Optimal. Leaf size=638 \[ \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} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.87, 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 = {988, 1074,
1049, 1043, 212, 210} \begin {gather*} \frac {\sqrt {\frac {1}{70} \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt {2}\right )} \text {ArcTan}\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 {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 (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} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 210
Rule 212
Rule 988
Rule 1043
Rule 1049
Rule 1074
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 ) \text {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 ) \text {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] Result contains complex when optimal does not.
time = 16.85, size = 1431, normalized size = 2.24 \begin {gather*} \text {Too large to display} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(86792\) vs.
\(2(518)=1036\).
time = 4.55, size = 86793, normalized size = 136.04
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 \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 \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 | \(\text {Expression too large to display}\) | \(641\) |
default | \(\text {Expression too large to display}\) | \(86793\) |
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 2775 vs.
\(2 (518) = 1036\).
time = 1.29, size = 2775, normalized size = 4.35 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \int \frac {1}{{\left (2\,x^2+x+1\right )}^{10}\,{\left (x^2-2\,x+3\right )}^{21/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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