Optimal. Leaf size=638 \[ -\frac {12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt {x^2-2 x+3}}-\frac {146548895467025 x+37857197792117}{2421216420000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}-\frac {4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (x^2-2 x+3\right )^{3/2}}+\frac {1384103301166 x+5488221294349}{276710448000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}-\frac {6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (x^2-2 x+3\right )^{5/2}}+\frac {310705340015 x+277010166219}{12353145000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (x^2-2 x+3\right )^{7/2}}+\frac {911061463974 x+592729157441}{29647548000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (x^2-2 x+3\right )^{9/2}}+\frac {813432205 x+447940041}{26471025000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (x^2-2 x+3\right )^{11/2}}+\frac {17459234 x+8837931}{605052000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (x^2-2 x+3\right )^{13/2}}+\frac {29371 x+14453}{1080450 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}+\frac {1942164996204584234 x+7851758375483333511}{15641058073200000000000 \left (x^2-2 x+3\right )^{15/2}}+\frac {2218 x+887}{88200 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (x^2-2 x+3\right )^{17/2}}-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}+\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (x^2-2 x+3\right )^{19/2}}+\frac {\sqrt {\frac {1}{70} \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )} \tan ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )}} \left (\left (656826642296538601431+464885615909893491590 \sqrt {2}\right ) x+191941026386645109841 \sqrt {2}+272944589523248381749\right )}{\sqrt {x^2-2 x+3}}\right )}{32282885600000000000000000}-\frac {\sqrt {\frac {1}{70} \left (57305922523001707126026363878666500308992 \sqrt {2}-81042225921274689605478944797800854846405\right )} \tanh ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (57305922523001707126026363878666500308992 \sqrt {2}-81042225921274689605478944797800854846405\right )}} \left (\left (656826642296538601431-464885615909893491590 \sqrt {2}\right ) x-191941026386645109841 \sqrt {2}+272944589523248381749\right )}{\sqrt {x^2-2 x+3}}\right )}{32282885600000000000000000} \]
[Out]
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Rubi [A] time = 1.40, antiderivative size = 638, normalized size of antiderivative = 1.00, number of steps used = 24, number of rules used = 6, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.261, Rules used = {974, 1060, 1035, 1029, 206, 204} \[ -\frac {12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt {x^2-2 x+3}}-\frac {146548895467025 x+37857197792117}{2421216420000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}-\frac {4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (x^2-2 x+3\right )^{3/2}}+\frac {1384103301166 x+5488221294349}{276710448000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}-\frac {6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (x^2-2 x+3\right )^{5/2}}+\frac {310705340015 x+277010166219}{12353145000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (x^2-2 x+3\right )^{7/2}}+\frac {911061463974 x+592729157441}{29647548000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (x^2-2 x+3\right )^{9/2}}+\frac {813432205 x+447940041}{26471025000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (x^2-2 x+3\right )^{11/2}}+\frac {17459234 x+8837931}{605052000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (x^2-2 x+3\right )^{13/2}}+\frac {29371 x+14453}{1080450 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}+\frac {1942164996204584234 x+7851758375483333511}{15641058073200000000000 \left (x^2-2 x+3\right )^{15/2}}+\frac {2218 x+887}{88200 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (x^2-2 x+3\right )^{17/2}}-\frac {1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}+\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (x^2-2 x+3\right )^{19/2}}+\frac {\sqrt {\frac {1}{70} \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )} \tan ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )}} \left (\left (656826642296538601431+464885615909893491590 \sqrt {2}\right ) x+191941026386645109841 \sqrt {2}+272944589523248381749\right )}{\sqrt {x^2-2 x+3}}\right )}{32282885600000000000000000}-\frac {\sqrt {\frac {1}{70} \left (57305922523001707126026363878666500308992 \sqrt {2}-81042225921274689605478944797800854846405\right )} \tanh ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (57305922523001707126026363878666500308992 \sqrt {2}-81042225921274689605478944797800854846405\right )}} \left (\left (656826642296538601431-464885615909893491590 \sqrt {2}\right ) x-191941026386645109841 \sqrt {2}+272944589523248381749\right )}{\sqrt {x^2-2 x+3}}\right )}{32282885600000000000000000} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 204
Rule 206
Rule 974
Rule 1029
Rule 1035
Rule 1060
Rubi steps
\begin {align*} \int \frac {1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}-\frac {\int \frac {-2960+3060 x-1800 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^9} \, dx}{3150}\\ &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}-\frac {\int \frac {-8066100+8650900 x-7541200 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^8} \, dx}{8820000}\\ &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}-\frac {\int \frac {-18577805000+18950890000 x-18797440000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^7} \, dx}{21609000000}\\ &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}-\frac {\int \frac {-34422218025000+37067282625000 x-39283276500000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^6} \, dx}{45378900000000}\\ &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}-\frac {\int \frac {-47542711206750000+57420932725500000 x-68328305220000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^5} \, dx}{79413075000000000}\\ &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}-\frac {\int \frac {-40751213836916250000+59562989955686250000 x-88828492737465000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^4} \, dx}{111178305000000000000}\\ &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}-\frac {\int \frac {-7802817431641312500000+24109394856584625000000 x-70467971115402000000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^3} \, dx}{116737220250000000000000}\\ &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {\int \frac {16833881379064542187500000-26649709913445904687500000 x-8992346134762856250000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^2} \, dx}{81716054175000000000000000}\\ &=-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-6456478383150221671875000000-27827888668333982156250000000 x+34622176554084656250000000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )} \, dx}{28600618961250000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {4967712444964210062187500000000-37459045941891614735625000000000 x+29819854396681437847500000000000 x^2}{\left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )} \, dx}{108682352052750000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {14762203931705757912393750000000000-35273795655183209407237500000000000 x+14195624224941607014000000000000000 x^2}{\left (3-2 x+x^2\right )^{17/2} \left (1+x+2 x^2\right )} \, dx}{369519996979350000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {17682321750123664132939125000000000000-22751442786535433811492750000000000000 x-3854226434967997412373000000000000000 x^2}{\left (3-2 x+x^2\right )^{15/2} \left (1+x+2 x^2\right )} \, dx}{1108559990938050000000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {13399310005134207269200312500000000000000-7942120150303904451111225000000000000000 x-14620749915106285745394600000000000000000 x^2}{\left (3-2 x+x^2\right )^{13/2} \left (1+x+2 x^2\right )} \, dx}{2882255976438930000000000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {6370652021675523452523402750000000000000000+1397569502668803779552737500000000000000000 x-14873447992206590376760170000000000000000000 x^2}{\left (3-2 x+x^2\right )^{11/2} \left (1+x+2 x^2\right )} \, dx}{6340963148165646000000000000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {1329917982742483936025158935000000000000000000+3615108788879230023346255290000000000000000000 x-9071784474158200631669632800000000000000000000 x^2}{\left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )} \, dx}{11413733666698162800000000000000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-420915070441561410503321633100000000000000000000+2181291929685915536692331929800000000000000000000 x-3486830438264921097598322474400000000000000000000 x^2}{\left (3-2 x+x^2\right )^{7/2} \left (1+x+2 x^2\right )} \, dx}{15979227133377427920000000000000000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac {6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-379110186022081999740742476990000000000000000000000+666051943754340912077121512700000000000000000000000 x-766779031495028265360690083040000000000000000000000 x^2}{\left (3-2 x+x^2\right )^{5/2} \left (1+x+2 x^2\right )} \, dx}{15979227133377427920000000000000000000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac {6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-96896452988962143502089877773000000000000000000000000+91746249937845836577877948114800000000000000000000000 x-69400489538857249491540692270400000000000000000000000 x^2}{\left (3-2 x+x^2\right )^{3/2} \left (1+x+2 x^2\right )} \, dx}{9587536280026456752000000000000000000000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac {6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-6260702387317500351852137783268000000000000000000000000+2570011459509637702693150504488000000000000000000000000 x}{\sqrt {3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{1917507256005291350400000000000000000000000000000000000000000}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac {6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {296985108420000000000000000000000000 \left (148672670724261260159-105404315061877410477 \sqrt {2}\right )-296985108420000000000000000000000000 \left (62135959399493560795-43268355662383849682 \sqrt {2}\right ) x}{\sqrt {3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{19175072560052913504000000000000000000000000000000000000000000 \sqrt {2}}+\frac {\int \frac {296985108420000000000000000000000000 \left (148672670724261260159+105404315061877410477 \sqrt {2}\right )-296985108420000000000000000000000000 \left (62135959399493560795+43268355662383849682 \sqrt {2}\right ) x}{\sqrt {3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{19175072560052913504000000000000000000000000000000000000000000 \sqrt {2}}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac {6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac {\left (3788075362500000 \left (114611845046003414252052727757333000617984-81042225921274689605478944797800854846405 \sqrt {2}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-617401082362674084274800000000000000000000000000000000000000000000000000 \left (81042225921274689605478944797800854846405-57305922523001707126026363878666500308992 \sqrt {2}\right )-5 x^2} \, dx,x,\frac {296985108420000000000000000000000000 \left (272944589523248381749-191941026386645109841 \sqrt {2}\right )+296985108420000000000000000000000000 \left (656826642296538601431-464885615909893491590 \sqrt {2}\right ) x}{\sqrt {3-2 x+x^2}}\right )}{823543}-\frac {\left (3788075362500000 \left (114611845046003414252052727757333000617984+81042225921274689605478944797800854846405 \sqrt {2}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-617401082362674084274800000000000000000000000000000000000000000000000000 \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )-5 x^2} \, dx,x,\frac {296985108420000000000000000000000000 \left (272944589523248381749+191941026386645109841 \sqrt {2}\right )+296985108420000000000000000000000000 \left (656826642296538601431+464885615909893491590 \sqrt {2}\right ) x}{\sqrt {3-2 x+x^2}}\right )}{823543}\\ &=\frac {37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac {476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac {7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac {11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac {3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac {838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac {6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac {887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac {14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac {8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac {447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac {592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac {277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac {5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac {37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}+\frac {\sqrt {\frac {1}{70} \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )} \tan ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )}} \left (272944589523248381749+191941026386645109841 \sqrt {2}+\left (656826642296538601431+464885615909893491590 \sqrt {2}\right ) x\right )}{\sqrt {3-2 x+x^2}}\right )}{32282885600000000000000000}-\frac {\sqrt {\frac {1}{70} \left (-81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )} \tanh ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (-81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )}} \left (272944589523248381749-191941026386645109841 \sqrt {2}+\left (656826642296538601431-464885615909893491590 \sqrt {2}\right ) x\right )}{\sqrt {3-2 x+x^2}}\right )}{32282885600000000000000000}\\ \end {align*}
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Mathematica [C] time = 11.60, size = 1431, normalized size = 2.24 \[ \text {result too large to display} \]
Warning: Unable to verify antiderivative.
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fricas [B] time = 1.55, size = 2775, normalized size = 4.35 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 5.03, size = 86793, normalized size = 136.04 \[ \text {output too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (2 \, x^{2} + x + 1\right )}^{10} {\left (x^{2} - 2 \, x + 3\right )}^{\frac {21}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {1}{{\left (2\,x^2+x+1\right )}^{10}\,{\left (x^2-2\,x+3\right )}^{21/2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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