {60 \left (168295474549172136 x^2-211409077626196062 x+28036472352531697\right )}{\left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}dx}{3800}+\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \int \frac {168295474549172136 x^2-211409077626196062 x+28036472352531697}{\left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}dx\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {\int \frac {20 \left (4005819887108742720 x^2-9953804770422069674 x+4165701285842894649\right )}{\left (x^2-2 x+3\right )^{17/2} \left (2 x^2+x+1\right )}dx}{3400}-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \int \frac {4005819887108742720 x^2-9953804770422069674 x+4165701285842894649}{\left (x^2-2 x+3\right )^{17/2} \left (2 x^2+x+1\right )}dx-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \left (\frac {\int \frac {20 \left (-54380619893728358552 x^2-321008011097501711626 x+249486021165765984239\right )}{\left (x^2-2 x+3\right )^{15/2} \left (2 x^2+x+1\right )}dx}{3000}-\frac {1942164996204584234 x+7851758375483333511}{150 \left (x^2-2 x+3\right )^{15/2}}\right )-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \left (\frac {1}{150} \int \frac {-54380619893728358552 x^2-321008011097501711626 x+249486021165765984239}{\left (x^2-2 x+3\right )^{15/2} \left (2 x^2+x+1\right )}dx-\frac {1942164996204584234 x+7851758375483333511}{150 \left (x^2-2 x+3\right )^{15/2}}\right )-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \left (\frac {1}{150} \left (\frac {\int \frac {3900 \left (-52894677031994883536 x^2-28732854521065090946 x+48475774449904426425\right )}{\left (x^2-2 x+3\right )^{13/2} \left (2 x^2+x+1\right )}dx}{2600}+\frac {11 (7502325106308201089-7813986379726516886 x)}{26 \left (x^2-2 x+3\right )^{13/2}}\right )-\frac {1942164996204584234 x+7851758375483333511}{150 \left (x^2-2 x+3\right )^{15/2}}\right )-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \left (\frac {1}{150} \left (\frac {3}{2} \int \frac {-52894677031994883536 x^2-28732854521065090946 x+48475774449904426425}{\left (x^2-2 x+3\right )^{13/2} \left (2 x^2+x+1\right )}dx+\frac {11 (7502325106308201089-7813986379726516886 x)}{26 \left (x^2-2 x+3\right )^{13/2}}\right )-\frac {1942164996204584234 x+7851758375483333511}{150 \left (x^2-2 x+3\right )^{15/2}}\right )-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \left (\frac {1}{150} \left (\frac {3}{2} \left (\frac {\int \frac {220 \left (-244585833791008832760 x^2+22982277026164021650 x+104761938007268837377\right )}{\left (x^2-2 x+3\right )^{11/2} \left (2 x^2+x+1\right )}dx}{2200}+\frac {3 (69053268515296359011-44840736195018286006 x)}{110 \left (x^2-2 x+3\right )^{11/2}}\right )+\frac {11 (7502325106308201089-7813986379726516886 x)}{26 \left (x^2-2 x+3\right )^{13/2}}\right )-\frac {1942164996204584234 x+7851758375483333511}{150 \left (x^2-2 x+3\right )^{15/2}}\right )-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \left (\frac {1}{150} \left (\frac {3}{2} \left (\frac {1}{10} \int \frac {-244585833791008832760 x^2+22982277026164021650 x+104761938007268837377}{\left (x^2-2 x+3\right )^{11/2} \left (2 x^2+x+1\right )}dx+\frac {3 (69053268515296359011-44840736195018286006 x)}{110 \left (x^2-2 x+3\right )^{11/2}}\right )+\frac {11 (7502325106308201089-7813986379726516886 x)}{26 \left (x^2-2 x+3\right )^{13/2}}\right )-\frac {1942164996204584234 x+7851758375483333511}{150 \left (x^2-2 x+3\right )^{15/2}}\right )-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 2135 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \left (\frac {1}{150} \left (\frac {3}{2} \left (\frac {1}{10} \left (\frac {\int \frac {60 \left (-2486343416297886100640 x^2+990808584797707100402 x+364496404211010919403\right )}{\left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )}dx}{1800}+\frac {838519439380295335657-466189390555853643870 x}{90 \left (x^2-2 x+3\right )^{9/2}}\right )+\frac {3 (69053268515296359011-44840736195018286006 x)}{110 \left (x^2-2 x+3\right )^{11/2}}\right )+\frac {11 (7502325106308201089-7813986379726516886 x)}{26 \left (x^2-2 x+3\right )^{13/2}}\right )-\frac {1942164996204584234 x+7851758375483333511}{150 \left (x^2-2 x+3\right )^{15/2}}\right )-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{315} \left (\frac {1}{560} \left (\frac {1}{49} \left (\frac {1}{140} \left (\frac {1}{175} \left (\frac {3}{280} \left (\frac {1}{28} \left (\frac {1}{35} \left (\frac {37358055634422583-14024622879097678 x}{190 \left (x^2-2 x+3\right )^{19/2}}-\frac {3}{190} \left (\frac {1}{170} \left (\frac {1}{150} \left (\frac {3}{2} \left (\frac {1}{10} \left (\frac {1}{30} \int \frac {-2486343416297886100640 x^2+990808584797707100402 x+364496404211010919403}{\left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )}dx+\frac {838519439380295335657-466189390555853643870 x}{90 \left (x^2-2 x+3\right )^{9/2}}\right )+\frac {3 (69053268515296359011-44840736195018286006 x)}{110 \left (x^2-2 x+3\right )^{11/2}}\right )+\frac {11 (7502325106308201089-7813986379726516886 x)}{26 \left (x^2-2 x+3\right )^{13/2}}\right )-\frac {1942164996204584234 x+7851758375483333511}{150 \left (x^2-2 x+3\right )^{15/2}}\right )-\frac {476849951294984711-125181871472148210 x}{170 \left (x^2-2 x+3\right )^{17/2}}\right )\right )-\frac {4 (146548895467025 x+37857197792117)}{35 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}\right )+\frac {4 (310705340015 x+277010166219)}{5 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1384103301166 x+5488221294349}{28 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}\right )+\frac {911061463974 x+592729157441}{280 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {4 (813432205 x+447940041)}{175 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {17459234 x+8837931}{140 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {4 (29371 x+14453)}{49 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {2218 x+887}{560 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}\right )-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}\) |
3.1.51.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_)*((d_.) + (e_.)*(x_) + (f_.)*(x _)^2)^(q_), x_Symbol] :> Simp[(2*a*c^2*e - b^2*c*e + b^3*f + b*c*(c*d - 3*a *f) + c*(2*c^2*d + b^2*f - c*(b*e + 2*a*f))*x)*(a + b*x + c*x^2)^(p + 1)*(( d + e*x + f*x^2)^(q + 1)/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1))), x] - Simp[1/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*( c*e - b*f))*(p + 1)) Int[(a + b*x + c*x^2)^(p + 1)*(d + e*x + f*x^2)^q*Si mp[2*c*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1) - (2*c^2*d + b^2*f - c*(b*e + 2*a*f))*(a*f*(p + 1) - c*d*(p + 2)) - e*(b^2*c*e - 2*a*c^2*e - b^3*f - b*c*(c*d - 3*a*f))*(p + q + 2) + (2*f*(2*a*c^2*e - b^2*c*e + b^3*f + b*c*(c*d - 3*a*f))*(p + q + 2) - (2*c^2*d + b^2*f - c*(b*e + 2*a*f))*(b*f *(p + 1) - c*e*(2*p + q + 4)))*x + c*f*(2*c^2*d + b^2*f - c*(b*e + 2*a*f))* (2*p + 2*q + 5)*x^2, x], x], x] /; FreeQ[{a, b, c, d, e, f, q}, x] && NeQ[b ^2 - 4*a*c, 0] && NeQ[e^2 - 4*d*f, 0] && LtQ[p, -1] && NeQ[(c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f), 0] && !( !IntegerQ[p] && ILtQ[q, -1]) && !IGtQ[q , 0]
Int[(Px_)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_)*((d_) + (e_.)*(x_) + (f_. )*(x_)^2)^(q_), x_Symbol] :> With[{A = Coeff[Px, x, 0], B = Coeff[Px, x, 1] , C = Coeff[Px, x, 2]}, Simp[(a + b*x + c*x^2)^(p + 1)*((d + e*x + f*x^2)^( q + 1)/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1)))*( (A*c - a*C)*(2*a*c*e - b*(c*d + a*f)) + (A*b - a*B)*(2*c^2*d + b^2*f - c*(b *e + 2*a*f)) + c*(A*(2*c^2*d + b^2*f - c*(b*e + 2*a*f)) - B*(b*c*d - 2*a*c* e + a*b*f) + C*(b^2*d - a*b*e - 2*a*(c*d - a*f)))*x), x] + Simp[1/((b^2 - 4 *a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1)) Int[(a + b*x + c *x^2)^(p + 1)*(d + e*x + f*x^2)^q*Simp[(b*B - 2*A*c - 2*a*C)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1) + (b^2*(C*d + A*f) - b*(B*c*d + A*c*e + a*C*e + a*B*f) + 2*(A*c*(c*d - a*f) - a*(c*C*d - B*c*e - a*C*f)))*(a*f*(p + 1) - c*d*(p + 2)) - e*((A*c - a*C)*(2*a*c*e - b*(c*d + a*f)) + (A*b - a*B )*(2*c^2*d + b^2*f - c*(b*e + 2*a*f)))*(p + q + 2) - (2*f*((A*c - a*C)*(2*a *c*e - b*(c*d + a*f)) + (A*b - a*B)*(2*c^2*d + b^2*f - c*(b*e + 2*a*f)))*(p + q + 2) - (b^2*(C*d + A*f) - b*(B*c*d + A*c*e + a*C*e + a*B*f) + 2*(A*c*( c*d - a*f) - a*(c*C*d - B*c*e - a*C*f)))*(b*f*(p + 1) - c*e*(2*p + q + 4))) *x - c*f*(b^2*(C*d + A*f) - b*(B*c*d + A*c*e + a*C*e + a*B*f) + 2*(A*c*(c*d - a*f) - a*(c*C*d - B*c*e - a*C*f)))*(2*p + 2*q + 5)*x^2, x], x], x]] /; F reeQ[{a, b, c, d, e, f, q}, x] && PolyQ[Px, x, 2] && LtQ[p, -1] && NeQ[(c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f), 0] && !( !IntegerQ[p] && ILtQ[q, -1]) && !IGtQ[q, 0]
Time = 6.78 (sec) , antiderivative size = 552, normalized size of antiderivative = 0.87
| method | result | size |
| risch | \(\frac {3372249001933422237824271360 x^{37}-53502205399640031394796147712 x^{36}+469149394082989701729494575872 x^{35}-2847499220912667753383035299072 x^{34}+13254252261100740556512388253568 x^{33}-49770080058525077628064229832576 x^{32}+156010734937008739388220889457760 x^{31}-417516398850754397130111919794336 x^{30}+971538171913365251873706873353652 x^{29}-1993653213575521837888601204380228 x^{28}+3655553471852957606257345414140031 x^{27}-6054769996581738503753686155104785 x^{26}+9155494158513869230271529746307221 x^{25}-12740106677685048178693605103009787 x^{24}+16442770202470076313197215936814318 x^{23}-19772569734288744720189854470201506 x^{22}+22286437617621909921609206629636086 x^{21}-23584986647560742443188031208946882 x^{20}+23579397211179175240196614296051673 x^{19}-22218747553941794885903840542461607 x^{18}+19912295454080246583636391613811979 x^{17}-16801760806053390242995145349148613 x^{16}+13613407965006475288139078599341572 x^{15}-10279305650733178669223634020962076 x^{14}+7606288378303449524327938977040824 x^{13}-5069838234992751929471190426115248 x^{12}+3507425970596197680016078213030977 x^{11}-1974814483061344405275851094534735 x^{10}+1357002388430055881833293557852283 x^{9}-566969010759169461615951049236597 x^{8}+458426000073846882432457044306894 x^{7}-94704557665253489332536549937026 x^{6}+135183920426913231415208872303230 x^{5}-1023095318901774638403186272874 x^{4}+29398041153524973343917601742151 x^{3}+1933957195570062708781629134823 x^{2}+3397462350398947848063583843461 x -80038710871555316861345369643}{13420027826805600000000000000000 \left (x^{2}-2 x +3\right )^{\frac {19}{2}} \left (2 x^{2}+x +1\right )^{9}}+\frac {\sqrt {4}\, \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}\, \sqrt {2}\, \left (7003218138761840939875 \sqrt {-6050+4280 \sqrt {2}}\, \arctan \left (\frac {\sqrt {-6050+4280 \sqrt {2}}\, \left (40 \sqrt {2}+57\right ) \left (\sqrt {2}-1+x \right )}{49 \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}\, \left (\sqrt {2}+1-x \right )}\right ) \sqrt {-350+280 \sqrt {2}}\, \sqrt {2}+9903469297471243727348 \sqrt {-6050+4280 \sqrt {2}}\, \arctan \left (\frac {\sqrt {-6050+4280 \sqrt {2}}\, \left (40 \sqrt {2}+57\right ) \left (\sqrt {2}-1+x \right )}{49 \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}\, \left (\sqrt {2}+1-x \right )}\right ) \sqrt {-350+280 \sqrt {2}}+321845054725303914701190 \,\operatorname {arctanh}\left (\frac {7 \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}}{\sqrt {-350+280 \sqrt {2}}}\right ) \sqrt {2}-455587903591695621758200 \,\operatorname {arctanh}\left (\frac {7 \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}}{\sqrt {-350+280 \sqrt {2}}}\right )\right )}{63274455776000000000000000000 \sqrt {\frac {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}{\left (\frac {\sqrt {2}-1+x}{\sqrt {2}+1-x}+1\right )^{2}}}\, \left (\frac {\sqrt {2}-1+x}{\sqrt {2}+1-x}+1\right ) \sqrt {-350+280 \sqrt {2}}}\) | \(552\) |
| trager | \(\text {Expression too large to display}\) | \(642\) |
| default | \(\text {Expression too large to display}\) | \(86793\) |
1/13420027826805600000000000000000*(3372249001933422237824271360*x^37-5350 2205399640031394796147712*x^36+469149394082989701729494575872*x^35-2847499 220912667753383035299072*x^34+13254252261100740556512388253568*x^33-497700 80058525077628064229832576*x^32+156010734937008739388220889457760*x^31-417 516398850754397130111919794336*x^30+971538171913365251873706873353652*x^29 -1993653213575521837888601204380228*x^28+365555347185295760625734541414003 1*x^27-6054769996581738503753686155104785*x^26+915549415851386923027152974 6307221*x^25-12740106677685048178693605103009787*x^24+16442770202470076313 197215936814318*x^23-19772569734288744720189854470201506*x^22+222864376176 21909921609206629636086*x^21-23584986647560742443188031208946882*x^20+2357 9397211179175240196614296051673*x^19-22218747553941794885903840542461607*x ^18+19912295454080246583636391613811979*x^17-16801760806053390242995145349 148613*x^16+13613407965006475288139078599341572*x^15-102793056507331786692 23634020962076*x^14+7606288378303449524327938977040824*x^13-50698382349927 51929471190426115248*x^12+3507425970596197680016078213030977*x^11-19748144 83061344405275851094534735*x^10+1357002388430055881833293557852283*x^9-566 969010759169461615951049236597*x^8+458426000073846882432457044306894*x^7-9 4704557665253489332536549937026*x^6+135183920426913231415208872303230*x^5- 1023095318901774638403186272874*x^4+29398041153524973343917601742151*x^3+1 933957195570062708781629134823*x^2+3397462350398947848063583843461*x-80...
Result contains complex when optimal does not.
Time = 0.32 (sec) , antiderivative size = 1569, normalized size of antiderivative = 2.46 \[ \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\text {Too large to display} \]
1/939401947876392000000000000000000*(236057430135339556647698995200*x^38 - 3658890167097763128039334425600*x^37 + 31513666923067830812467815859200*x ^36 - 188019743102797956869892249676800*x^35 + 861226026670019454984548821 612800*x^34 - 3183721313824708059229806829449600*x^33 + 983137886463415569 0152529676838400*x^32 - 25933999577342884900069590431438400*x^31 + 5953780 1053669957636238873995743000*x^30 - 120659917686431634864896285011569300*x ^29 + 218815205755728685314344512920641100*x^28 - 358981964316724903316209 908944483400*x^27 + 538611677703407694971607759062726400*x^26 - 7447470585 99416616000621120456199500*x^25 + 956690308445988798962145796617987300*x^2 4 - 1146215696378789191186353021849349200*x^23 + 1289373540942278637875926 769729056200*x^22 - 1362598128377218516278181645663204500*x^21 + 136327109 2148660247173548652450625900*x^20 - 1285053072164246491655277964217182200* x^19 + 1156090273753138114015372080442309200*x^18 - 9766620312336288205738 07397218635500*x^17 + 798237355988012151640630610578068900*x^16 - 60237857 5789760029562840059112791200*x^15 + 453947813134211818985370625408991400*x ^14 - 299561768273477509253114104689745500*x^13 + 216090200276716466450059 917698391300*x^12 - 116372548125131610054621102465641400*x^11 + 8869828798 9963515100607660442952800*x^10 - 31524301955764963385813894907485700*x^9 + 33341076472331463305896468245703500*x^8 - 3040034262620530630502524237160 400*x^7 + 11599438873255147841572220445070200*x^6 + 1565914164733200701...
Timed out. \[ \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\text {Timed out} \]
\[ \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\int { \frac {1}{{\left (2 \, x^{2} + x + 1\right )}^{10} {\left (x^{2} - 2 \, x + 3\right )}^{\frac {21}{2}}} \,d x } \]
Timed out. \[ \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\text {Timed out} \]
Timed out. \[ \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\int \frac {1}{{\left (2\,x^2+x+1\right )}^{10}\,{\left (x^2-2\,x+3\right )}^{21/2}} \,d x \]
\[ \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\int \frac {\sqrt {x^{2}-2 x +3}}{1024 x^{42}-17408 x^{41}+163072 x^{40}-1059840 x^{39}+5294720 x^{38}-21409152 x^{37}+72501024 x^{36}-210353856 x^{35}+532338420 x^{34}-1191461700 x^{33}+2387723889 x^{32}-4329193728 x^{31}+7171025142 x^{30}-10938959220 x^{29}+15482374950 x^{28}-20441554296 x^{27}+25316000622 x^{26}-29502127788 x^{25}+32502050290 x^{24}-33883949360 x^{23}+33595551166 x^{22}-31604802132 x^{21}+28438741598 x^{20}-24253023240 x^{19}+19949752830 x^{18}-15409638228 x^{17}+11697087396 x^{16}-8094599584 x^{15}+5789499650 x^{14}-3456463420 x^{13}+2465340786 x^{12}-1136849672 x^{11}+940451658 x^{10}-234461700 x^{9}+339398910 x^{8}+4848336 x^{7}+110547018 x^{6}+20741508 x^{5}+26309610 x^{4}+5511240 x^{3}+3503574 x^{2}+472392 x +177147}d x \]
int(1/(sqrt(x**2 - 2*x + 3)*(1024*x**40 - 15360*x**39 + 129280*x**38 - 755 200*x**37 + 3396480*x**36 - 12350592*x**35 + 37610400*x**34 - 98081280*x** 33 + 223344660*x**32 - 450528540*x**31 + 816632829*x**30 - 1344342450*x**2 9 + 2032441755*x**28 - 2841048360*x**27 + 3702952965*x**26 - 4512503286*x* *25 + 5182135155*x**24 - 5600347620*x**23 + 5754949585*x**22 - 5573007330* x**21 + 5184687751*x**20 - 4516404640*x**19 + 3851869065*x**18 - 300007119 0*x**17 + 2394003255*x**16 - 1621418148*x**15 + 1272241335*x**14 - 6858624 70*x**13 + 601050705*x**12 - 196774600*x**11 + 268639471*x**10 - 9246930*x **9 + 116039385*x**8 + 25357860*x**7 + 41996475*x**6 + 12767706*x**5 + 100 93005*x**4 + 2624400*x**3 + 1279395*x**2 + 196830*x + 59049)),x)
int(sqrt(x**2 - 2*x + 3)/(1024*x**42 - 17408*x**41 + 163072*x**40 - 105984 0*x**39 + 5294720*x**38 - 21409152*x**37 + 72501024*x**36 - 210353856*x**3 5 + 532338420*x**34 - 1191461700*x**33 + 2387723889*x**32 - 4329193728*x** 31 + 7171025142*x**30 - 10938959220*x**29 + 15482374950*x**28 - 2044155429 6*x**27 + 25316000622*x**26 - 29502127788*x**25 + 32502050290*x**24 - 3388 3949360*x**23 + 33595551166*x**22 - 31604802132*x**21 + 28438741598*x**20 - 24253023240*x**19 + 19949752830*x**18 - 15409638228*x**17 + 11697087396* x**16 - 8094599584*x**15 + 5789499650*x**14 - 3456463420*x**13 + 246534078 6*x**12 - 1136849672*x**11 + 940451658*x**10 - 234461700*x**9 + 339398910* x**8 + 4848336*x**7 + 110547018*x**6 + 20741508*x**5 + 26309610*x**4 + 551 1240*x**3 + 3503574*x**2 + 472392*x + 177147),x)