3.48 \(\int \frac{1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx\)

Optimal. Leaf size=648 \[ \text{result too large to display} \]

[Out]

4718120139975/(351733660450816*(3 - 2*x)^(19/2)) - 815900548375/(629418129227776
*(3 - 2*x)^(17/2)) - 3029508823715/(1555033025150976*(3 - 2*x)^(15/2)) - 1351574
3021825/(13476952884641792*(3 - 2*x)^(13/2)) - 5846828446875/(14513641568075776*
(3 - 2*x)^(11/2)) - 37283626871975/(261245548225363968*(3 - 2*x)^(9/2)) - 132355
162272575/(2844673747342852096*(3 - 2*x)^(7/2)) - 11557581705725/(81276392781224
3456*(3 - 2*x)^(5/2)) - 46601678385075/(11378694989371408384*(3 - 2*x)^(3/2)) -
24229218097975/(22757389978742816768*Sqrt[3 - 2*x]) + x/(63*(3 - 2*x)^(19/2)*(1
+ x + 2*x^2)^9) + (53 + 173*x)/(7056*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^8) + (8477
+ 21409*x)/(691488*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^7) + (5*(21409 + 47471*x))/
(6453888*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^6) + (41*(47471 + 92875*x))/(90354432*
(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^5) + (41*(3436375 + 5677637*x))/(5059848192*(3
- 2*x)^(19/2)*(1 + x + 2*x^2)^4) + (451*(811091 + 998691*x))/(10119696384*(3 - 2
*x)^(19/2)*(1 + x + 2*x^2)^3) + (451*(28962039 + 14627273*x))/(283351498752*(3 -
2*x)^(19/2)*(1 + x + 2*x^2)^2) + (11275*(14627273 - 35058731*x))/(3966920982528
*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)) + (11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589235
+ 2148932869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7
+ 2*Sqrt[14]]])/318603459702399434752 - (11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589
235 + 2148932869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[3 - 2*x])/Sqrt[
-7 + 2*Sqrt[14]]])/318603459702399434752 + (11275*(9756589235 - 2148932869*Sqrt[
14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 -
2*x] - 2*x])/637206919404798869504 - (11275*(9756589235 - 2148932869*Sqrt[14])*S
qrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] -
2*x])/637206919404798869504

_______________________________________________________________________________________

Rubi [A]  time = 2.68597, antiderivative size = 648, normalized size of antiderivative = 1., number of steps used = 29, number of rules used = 9, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.45 \[ \frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}+\frac{451 (14627273 x+28962039)}{283351498752 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}+\frac{451 (998691 x+811091)}{10119696384 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}+\frac{41 (5677637 x+3436375)}{5059848192 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}+\frac{41 (92875 x+47471)}{90354432 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}+\frac{5 (47471 x+21409)}{6453888 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}+\frac{21409 x+8477}{691488 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}+\frac{173 x+53}{7056 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}+\frac{x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac{11275 \left (9756589235-2148932869 \sqrt{14}\right ) \sqrt{\frac{1}{2} \left (2 \sqrt{14}-7\right )} \log \left (-2 x-\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right )}{637206919404798869504}-\frac{11275 \left (9756589235-2148932869 \sqrt{14}\right ) \sqrt{\frac{1}{2} \left (2 \sqrt{14}-7\right )} \log \left (-2 x+\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right )}{637206919404798869504}+\frac{11275 \sqrt{\frac{1}{2} \left (7+2 \sqrt{14}\right )} \left (9756589235+2148932869 \sqrt{14}\right ) \tan ^{-1}\left (\frac{\sqrt{7+2 \sqrt{14}}-2 \sqrt{3-2 x}}{\sqrt{2 \sqrt{14}-7}}\right )}{318603459702399434752}-\frac{11275 \sqrt{\frac{1}{2} \left (7+2 \sqrt{14}\right )} \left (9756589235+2148932869 \sqrt{14}\right ) \tan ^{-1}\left (\frac{2 \sqrt{3-2 x}+\sqrt{7+2 \sqrt{14}}}{\sqrt{2 \sqrt{14}-7}}\right )}{318603459702399434752} \]

Antiderivative was successfully verified.

[In]  Int[1/((3 - 2*x)^(21/2)*(1 + x + 2*x^2)^10),x]

[Out]

4718120139975/(351733660450816*(3 - 2*x)^(19/2)) - 815900548375/(629418129227776
*(3 - 2*x)^(17/2)) - 3029508823715/(1555033025150976*(3 - 2*x)^(15/2)) - 1351574
3021825/(13476952884641792*(3 - 2*x)^(13/2)) - 5846828446875/(14513641568075776*
(3 - 2*x)^(11/2)) - 37283626871975/(261245548225363968*(3 - 2*x)^(9/2)) - 132355
162272575/(2844673747342852096*(3 - 2*x)^(7/2)) - 11557581705725/(81276392781224
3456*(3 - 2*x)^(5/2)) - 46601678385075/(11378694989371408384*(3 - 2*x)^(3/2)) -
24229218097975/(22757389978742816768*Sqrt[3 - 2*x]) + x/(63*(3 - 2*x)^(19/2)*(1
+ x + 2*x^2)^9) + (53 + 173*x)/(7056*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^8) + (8477
+ 21409*x)/(691488*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^7) + (5*(21409 + 47471*x))/
(6453888*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^6) + (41*(47471 + 92875*x))/(90354432*
(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^5) + (41*(3436375 + 5677637*x))/(5059848192*(3
- 2*x)^(19/2)*(1 + x + 2*x^2)^4) + (451*(811091 + 998691*x))/(10119696384*(3 - 2
*x)^(19/2)*(1 + x + 2*x^2)^3) + (451*(28962039 + 14627273*x))/(283351498752*(3 -
2*x)^(19/2)*(1 + x + 2*x^2)^2) + (11275*(14627273 - 35058731*x))/(3966920982528
*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)) + (11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589235
+ 2148932869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7
+ 2*Sqrt[14]]])/318603459702399434752 - (11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589
235 + 2148932869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[3 - 2*x])/Sqrt[
-7 + 2*Sqrt[14]]])/318603459702399434752 + (11275*(9756589235 - 2148932869*Sqrt[
14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 -
2*x] - 2*x])/637206919404798869504 - (11275*(9756589235 - 2148932869*Sqrt[14])*S
qrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] -
2*x])/637206919404798869504

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x}{63 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{9}} + \frac{- 15435719146659136558464000 x + 6440121232839552246912000}{154905798615955861175009280 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )} + \frac{\int \frac{- 11813932218388106205374976000000 x - 6249079685931055968022769664000}{\left (- 2 x + 3\right )^{\frac{11}{2}} \left (2 x^{2} + x + 1\right )}\, dx}{2665985799514491042578822112215040} - \frac{5846828446875}{14513641568075776 \left (- 2 x + 3\right )^{\frac{11}{2}}} - \frac{13515743021825}{13476952884641792 \left (- 2 x + 3\right )^{\frac{13}{2}}} - \frac{3029508823715}{1555033025150976 \left (- 2 x + 3\right )^{\frac{15}{2}}} - \frac{815900548375}{629418129227776 \left (- 2 x + 3\right )^{\frac{17}{2}}} + \frac{67816 x + 20776}{2765952 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{8}} + \frac{117492592 x + 46521776}{3794886144 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{7}} + \frac{164128134240 x + 74020332960}{4462786105344 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{6}} + \frac{184316990760000 x + 94209549053760}{4373530383237120 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{5}} + \frac{157747397367934080 x + 95476201213680000}{3428847820457902080 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{4}} + \frac{89735798552133000960 x + 72879297583985544960}{2016162518429246423040 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{3}} + \frac{18400346379541577848320 x + 36432734212165998389760}{790335707224264597831680 \left (- 2 x + 3\right )^{\frac{19}{2}} \left (2 x^{2} + x + 1\right )^{2}} + \frac{4718120139975}{351733660450816 \left (- 2 x + 3\right )^{\frac{19}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(3-2*x)**(21/2)/(2*x**2+x+1)**10,x)

[Out]

x/(63*(-2*x + 3)**(19/2)*(2*x**2 + x + 1)**9) + (-15435719146659136558464000*x +
6440121232839552246912000)/(154905798615955861175009280*(-2*x + 3)**(19/2)*(2*x
**2 + x + 1)) + Integral((-11813932218388106205374976000000*x - 6249079685931055
968022769664000)/((-2*x + 3)**(11/2)*(2*x**2 + x + 1)), x)/266598579951449104257
8822112215040 - 5846828446875/(14513641568075776*(-2*x + 3)**(11/2)) - 135157430
21825/(13476952884641792*(-2*x + 3)**(13/2)) - 3029508823715/(1555033025150976*(
-2*x + 3)**(15/2)) - 815900548375/(629418129227776*(-2*x + 3)**(17/2)) + (67816*
x + 20776)/(2765952*(-2*x + 3)**(19/2)*(2*x**2 + x + 1)**8) + (117492592*x + 465
21776)/(3794886144*(-2*x + 3)**(19/2)*(2*x**2 + x + 1)**7) + (164128134240*x + 7
4020332960)/(4462786105344*(-2*x + 3)**(19/2)*(2*x**2 + x + 1)**6) + (1843169907
60000*x + 94209549053760)/(4373530383237120*(-2*x + 3)**(19/2)*(2*x**2 + x + 1)*
*5) + (157747397367934080*x + 95476201213680000)/(3428847820457902080*(-2*x + 3)
**(19/2)*(2*x**2 + x + 1)**4) + (89735798552133000960*x + 72879297583985544960)/
(2016162518429246423040*(-2*x + 3)**(19/2)*(2*x**2 + x + 1)**3) + (1840034637954
1577848320*x + 36432734212165998389760)/(790335707224264597831680*(-2*x + 3)**(1
9/2)*(2*x**2 + x + 1)**2) + 4718120139975/(351733660450816*(-2*x + 3)**(19/2))

_______________________________________________________________________________________

Mathematica [C]  time = 6.07724, size = 662, normalized size = 1.02 \[ -\frac{44193 \sqrt{3-2 x}-11993 (3-2 x)^{3/2}}{948721536 \left ((3-2 x)^2-7 (3-2 x)+14\right )^8}+\frac{891605}{12401793332096 \sqrt{3-2 x}}-\frac{55 \left (1410835658499 (3-2 x)^{3/2}-4751425354423 \sqrt{3-2 x}\right )}{68272169936228450304 \left ((3-2 x)^2-7 (3-2 x)+14\right )}+\frac{8519225}{260437659974016 (3-2 x)^{3/2}}-\frac{11 \left (1953387138017 (3-2 x)^{3/2}-6489356793153 \sqrt{3-2 x}\right )}{17068042484057112576 \left ((3-2 x)^2-7 (3-2 x)+14\right )^2}+\frac{75933}{3100448333024 (3-2 x)^{5/2}}-\frac{1406968826615 (3-2 x)^{3/2}-4402987778403 \sqrt{3-2 x}}{914359418788773888 \left ((3-2 x)^2-7 (3-2 x)+14\right )^3}+\frac{854095}{43406276662336 (3-2 x)^{7/2}}-\frac{52802422641 (3-2 x)^{3/2}-132204145097 \sqrt{3-2 x}}{32655693528170496 \left ((3-2 x)^2-7 (3-2 x)+14\right )^4}+\frac{30349}{1993145356944 (3-2 x)^{9/2}}-\frac{5 \left (38010319 (3-2 x)^{3/2}[phone] \sqrt{3-2 x}\right )}{291568692215808 \left ((3-2 x)^2-7 (3-2 x)+14\right )^5}+\frac{2365}{221460595216 (3-2 x)^{11/2}}+\frac{5 \left (5912661 (3-2 x)^{3/2}-37938085 \sqrt{3-2 x}\right )}{10413167579136 \left ((3-2 x)^2-7 (3-2 x)+14\right )^6}+\frac{165}{25705247659 (3-2 x)^{13/2}}+\frac{5 \left (340449 (3-2 x)^{3/2}-1574149 \sqrt{3-2 x}\right )}{185949421056 \left ((3-2 x)^2-7 (3-2 x)+14\right )^7}+\frac{73}{23727920916 (3-2 x)^{15/2}}+\frac{5}{4802079233 (3-2 x)^{17/2}}-\frac{47 \sqrt{3-2 x}-23 (3-2 x)^{3/2}}{4235364 \left ((3-2 x)^2-7 (3-2 x)+14\right )^9}+\frac{1}{5367029731 (3-2 x)^{19/2}}-\frac{11275 \left (2148932869 \sqrt{7}-34555708553 i\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{3-2 x}}{\sqrt{-7-i \sqrt{7}}}\right )}{22757389978742816768 \sqrt{14 \left (-7-i \sqrt{7}\right )}}-\frac{11275 \left (2148932869 \sqrt{7}[phone] i\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{3-2 x}}{\sqrt{-7+i \sqrt{7}}}\right )}{22757389978742816768 \sqrt{14 \left (-7+i \sqrt{7}\right )}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((3 - 2*x)^(21/2)*(1 + x + 2*x^2)^10),x]

[Out]

-(47*Sqrt[3 - 2*x] - 23*(3 - 2*x)^(3/2))/(4235364*(14 - 7*(3 - 2*x) + (3 - 2*x)^
2)^9) - (44193*Sqrt[3 - 2*x] - 11993*(3 - 2*x)^(3/2))/(948721536*(14 - 7*(3 - 2*
x) + (3 - 2*x)^2)^8) + (5*(-1574149*Sqrt[3 - 2*x] + 340449*(3 - 2*x)^(3/2)))/(18
5949421056*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^7) + (5*(-37938085*Sqrt[3 - 2*x] + 5
912661*(3 - 2*x)^(3/2)))/(10413167579136*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^6) - (
5*(107643741*Sqrt[3 - 2*x] + 38010319*(3 - 2*x)^(3/2)))/(291568692215808*(14 - 7
*(3 - 2*x) + (3 - 2*x)^2)^5) - (-132204145097*Sqrt[3 - 2*x] + 52802422641*(3 - 2
*x)^(3/2))/(32655693528170496*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^4) - (-4402987778
403*Sqrt[3 - 2*x] + 1406968826615*(3 - 2*x)^(3/2))/(914359418788773888*(14 - 7*(
3 - 2*x) + (3 - 2*x)^2)^3) - (11*(-6489356793153*Sqrt[3 - 2*x] + 1953387138017*(
3 - 2*x)^(3/2)))/(17068042484057112576*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^2) - (55
*(-4751425354423*Sqrt[3 - 2*x] + 1410835658499*(3 - 2*x)^(3/2)))/(68272169936228
450304*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)) + 1/(5367029731*(3 - 2*x)^(19/2)) + 5/(
4802079233*(3 - 2*x)^(17/2)) + 73/(23727920916*(3 - 2*x)^(15/2)) + 165/(25705247
659*(3 - 2*x)^(13/2)) + 2365/(221460595216*(3 - 2*x)^(11/2)) + 30349/(1993145356
944*(3 - 2*x)^(9/2)) + 854095/(43406276662336*(3 - 2*x)^(7/2)) + 75933/(31004483
33024*(3 - 2*x)^(5/2)) + 8519225/(260437659974016*(3 - 2*x)^(3/2)) + 891605/(124
01793332096*Sqrt[3 - 2*x]) - (11275*(-34555708553*I + 2148932869*Sqrt[7])*ArcTan
[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[-7 - I*Sqrt[7]]])/(22757389978742816768*Sqrt[14*(-
7 - I*Sqrt[7])]) - (11275*(34555708553*I + 2148932869*Sqrt[7])*ArcTan[(Sqrt[2]*S
qrt[3 - 2*x])/Sqrt[-7 + I*Sqrt[7]]])/(22757389978742816768*Sqrt[14*(-7 + I*Sqrt[
7])])

_______________________________________________________________________________________

Maple [A]  time = 0.072, size = 719, normalized size = 1.1 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(3-2*x)^(21/2)/(2*x^2+x+1)^10,x)

[Out]

1/86812553324672*(-165574989211387894481/65536*(3-2*x)^(23/2)+454060016891836885
81/131072*(3-2*x)^(25/2)-43462358811134257841/1179648*(3-2*x)^(27/2)[phone]
1874197/65536*(3-2*x)^(29/2)-1352841099712333/8192*(3-2*x)^(31/2)[phone]
85/786432*(3-2*x)^(33/2)-25865320405815/262144*(3-2*x)^(35/2)+544765170330150812
273/1024*(3-2*x)^(1/2)-3476987783905860258979/1536*(3-2*x)^(3/2)[phone]
8741137/2048*(3-2*x)^(5/2)-23851905772903279054347/4096*(3-2*x)^(7/2)[phone]
95383541041317/36864*(3-2*x)^(9/2)-57758421475348449750643/16384*(3-2*x)^(11/2)+
60333035869584695411551/32768*(3-2*x)^(13/2)-149770885083493978040723/196608*(3-
2*x)^(15/2)+66256899944582155696811/262144*(3-2*x)^(17/2)-1772997884154363040547
1/262144*(3-2*x)^(19/2)+2869878271121283060373/196608*(3-2*x)^(21/2))/((3-2*x)^2
-7+14*x)^9-206922416016525/1274413838809597739008*ln(3-2*x+14^(1/2)-(3-2*x)^(1/2
)*(7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))^(1/2)*14^(1/2)[phone]/6372069194
04798869504*ln(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))
^(1/2)-206922416016525/637206919404798869504/(-7+2*14^(1/2))^(1/2)*arctan((2*(3-
2*x)^(1/2)-(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))*14^(1/2)+
389615613935075/318603459702399434752/(-7+2*14^(1/2))^(1/2)*arctan((2*(3-2*x)^(1
/2)-(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))-110005543624625/
318603459702399434752/(-7+2*14^(1/2))^(1/2)*arctan((2*(3-2*x)^(1/2)-(7+2*14^(1/2
))^(1/2))/(-7+2*14^(1/2))^(1/2))*14^(1/2)[phone]/1274413838809597739008
*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))^(1/2)*14^(
1/2)-389615613935075/637206919404798869504*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*
14^(1/2))^(1/2))*(7+2*14^(1/2))^(1/2)-206922416016525/637206919404798869504/(-7+
2*14^(1/2))^(1/2)*arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^
(1/2))*(7+2*14^(1/2))*14^(1/2)[phone]/318603459702399434752/(-7+2*14^(1
/2))^(1/2)*arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*
(7+2*14^(1/2))-110005543624625/318603459702399434752/(-7+2*14^(1/2))^(1/2)*arcta
n((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*14^(1/2)+1/53670
29731/(3-2*x)^(19/2)+5/4802079233/(3-2*x)^(17/2)+73/23727920916/(3-2*x)^(15/2)+1
65/25705247659/(3-2*x)^(13/2)+2365/221460595216/(3-2*x)^(11/2)+30349/19931453569
44/(3-2*x)^(9/2)+854095/43406276662336/(3-2*x)^(7/2)+75933/3100448333024/(3-2*x)
^(5/2)+8519225/260437659974016/(3-2*x)^(3/2)+891605/12401793332096/(3-2*x)^(1/2)

_______________________________________________________________________________________

Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{10}{\left (-2 \, x + 3\right )}^{\frac{21}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((2*x^2 + x + 1)^10*(-2*x + 3)^(21/2)),x, algorithm="maxima")

[Out]

integrate(1/((2*x^2 + x + 1)^10*(-2*x + 3)^(21/2)), x)

_______________________________________________________________________________________

Fricas [A]  time = 0.340481, size = 2839, normalized size = 4.38 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((2*x^2 + x + 1)^10*(-2*x + 3)^(21/2)),x, algorithm="fricas")

[Out]

1/5520330666373161526201587121296845762985984*sqrt(1169607525756986)*2744^(3/4)*
(52052026180937767452848051100*sqrt(584803762878493)*sqrt(14)*(262144*x^27 - 235
9296*x^26 + 8847360*x^25 - 19070976*x^24 + 31260672*x^23 - 50135040*x^22 + 72400
896*x^21 - 84787200*x^20 + 97449984*x^19 - 111622144*x^18 + 102818304*x^17 - 940
63104*x^16 + 92761344*x^15 - 66772224*x^14 + 51609024*x^13 - 46803648*x^12 + 230
42340*x^11 - 18046404*x^10 + 14741135*x^9 - 2785131*x^8 + 5374836*x^7 - 1955988*
x^6 - 185166*x^5 - 1395306*x^4 - 454896*x^3 - 314928*x^2 - 59049*x - 19683)*sqrt
(-2*x + 3)*arctan(16374505360597804*sqrt(584803762878493)*(34555708553*sqrt(14)*
sqrt(7) - 128466244977*sqrt(7))/(sqrt(1169607525756986)*sqrt(584803762878493)*27
44^(1/4)*(327571850528462403199*sqrt(14)*sqrt(7) - 1226422380928157351936*sqrt(7
))*sqrt(-sqrt(14)*(sqrt(1169607525756986)*sqrt(584803762878493)*2744^(1/4)*sqrt(
-2*x + 3)*(175320511461144249215884155105036697334780557825844346777597368604642
24411*sqrt(14) - 655989286765353399282614782661181821311507917509232773908588405
51081105174)*sqrt((327571850528462403199*sqrt(14) - 1226422380928157351936)/(401
741448850159339627110059970918575243264*sqrt(14) - 15031791490312343499602852179
20460999509255)) + 1169607525756986*sqrt(14)*(9851038797403007693481164496466631
11706904845321946338203465849*sqrt(14)*(2*x - 3) - 73718424171802007461447271393
14482572723741509811671017998778368*x + 1105776362577030111921709070897172385908
5612264717506526998167552) - 161305887595532493954271272717628366348235659335650
15784697865123790835338395596*sqrt(14) + 603551365887997350439914133026453820377
41125045785121622154554520755897091751936)/(985103879740300769348116449646663111
706904845321946338203465849*sqrt(14) - 36859212085901003730723635696572412863618
70754905835508999389184))*sqrt((327571850528462403199*sqrt(14) - 122642238092815
7351936)/(401741448850159339627110059970918575243264*sqrt(14) - 1503179149031234
349960285217920460999509255)) + 8187252680298902*sqrt(1169607525756986)*2744^(1/
4)*sqrt(-2*x + 3)*(327571850528462403199*sqrt(14) - 1226422380928157351936)*sqrt
((327571850528462403199*sqrt(14) - 1226422380928157351936)/(40174144885015933962
7110059970918575243264*sqrt(14) - 1503179149031234349960285217920460999509255))
- 114621537524184628*sqrt(584803762878493)*(2148932869*sqrt(14) - 9756589235)))
+ 52052026180937767452848051100*sqrt(584803762878493)*sqrt(14)*(262144*x^27 - 23
59296*x^26 + 8847360*x^25 - 19070976*x^24 + 31260672*x^23 - 50135040*x^22 + 7240
0896*x^21 - 84787200*x^20 + 97449984*x^19 - 111622144*x^18 + 102818304*x^17 - 94
063104*x^16 + 92761344*x^15 - 66772224*x^14 + 51609024*x^13 - 46803648*x^12 + 23
042340*x^11 - 18046404*x^10 + 14741135*x^9 - 2785131*x^8 + 5374836*x^7 - 1955988
*x^6 - 185166*x^5 - 1395306*x^4 - 454896*x^3 - 314928*x^2 - 59049*x - 19683)*sqr
t(-2*x + 3)*arctan(16374505360597804*sqrt(584803762878493)*(34555708553*sqrt(14)
*sqrt(7) - 128466244977*sqrt(7))/(sqrt(1169607525756986)*sqrt(584803762878493)*2
744^(1/4)*(327571850528462403199*sqrt(14)*sqrt(7) - 1226422380928157351936*sqrt(
7))*sqrt(sqrt(14)*(sqrt(1169607525756986)*sqrt(584803762878493)*2744^(1/4)*sqrt(
-2*x + 3)*(175320511461144249215884155105036697334780557825844346777597368604642
24411*sqrt(14) - 655989286765353399282614782661181821311507917509232773908588405
51081105174)*sqrt((327571850528462403199*sqrt(14) - 1226422380928157351936)/(401
741448850159339627110059970918575243264*sqrt(14) - 15031791490312343499602852179
20460999509255)) - 1169607525756986*sqrt(14)*(9851038797403007693481164496466631
11706904845321946338203465849*sqrt(14)*(2*x - 3) - 73718424171802007461447271393
14482572723741509811671017998778368*x + 1105776362577030111921709070897172385908
5612264717506526998167552) + 161305887595532493954271272717628366348235659335650
15784697865123790835338395596*sqrt(14) - 603551365887997350439914133026453820377
41125045785121622154554520755897091751936)/(985103879740300769348116449646663111
706904845321946338203465849*sqrt(14) - 36859212085901003730723635696572412863618
70754905835508999389184))*sqrt((327571850528462403199*sqrt(14) - 122642238092815
7351936)/(401741448850159339627110059970918575243264*sqrt(14) - 1503179149031234
349960285217920460999509255)) + 8187252680298902*sqrt(1169607525756986)*2744^(1/
4)*sqrt(-2*x + 3)*(327571850528462403199*sqrt(14) - 1226422380928157351936)*sqrt
((327571850528462403199*sqrt(14) - 1226422380928157351936)/(40174144885015933962
7110059970918575243264*sqrt(14) - 1503179149031234349960285217920460999509255))
+ 114621537524184628*sqrt(584803762878493)*(2148932869*sqrt(14) - 9756589235)))
+ 426093525*sqrt(584803762878493)*(327571850528462403199*sqrt(14)*sqrt(7)*(26214
4*x^27 - 2359296*x^26 + 8847360*x^25 - 19070976*x^24 + 31260672*x^23 - 50135040*
x^22 + 72400896*x^21 - 84787200*x^20 + 97449984*x^19 - 111622144*x^18 + 10281830
4*x^17 - 94063104*x^16 + 92761344*x^15 - 66772224*x^14 + 51609024*x^13 - 4680364
8*x^12 + 23042340*x^11 - 18046404*x^10 + 14741135*x^9 - 2785131*x^8 + 5374836*x^
7 - 1955988*x^6 - 185166*x^5 - 1395306*x^4 - 454896*x^3 - 314928*x^2 - 59049*x -
19683) - 1226422380928157351936*sqrt(7)*(262144*x^27 - 2359296*x^26 + 8847360*x
^25 - 19070976*x^24 + 31260672*x^23 - 50135040*x^22 + 72400896*x^21 - 84787200*x
^20 + 97449984*x^19 - 111622144*x^18 + 102818304*x^17 - 94063104*x^16 + 92761344
*x^15 - 66772224*x^14 + 51609024*x^13 - 46803648*x^12 + 23042340*x^11 - 18046404
*x^10 + 14741135*x^9 - 2785131*x^8 + 5374836*x^7 - 1955988*x^6 - 185166*x^5 - 13
95306*x^4 - 454896*x^3 - 314928*x^2 - 59049*x - 19683))*sqrt(-2*x + 3)*log(-7434
3543858280221683125/4*sqrt(14)*(sqrt(1169607525756986)*sqrt(584803762878493)*274
4^(1/4)*sqrt(-2*x + 3)*(17532051146114424921588415510503669733478055782584434677
759736860464224411*sqrt(14) - 65598928676535339928261478266118182131150791750923
277390858840551081105174)*sqrt((327571850528462403199*sqrt(14) - 122642238092815
7351936)/(401741448850159339627110059970918575243264*sqrt(14) - 1503179149031234
349960285217920460999509255)) + 1169607525756986*sqrt(14)*(985103879740300769348
116449646663111706904845321946338203465849*sqrt(14)*(2*x - 3) - 7371842417180200
746144727139314482572723741509811671017998778368*x + 110577636257703011192170907
08971723859085612264717506526998167552) - 16130588759553249395427127271762836634
823565933565015784697865123790835338395596*sqrt(14) + 60355136588799735043991413
302645382037741125045785121622154554520755897091751936)/(98510387974030076934811
6449646663111706904845321946338203465849*sqrt(14) - 3685921208590100373072363569
657241286361870754905835508999389184)) - 426093525*sqrt(584803762878493)*(327571
850528462403199*sqrt(14)*sqrt(7)*(262144*x^27 - 2359296*x^26 + 8847360*x^25 - 19
070976*x^24 + 31260672*x^23 - 50135040*x^22 + 72400896*x^21 - 84787200*x^20 + 97
449984*x^19 - 111622144*x^18 + 102818304*x^17 - 94063104*x^16 + 92761344*x^15 -
66772224*x^14 + 51609024*x^13 - 46803648*x^12 + 23042340*x^11 - 18046404*x^10 +
14741135*x^9 - 2785131*x^8 + 5374836*x^7 - 1955988*x^6 - 185166*x^5 - 1395306*x^
4 - 454896*x^3 - 314928*x^2 - 59049*x - 19683) - 1226422380928157351936*sqrt(7)*
(262144*x^27 - 2359296*x^26 + 8847360*x^25 - 19070976*x^24 + 31260672*x^23 - 501
35040*x^22 + 72400896*x^21 - 84787200*x^20 + 97449984*x^19 - 111622144*x^18 + 10
2818304*x^17 - 94063104*x^16 + 92761344*x^15 - 66772224*x^14 + 51609024*x^13 - 4
6803648*x^12 + 23042340*x^11 - 18046404*x^10 + 14741135*x^9 - 2785131*x^8 + 5374
836*x^7 - 1955988*x^6 - 185166*x^5 - 1395306*x^4 - 454896*x^3 - 314928*x^2 - 590
49*x - 19683))*sqrt(-2*x + 3)*log(74343543858280221683125/4*sqrt(14)*(sqrt(11696
07525756986)*sqrt(584803762878493)*2744^(1/4)*sqrt(-2*x + 3)*(175320511461144249
21588415510503669733478055782584434677759736860464224411*sqrt(14) - 655989286765
35339928261478266118182131150791750923277390858840551081105174)*sqrt((3275718505
28462403199*sqrt(14) - 1226422380928157351936)/(40174144885015933962711005997091
8575243264*sqrt(14) - 1503179149031234349960285217920460999509255)) - 1169607525
756986*sqrt(14)*(985103879740300769348116449646663111706904845321946338203465849
*sqrt(14)*(2*x - 3) - 7371842417180200746144727139314482572723741509811671017998
778368*x + 11057763625770301119217090708971723859085612264717506526998167552) +
16130588759553249395427127271762836634823565933565015784697865123790835338395596
*sqrt(14) - 60355136588799735043991413302645382037741125045785121622154554520755
897091751936)/(985103879740300769348116449646663111706904845321946338203465849*s
qrt(14) - 3685921208590100373072363569657241286361870754905835508999389184)) - 2
*sqrt(1169607525756986)*2744^(1/4)*(327571850528462403199*sqrt(14)*sqrt(7)*(2400
31204937714427494400*x^27 - 2621948941596237063782400*x^26 + 1236504505589681110
5484800*x^25 - 33969890064381284111155200*x^24 + 65360120291258796757811200*x^23
- 106701725825102321939251200*x^22 + 162290307223249502039654400*x^21 - 2166342
28326470609547509760*x^20 + 253788172995391086570485760*x^19 - 28727915918029130
5208156160*x^18 + 304010591010966811155955200*x^17 - 282644664539994827031006720
*x^16 + 258819256815163249845447936*x^15 - 229408132984166521977166336*x^14 + 17
2649692294614969274168896*x^13 - 133312541377246386115890240*x^12 + 102031573634
317834547976132*x^11 - 59791102681494117572149176*x^10 + 41613884937255303086792
337*x^9 - 27246604251076689552043953*x^8 + 10718131725916893151555068*x^7 - 8685
973988079840377705700*x^6 + 3673303058277822225386926*x^5 - 80999036209504421005
4958*x^4 + 1362587089603925431664856*x^3 + 111926768697602999806116*x^2 + 205702
452014540322797289*x - 4884417100172357749737) - 1226422380928157351936*sqrt(7)*
(240031204937714427494400*x^27 - 2621948941596237063782400*x^26 + 12365045055896
811105484800*x^25 - 33969890064381284111155200*x^24 + 65360120291258796757811200
*x^23 - 106701725825102321939251200*x^22 + 162290307223249502039654400*x^21 - 21
6634228326470609547509760*x^20 + 253788172995391086570485760*x^19 - 287279159180
291305208156160*x^18 + 304010591010966811155955200*x^17 - 2826446645399948270310
06720*x^16 + 258819256815163249845447936*x^15 - 229408132984166521977166336*x^14
+ 172649692294614969274168896*x^13 - 133312541377246386115890240*x^12 + 1020315
73634317834547976132*x^11 - 59791102681494117572149176*x^10 + 416138849372553030
86792337*x^9 - 27246604251076689552043953*x^8 + 10718131725916893151555068*x^7 -
8685973988079840377705700*x^6 + 3673303058277822225386926*x^5 - 809990362095044
210054958*x^4 + 1362587089603925431664856*x^3 + 111926768697602999806116*x^2 + 2
05702452014540322797289*x - 4884417100172357749737))*sqrt((327571850528462403199
*sqrt(14) - 1226422380928157351936)/(401741448850159339627110059970918575243264*
sqrt(14) - 1503179149031234349960285217920460999509255)))/((32757185052846240319
9*sqrt(14)*sqrt(7)*(262144*x^27 - 2359296*x^26 + 8847360*x^25 - 19070976*x^24 +
31260672*x^23 - 50135040*x^22 + 72400896*x^21 - 84787200*x^20 + 97449984*x^19 -
111622144*x^18 + 102818304*x^17 - 94063104*x^16 + 92761344*x^15 - 66772224*x^14
+ 51609024*x^13 - 46803648*x^12 + 23042340*x^11 - 18046404*x^10 + 14741135*x^9 -
2785131*x^8 + 5374836*x^7 - 1955988*x^6 - 185166*x^5 - 1395306*x^4 - 454896*x^3
- 314928*x^2 - 59049*x - 19683) - 1226422380928157351936*sqrt(7)*(262144*x^27 -
2359296*x^26 + 8847360*x^25 - 19070976*x^24 + 31260672*x^23 - 50135040*x^22 + 7
2400896*x^21 - 84787200*x^20 + 97449984*x^19 - 111622144*x^18 + 102818304*x^17 -
94063104*x^16 + 92761344*x^15 - 66772224*x^14 + 51609024*x^13 - 46803648*x^12 +
23042340*x^11 - 18046404*x^10 + 14741135*x^9 - 2785131*x^8 + 5374836*x^7 - 1955
988*x^6 - 185166*x^5 - 1395306*x^4 - 454896*x^3 - 314928*x^2 - 59049*x - 19683))
*sqrt(-2*x + 3)*sqrt((327571850528462403199*sqrt(14) - 1226422380928157351936)/(
401741448850159339627110059970918575243264*sqrt(14) - 15031791490312343499602852
17920460999509255)))

_______________________________________________________________________________________

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/(3-2*x)**(21/2)/(2*x**2+x+1)**10,x)

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{10}{\left (-2 \, x + 3\right )}^{\frac{21}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((2*x^2 + x + 1)^10*(-2*x + 3)^(21/2)),x, algorithm="giac")

[Out]

integrate(1/((2*x^2 + x + 1)^10*(-2*x + 3)^(21/2)), x)