3.51 \(\int \frac{1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx\)
Optimal. Leaf size=638 \[ \text{result too large to display} \]
[Out]
(37358055634422583 - 14024622879097678*x)/(1840124479200000000*(3 - 2*x + x^2)^(
19/2)) + (476849951294984711 - 125181871472148210*x)/(104273720488000000000*(3 -
2*x + x^2)^(17/2)) + (7851758375483333511 + 1942164996204584234*x)/(15641058073
200000000000*(3 - 2*x + x^2)^(15/2)) - (11*(7502325106308201089 - 78139863797265
16886*x))/(406667509903200000000000*(3 - 2*x + x^2)^(13/2)) - (3*(69053268515296
359011 - 44840736195018286006*x))/(1147010925368000000000000*(3 - 2*x + x^2)^(11
/2)) - (838519439380295335657 - 466189390555853643870*x)/(9384634843920000000000
000*(3 - 2*x + x^2)^(9/2)) - (1117646664729238460189 - 568839749685437871554*x)/
(31282116146400000000000000*(3 - 2*x + x^2)^(7/2)) - (6551405511565449301689 - 3
127298559983309301910*x)/(521368602440000000000000000*(3 - 2*x + x^2)^(5/2)) - (
4179039782398459850819 - 1886993445589652402694*x)/(1042737204880000000000000000
*(3 - 2*x + x^2)^(3/2)) - (12105495874518671061833 - 5117656435043679338190*x)/(
10427372048800000000000000000*Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(630*(3 - 2*x +
x^2)^(19/2)*(1 + x + 2*x^2)^9) + (887 + 2218*x)/(88200*(3 - 2*x + x^2)^(19/2)*(1
+ x + 2*x^2)^8) + (14453 + 29371*x)/(1080450*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*
x^2)^7) + (8837931 + 17459234*x)/(605052000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^
2)^6) + (447940041 + 813432205*x)/(26471025000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2
*x^2)^5) + (592729157441 + 911061463974*x)/(29647548000000*(3 - 2*x + x^2)^(19/2
)*(1 + x + 2*x^2)^4) + (277010166219 + 310705340015*x)/(12353145000000*(3 - 2*x
+ x^2)^(19/2)*(1 + x + 2*x^2)^3) + (5488221294349 + 1384103301166*x)/(2767104480
00000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^2) - (37857197792117 + 146548895467
025*x)/(2421216420000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)) + (Sqrt[(810422
25921274689605478944797800854846405 + 57305922523001707126026363878666500308992*
Sqrt[2])/70]*ArcTan[(Sqrt[5/(7*(81042225921274689605478944797800854846405 + 5730
5922523001707126026363878666500308992*Sqrt[2]))]*(272944589523248381749 + 191941
026386645109841*Sqrt[2] + (656826642296538601431 + 464885615909893491590*Sqrt[2]
)*x))/Sqrt[3 - 2*x + x^2]])/32282885600000000000000000 - (Sqrt[(-810422259212746
89605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2])/
70]*ArcTanh[(Sqrt[5/(7*(-81042225921274689605478944797800854846405 + 57305922523
001707126026363878666500308992*Sqrt[2]))]*(272944589523248381749 - 1919410263866
45109841*Sqrt[2] + (656826642296538601431 - 464885615909893491590*Sqrt[2])*x))/S
qrt[3 - 2*x + x^2]])/32282885600000000000000000
_______________________________________________________________________________________
Rubi [A] time = 2.83471, antiderivative size = 638, normalized size of antiderivative = 1.,
number of steps used = 24, number of rules used = 6, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.261
\[ -\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] Int[1/((3 - 2*x + x^2)^(21/2)*(1 + x + 2*x^2)^10),x]
[Out]
(37358055634422583 - 14024622879097678*x)/(1840124479200000000*(3 - 2*x + x^2)^(
19/2)) + (476849951294984711 - 125181871472148210*x)/(104273720488000000000*(3 -
2*x + x^2)^(17/2)) + (7851758375483333511 + 1942164996204584234*x)/(15641058073
200000000000*(3 - 2*x + x^2)^(15/2)) - (11*(7502325106308201089 - 78139863797265
16886*x))/(406667509903200000000000*(3 - 2*x + x^2)^(13/2)) - (3*(69053268515296
359011 - 44840736195018286006*x))/(1147010925368000000000000*(3 - 2*x + x^2)^(11
/2)) - (838519439380295335657 - 466189390555853643870*x)/(9384634843920000000000
000*(3 - 2*x + x^2)^(9/2)) - (1117646664729238460189 - 568839749685437871554*x)/
(31282116146400000000000000*(3 - 2*x + x^2)^(7/2)) - (6551405511565449301689 - 3
127298559983309301910*x)/(521368602440000000000000000*(3 - 2*x + x^2)^(5/2)) - (
4179039782398459850819 - 1886993445589652402694*x)/(1042737204880000000000000000
*(3 - 2*x + x^2)^(3/2)) - (12105495874518671061833 - 5117656435043679338190*x)/(
10427372048800000000000000000*Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(630*(3 - 2*x +
x^2)^(19/2)*(1 + x + 2*x^2)^9) + (887 + 2218*x)/(88200*(3 - 2*x + x^2)^(19/2)*(1
+ x + 2*x^2)^8) + (14453 + 29371*x)/(1080450*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*
x^2)^7) + (8837931 + 17459234*x)/(605052000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^
2)^6) + (447940041 + 813432205*x)/(26471025000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2
*x^2)^5) + (592729157441 + 911061463974*x)/(29647548000000*(3 - 2*x + x^2)^(19/2
)*(1 + x + 2*x^2)^4) + (277010166219 + 310705340015*x)/(12353145000000*(3 - 2*x
+ x^2)^(19/2)*(1 + x + 2*x^2)^3) + (5488221294349 + 1384103301166*x)/(2767104480
00000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^2) - (37857197792117 + 146548895467
025*x)/(2421216420000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)) + (Sqrt[(810422
25921274689605478944797800854846405 + 57305922523001707126026363878666500308992*
Sqrt[2])/70]*ArcTan[(Sqrt[5/(7*(81042225921274689605478944797800854846405 + 5730
5922523001707126026363878666500308992*Sqrt[2]))]*(272944589523248381749 + 191941
026386645109841*Sqrt[2] + (656826642296538601431 + 464885615909893491590*Sqrt[2]
)*x))/Sqrt[3 - 2*x + x^2]])/32282885600000000000000000 - (Sqrt[(-810422259212746
89605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2])/
70]*ArcTanh[(Sqrt[5/(7*(-81042225921274689605478944797800854846405 + 57305922523
001707126026363878666500308992*Sqrt[2]))]*(272944589523248381749 - 1919410263866
45109841*Sqrt[2] + (656826642296538601431 - 464885615909893491590*Sqrt[2])*x))/S
qrt[3 - 2*x + x^2]])/32282885600000000000000000
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{- 443613257029425219187500000000000 x + 1689837014901602069606250000000000}{369519996979350000000000000000000000 \left (x^{2} - 2 x + 3\right )^{\frac{17}{2}}} + \frac{- 828329288796706606875000000000 x + 2206460160908083808437500000000}{108682352052750000000000000000000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}}} - \frac{- 50 x + 5}{3150 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{9}} + \frac{221800 x + 88700}{8820000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{8}} + \frac{587420000 x + 289060000}{21609000000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{7}} + \frac{1309442550000 x + 662844825000}{45378900000000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{6}} + \frac{2440296615000000 x + 1343820123000000}{79413075000000000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{5}} + \frac{3416480489902500000 x + 2222734340403750000}{111178305000000000000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{4}} + \frac{2936165463141750000000 x + 2617746070769550000000}{116737220250000000000000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{3}} + \frac{408743006125584375000000 x + 1620740350987439062500000}{81716054175000000000000000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{2}} - \frac{1731108827704232812500000000 x + 447188148919382062500000000}{28600618961250000000000000000 \left (x^{2} - 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )} - \frac{\int \frac{14195624224941607014000000000000000 x^{2} - 35273795655183209407237500000000000 x + 14762203931705757912393750000000000}{\left (x^{2} - 2 x + 3\right )^{\frac{17}{2}} \left (2 x^{2} + x + 1\right )}\, dx}{369519996979350000000000000000000000} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**2-2*x+3)**(21/2)/(2*x**2+x+1)**10,x)
[Out]
(-443613257029425219187500000000000*x + 1689837014901602069606250000000000)/(369
519996979350000000000000000000000*(x**2 - 2*x + 3)**(17/2)) + (-8283292887967066
06875000000000*x + 2206460160908083808437500000000)/(108682352052750000000000000
000000*(x**2 - 2*x + 3)**(19/2)) - (-50*x + 5)/(3150*(x**2 - 2*x + 3)**(19/2)*(2
*x**2 + x + 1)**9) + (221800*x + 88700)/(8820000*(x**2 - 2*x + 3)**(19/2)*(2*x**
2 + x + 1)**8) + (587420000*x + 289060000)/(21609000000*(x**2 - 2*x + 3)**(19/2)
*(2*x**2 + x + 1)**7) + (1309442550000*x + 662844825000)/(45378900000000*(x**2 -
2*x + 3)**(19/2)*(2*x**2 + x + 1)**6) + (2440296615000000*x + 1343820123000000)
/(79413075000000000*(x**2 - 2*x + 3)**(19/2)*(2*x**2 + x + 1)**5) + (34164804899
02500000*x + 2222734340403750000)/(111178305000000000000*(x**2 - 2*x + 3)**(19/2
)*(2*x**2 + x + 1)**4) + (2936165463141750000000*x + 2617746070769550000000)/(11
6737220250000000000000*(x**2 - 2*x + 3)**(19/2)*(2*x**2 + x + 1)**3) + (40874300
6125584375000000*x + 1620740350987439062500000)/(81716054175000000000000000*(x**
2 - 2*x + 3)**(19/2)*(2*x**2 + x + 1)**2) - (1731108827704232812500000000*x + 44
7188148919382062500000000)/(28600618961250000000000000000*(x**2 - 2*x + 3)**(19/
2)*(2*x**2 + x + 1)) - Integral((14195624224941607014000000000000000*x**2 - 3527
3795655183209407237500000000000*x + 14762203931705757912393750000000000)/((x**2
- 2*x + 3)**(17/2)*(2*x**2 + x + 1)), x)/369519996979350000000000000000000000
_______________________________________________________________________________________
Mathematica [C] time = 6.71662, size = 1431, normalized size = 2.24 \[ \text{result too large to display} \]
Antiderivative was successfully verified.
[In] Integrate[1/((3 - 2*x + x^2)^(21/2)*(1 + x + 2*x^2)^10),x]
[Out]
Sqrt[3 - 2*x + x^2]*((1 - x)/(11875000000*(3 - 2*x + x^2)^10) + (265 - 113*x)/(4
03750000000*(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) + (-1340879383 + 430593031*x)/(1816875000
00000000*(3 - 2*x + x^2)^4) - (11*(1626125723 + 112950205*x))/(30281250000000000
00*(3 - 2*x + x^2)^3) - (11*(3311570647 + 15286717673*x))/(36337500000000000000*
(3 - 2*x + x^2)^2) - (11*(-411521923277 + 484788625685*x))/(36337500000000000000
0*(3 - 2*x + x^2)) + (251943 + 221770*x)/(6300000000000*(1 + x + 2*x^2)^9) - (73
*(-888423 + 1604678*x))/(882000000000000*(1 + x + 2*x^2)^8) + (-2596903794 - 496
5311863*x)/(10804500000000000*(1 + x + 2*x^2)^7) + (-539608494637 - 334647150510
*x)/(1210104000000000000*(1 + x + 2*x^2)^6) + (-40800462989458 + 56711874696335*
x)/(264710250000000000000*(1 + x + 2*x^2)^5) + (42018358198215561 + 129196597088
670934*x)/(296475480000000000000000*(1 + x + 2*x^2)^4) + (62819559864314747 + 16
9630389653846945*x)/(370594350000000000000000*(1 + x + 2*x^2)^3) + (108242210919
6374795 + 4797048907791526114*x)/(8301313440000000000000000*(1 + x + 2*x^2)^2) +
(65571203144429922747 + 367152793968978953465*x)/(363182463000000000000000000*(
1 + x + 2*x^2))) + ((232442807954946745795*I + 21634177831191924841*Sqrt[7])*Arc
Tan[(-135063738860435016899586558948733259113515 + (1886308946264666902168552859
95045889396405*I)*Sqrt[7] - 1506241361872688008559268776761430483700000*x - (105
711500937472192718115651350352447938680*I)*Sqrt[7]*x + 4911535405084435870258097
89813541985707360*x^2 - (460764064177139993399975100872663310399420*I)*Sqrt[7]*x
^2 - 180084985147246689199448745264977678818020*x^3 + (1978682963779138708638376
80953446009396860*I)*Sqrt[7]*x^3 - 176004816500761880926774485599831047775825*x^
4 - (207342833228459577163557043035558264835165*I)*Sqrt[7]*x^4 + (18624424819975
5548159585682605666126004224*I)*Sqrt[10*(-5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] +
(114611845046003414252052727757333000617984*I)*Sqrt[10*(-5 + I*Sqrt[7])]*x*Sqrt[
3 - 2*x + x^2] + (300856093245758962411638410362999126622208*I)*Sqrt[10*(-5 + I*
Sqrt[7])]*x^2*Sqrt[3 - 2*x + x^2] - (143264806307504267815065909696666250772480*
I)*Sqrt[10*(-5 + I*Sqrt[7])]*x^3*Sqrt[3 - 2*x + x^2])/(2368773290838836979864678
493023884746594823*I + 423642940259238735473942663180025956729505*Sqrt[7] + (189
0613486065620301760074218556745311646936*I)*x + 61505745593112282583943287779420
59796320*Sqrt[7]*x + (2511300259855822962340893027852239157667820*I)*x^2 - 20278
67550801106189867763431094227596320*Sqrt[7]*x^2 - (31342177462307603571283187974
99380812303788*I)*x^3 + 63430431602720043279192866968369397935660*Sqrt[7]*x^3 +
(944749064886626467328385369190460703669697*I)*x^4 + 163813177651072647894629172
21030750634835*Sqrt[7]*x^4)])/(16141442800000000000000000*Sqrt[70*(-5 + I*Sqrt[7
])]) - ((I/16141442800000000000000000)*(-232442807954946745795*I + 2163417783119
1924841*Sqrt[7])*ArcTan[(35*(4362494290663946676585186218212607628595*I + 121040
84007406821013541218948000741620843*Sqrt[7] - (409190315966173327071960945007832
37405000*I)*x + 175730701694606521668409393655487422752*Sqrt[7]*x + (26487288329
265127577733965853364310310620*I)*x^2 - 57939072880031605424793240888406502752*S
qrt[7]*x^2 - (15238894149752825683924814021007863070620*I)*x^3 + 181229804579200
1236548367627667697083876*Sqrt[7]*x^3 - (795837271959975808913244203765619963595
*I)*x^4 + 468037650431636136841797634886592875281*Sqrt[7]*x^4))/(135063738860435
016899586558948733259113515 + (188630894626466690216855285995045889396405*I)*Sqr
t[7] + 1506241361872688008559268776761430483700000*x - (105711500937472192718115
651350352447938680*I)*Sqrt[7]*x - 491153540508443587025809789813541985707360*x^2
- (460764064177139993399975100872663310399420*I)*Sqrt[7]*x^2 + 1800849851472466
89199448745264977678818020*x^3 + (197868296377913870863837680953446009396860*I)*
Sqrt[7]*x^3 + 176004816500761880926774485599831047775825*x^4 - (2073428332284595
77163557043035558264835165*I)*Sqrt[7]*x^4 - (14326480630750426781506590969666625
077248*I)*Sqrt[70*(5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] - (1432648063075042678150
6590969666625077248*I)*Sqrt[70*(5 + I*Sqrt[7])]*x^2*Sqrt[3 - 2*x + x^2] + (28652
961261500853563013181939333250154496*I)*Sqrt[70*(5 + I*Sqrt[7])]*x^3*Sqrt[3 - 2*
x + x^2])])/Sqrt[70*(5 + I*Sqrt[7])] - ((-232442807954946745795*I + 216341778311
91924841*Sqrt[7])*Log[(-I + Sqrt[7] - (4*I)*x)^2*(I + Sqrt[7] + (4*I)*x)^2])/(32
282885600000000000000000*Sqrt[70*(5 + I*Sqrt[7])]) + ((I/32282885600000000000000
000)*(232442807954946745795*I + 21634177831191924841*Sqrt[7])*Log[(-I + Sqrt[7]
- (4*I)*x)^2*(I + Sqrt[7] + (4*I)*x)^2])/Sqrt[70*(-5 + I*Sqrt[7])] - ((I/3228288
5600000000000000000)*(232442807954946745795*I + 21634177831191924841*Sqrt[7])*Lo
g[(1 + x + 2*x^2)*(-13*I + 15*Sqrt[7] + (22*I)*x - 10*Sqrt[7]*x + (9*I)*x^2 + 5*
Sqrt[7]*x^2 + I*Sqrt[70*(-5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] - I*Sqrt[70*(-5 +
I*Sqrt[7])]*x*Sqrt[3 - 2*x + x^2])])/Sqrt[70*(-5 + I*Sqrt[7])] + ((-232442807954
946745795*I + 21634177831191924841*Sqrt[7])*Log[(1 + x + 2*x^2)*(-163*I + 15*Sqr
t[7] + (122*I)*x - 10*Sqrt[7]*x - (41*I)*x^2 + 5*Sqrt[7]*x^2 - (13*I)*Sqrt[10*(5
+ I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] + (5*I)*Sqrt[10*(5 + I*Sqrt[7])]*x*Sqrt[3 - 2
*x + x^2])])/(32282885600000000000000000*Sqrt[70*(5 + I*Sqrt[7])])
_______________________________________________________________________________________
Maple [B] time = 4.895, size = 86793, normalized size = 136. \[ \text{output too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^2-2*x+3)^(21/2)/(2*x^2+x+1)^10,x)
[Out]
result too large to display
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{10}{\left (x^{2} - 2 \, x + 3\right )}^{\frac{21}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x^2 + x + 1)^10*(x^2 - 2*x + 3)^(21/2)),x, algorithm="maxima")
[Out]
integrate(1/((2*x^2 + x + 1)^10*(x^2 - 2*x + 3)^(21/2)), x)
_______________________________________________________________________________________
Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x^2 + x + 1)^10*(x^2 - 2*x + 3)^(21/2)),x, algorithm="fricas")
[Out]
Timed out
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**2-2*x+3)**(21/2)/(2*x**2+x+1)**10,x)
[Out]
Timed out
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.350931, size = 1, normalized size = 0. \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x^2 + x + 1)^10*(x^2 - 2*x + 3)^(21/2)),x, algorithm="giac")
[Out]
Done