3.84 \(\int \frac{1}{\sqrt{3-x+2 x^2} \left (2+3 x+5 x^2\right )^2} \, dx\)
Optimal. Leaf size=188 \[ \frac{\sqrt{2 x^2-x+3} (65 x+4)}{682 \left (5 x^2+3 x+2\right )}+\frac{\sqrt{\frac{1}{682} \left (2343727+1678700 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (2343727+1678700 \sqrt{2}\right )}} \left (\left (5751+3935 \sqrt{2}\right ) x+1816 \sqrt{2}+2119\right )}{\sqrt{2 x^2-x+3}}\right )}{1364}-\frac{\sqrt{\frac{1}{682} \left (1678700 \sqrt{2}-2343727\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (1678700 \sqrt{2}-2343727\right )}} \left (\left (5751-3935 \sqrt{2}\right ) x-1816 \sqrt{2}+2119\right )}{\sqrt{2 x^2-x+3}}\right )}{1364} \]
[Out]
((4 + 65*x)*Sqrt[3 - x + 2*x^2])/(682*(2 + 3*x + 5*x^2)) + (Sqrt[(2343727 + 1678
700*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(2343727 + 1678700*Sqrt[2]))]*(2119 + 1816
*Sqrt[2] + (5751 + 3935*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1364 - (Sqrt[(-234372
7 + 1678700*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-2343727 + 1678700*Sqrt[2]))]*(2
119 - 1816*Sqrt[2] + (5751 - 3935*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1364
_______________________________________________________________________________________
Rubi [A] time = 0.884934, antiderivative size = 188, normalized size of antiderivative = 1.,
number of steps used = 6, number of rules used = 5, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.185
\[ \frac{\sqrt{2 x^2-x+3} (65 x+4)}{682 \left (5 x^2+3 x+2\right )}+\frac{\sqrt{\frac{1}{682} \left (2343727+1678700 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (2343727+1678700 \sqrt{2}\right )}} \left (\left (5751+3935 \sqrt{2}\right ) x+1816 \sqrt{2}+2119\right )}{\sqrt{2 x^2-x+3}}\right )}{1364}-\frac{\sqrt{\frac{1}{682} \left (1678700 \sqrt{2}-2343727\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (1678700 \sqrt{2}-2343727\right )}} \left (\left (5751-3935 \sqrt{2}\right ) x-1816 \sqrt{2}+2119\right )}{\sqrt{2 x^2-x+3}}\right )}{1364} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^2),x]
[Out]
((4 + 65*x)*Sqrt[3 - x + 2*x^2])/(682*(2 + 3*x + 5*x^2)) + (Sqrt[(2343727 + 1678
700*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(2343727 + 1678700*Sqrt[2]))]*(2119 + 1816
*Sqrt[2] + (5751 + 3935*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1364 - (Sqrt[(-234372
7 + 1678700*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-2343727 + 1678700*Sqrt[2]))]*(2
119 - 1816*Sqrt[2] + (5751 - 3935*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1364
_______________________________________________________________________________________
Rubi in Sympy [A] time = 77.5236, size = 216, normalized size = 1.15 \[ \frac{\left (715 x + 44\right ) \sqrt{2 x^{2} - x + 3}}{7502 \left (5 x^{2} + 3 x + 2\right )} + \frac{\sqrt{682} \left (\frac{256399}{2} + 109868 \sqrt{2}\right ) \left (40172 \sqrt{2} + 64977\right ) \operatorname{atan}{\left (\frac{2 \sqrt{341} \left (x \left (\frac{476135 \sqrt{2}}{2} + \frac{695871}{2}\right ) + \frac{256399}{2} + 109868 \sqrt{2}\right )}{3751 \sqrt{2343727 + 1678700 \sqrt{2}} \sqrt{2 x^{2} - x + 3}} \right )}}{6809880484 \sqrt{2343727 + 1678700 \sqrt{2}}} + \frac{\sqrt{682} \left (- 109868 \sqrt{2} + \frac{256399}{2}\right ) \left (- 40172 \sqrt{2} + 64977\right ) \operatorname{atanh}{\left (\frac{2 \sqrt{341} \left (x \left (- \frac{476135 \sqrt{2}}{2} + \frac{695871}{2}\right ) - 109868 \sqrt{2} + \frac{256399}{2}\right )}{3751 \sqrt{-2343727 + 1678700 \sqrt{2}} \sqrt{2 x^{2} - x + 3}} \right )}}{6809880484 \sqrt{-2343727 + 1678700 \sqrt{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(5*x**2+3*x+2)**2/(2*x**2-x+3)**(1/2),x)
[Out]
(715*x + 44)*sqrt(2*x**2 - x + 3)/(7502*(5*x**2 + 3*x + 2)) + sqrt(682)*(256399/
2 + 109868*sqrt(2))*(40172*sqrt(2) + 64977)*atan(2*sqrt(341)*(x*(476135*sqrt(2)/
2 + 695871/2) + 256399/2 + 109868*sqrt(2))/(3751*sqrt(2343727 + 1678700*sqrt(2))
*sqrt(2*x**2 - x + 3)))/(6809880484*sqrt(2343727 + 1678700*sqrt(2))) + sqrt(682)
*(-109868*sqrt(2) + 256399/2)*(-40172*sqrt(2) + 64977)*atanh(2*sqrt(341)*(x*(-47
6135*sqrt(2)/2 + 695871/2) - 109868*sqrt(2) + 256399/2)/(3751*sqrt(-2343727 + 16
78700*sqrt(2))*sqrt(2*x**2 - x + 3)))/(6809880484*sqrt(-2343727 + 1678700*sqrt(2
)))
_______________________________________________________________________________________
Mathematica [C] time = 6.44877, size = 1147, normalized size = 6.1 \[ \frac{\sqrt{2 x^2-x+3} (65 x+4)}{682 \left (5 x^2+3 x+2\right )}-\frac{5 i \left (-787 i+41 \sqrt{31}\right ) \tan ^{-1}\left (\frac{31 \left (73964 \sqrt{31} x^4+299597 i x^4+291346 \sqrt{31} x^3-3529208 i x^3+311146 \sqrt{31} x^2+2284079 i x^2+310310 \sqrt{31} x-3387270 i x+546546 \sqrt{31}+802246 i\right )}{-31033201 i \sqrt{31} x^4+44012188 x^4+1342960 i \sqrt{682 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x^3-14709760 i \sqrt{31} x^3+81775210 x^3+470036 i \sqrt{682 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x^2-35512659 i \sqrt{31} x^2+27657146 x^2+335740 i \sqrt{682 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x-9626874 i \sqrt{31} x+148907198 x-134296 i \sqrt{682 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3}+5110826 i \sqrt{31}+20294274}\right )}{1364 \sqrt{682 \left (13+i \sqrt{31}\right )}}-\frac{5 i \left (787 i+41 \sqrt{31}\right ) \tanh ^{-1}\left (\frac{31033201 \sqrt{31} x^4-44012188 i x^4+7386280 \sqrt{22 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x^3+14709760 \sqrt{31} x^3-81775210 i x^3-16719852 \sqrt{22 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x^2+35512659 \sqrt{31} x^2-27657146 i x^2-9736460 \sqrt{22 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x+9626874 \sqrt{31} x-148907198 i x-8460648 \sqrt{22 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3}-5110826 \sqrt{31}-20294274 i}{2292884 \sqrt{31} x^4+155225093 i x^4+9031726 \sqrt{31} x^3-298854392 i x^3+9645526 \sqrt{31} x^2+362298151 i x^2+9619610 \sqrt{31} x+305106410 i x+16942926 \sqrt{31}+243722374 i}\right )}{1364 \sqrt{682 \left (-13+i \sqrt{31}\right )}}+\frac{5 i \left (787 i+41 \sqrt{31}\right ) \log \left (\left (-10 i x+\sqrt{31}-3 i\right )^2 \left (10 i x+\sqrt{31}+3 i\right )^2\right )}{2728 \sqrt{682 \left (-13+i \sqrt{31}\right )}}-\frac{5 \left (-787 i+41 \sqrt{31}\right ) \log \left (\left (-10 i x+\sqrt{31}-3 i\right )^2 \left (10 i x+\sqrt{31}+3 i\right )^2\right )}{2728 \sqrt{682 \left (13+i \sqrt{31}\right )}}-\frac{5 i \left (787 i+41 \sqrt{31}\right ) \log \left (\left (5 x^2+3 x+2\right ) \left (44 \sqrt{31} x^2+327 i x^2-4 i \sqrt{682 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x-22 \sqrt{31} x+469 i x+i \sqrt{682 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3}+66 \sqrt{31}-142 i\right )\right )}{2728 \sqrt{682 \left (-13+i \sqrt{31}\right )}}+\frac{5 \left (-787 i+41 \sqrt{31}\right ) \log \left (\left (5 x^2+3 x+2\right ) \left (44 \sqrt{31} x^2-817 i x^2+22 i \sqrt{22 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x-22 \sqrt{31} x+1041 i x-63 i \sqrt{22 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3}+66 \sqrt{31}-1858 i\right )\right )}{2728 \sqrt{682 \left (13+i \sqrt{31}\right )}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^2),x]
[Out]
((4 + 65*x)*Sqrt[3 - x + 2*x^2])/(682*(2 + 3*x + 5*x^2)) - (((5*I)/1364)*(-787*I
+ 41*Sqrt[31])*ArcTan[(31*(802246*I + 546546*Sqrt[31] - (3387270*I)*x + 310310*
Sqrt[31]*x + (2284079*I)*x^2 + 311146*Sqrt[31]*x^2 - (3529208*I)*x^3 + 291346*Sq
rt[31]*x^3 + (299597*I)*x^4 + 73964*Sqrt[31]*x^4))/(20294274 + (5110826*I)*Sqrt[
31] + 148907198*x - (9626874*I)*Sqrt[31]*x + 27657146*x^2 - (35512659*I)*Sqrt[31
]*x^2 + 81775210*x^3 - (14709760*I)*Sqrt[31]*x^3 + 44012188*x^4 - (31033201*I)*S
qrt[31]*x^4 - (134296*I)*Sqrt[682*(13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2] + (3357
40*I)*Sqrt[682*(13 + I*Sqrt[31])]*x*Sqrt[3 - x + 2*x^2] + (470036*I)*Sqrt[682*(1
3 + I*Sqrt[31])]*x^2*Sqrt[3 - x + 2*x^2] + (1342960*I)*Sqrt[682*(13 + I*Sqrt[31]
)]*x^3*Sqrt[3 - x + 2*x^2])])/Sqrt[682*(13 + I*Sqrt[31])] - (((5*I)/1364)*(787*I
+ 41*Sqrt[31])*ArcTanh[(-20294274*I - 5110826*Sqrt[31] - (148907198*I)*x + 9626
874*Sqrt[31]*x - (27657146*I)*x^2 + 35512659*Sqrt[31]*x^2 - (81775210*I)*x^3 + 1
4709760*Sqrt[31]*x^3 - (44012188*I)*x^4 + 31033201*Sqrt[31]*x^4 - 8460648*Sqrt[2
2*(-13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2] - 9736460*Sqrt[22*(-13 + I*Sqrt[31])]*
x*Sqrt[3 - x + 2*x^2] - 16719852*Sqrt[22*(-13 + I*Sqrt[31])]*x^2*Sqrt[3 - x + 2*
x^2] + 7386280*Sqrt[22*(-13 + I*Sqrt[31])]*x^3*Sqrt[3 - x + 2*x^2])/(243722374*I
+ 16942926*Sqrt[31] + (305106410*I)*x + 9619610*Sqrt[31]*x + (362298151*I)*x^2
+ 9645526*Sqrt[31]*x^2 - (298854392*I)*x^3 + 9031726*Sqrt[31]*x^3 + (155225093*I
)*x^4 + 2292884*Sqrt[31]*x^4)])/Sqrt[682*(-13 + I*Sqrt[31])] - (5*(-787*I + 41*S
qrt[31])*Log[(-3*I + Sqrt[31] - (10*I)*x)^2*(3*I + Sqrt[31] + (10*I)*x)^2])/(272
8*Sqrt[682*(13 + I*Sqrt[31])]) + (((5*I)/2728)*(787*I + 41*Sqrt[31])*Log[(-3*I +
Sqrt[31] - (10*I)*x)^2*(3*I + Sqrt[31] + (10*I)*x)^2])/Sqrt[682*(-13 + I*Sqrt[3
1])] - (((5*I)/2728)*(787*I + 41*Sqrt[31])*Log[(2 + 3*x + 5*x^2)*(-142*I + 66*Sq
rt[31] + (469*I)*x - 22*Sqrt[31]*x + (327*I)*x^2 + 44*Sqrt[31]*x^2 + I*Sqrt[682*
(-13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2] - (4*I)*Sqrt[682*(-13 + I*Sqrt[31])]*x*S
qrt[3 - x + 2*x^2])])/Sqrt[682*(-13 + I*Sqrt[31])] + (5*(-787*I + 41*Sqrt[31])*L
og[(2 + 3*x + 5*x^2)*(-1858*I + 66*Sqrt[31] + (1041*I)*x - 22*Sqrt[31]*x - (817*
I)*x^2 + 44*Sqrt[31]*x^2 - (63*I)*Sqrt[22*(13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2]
+ (22*I)*Sqrt[22*(13 + I*Sqrt[31])]*x*Sqrt[3 - x + 2*x^2])])/(2728*Sqrt[682*(13
+ I*Sqrt[31])])
_______________________________________________________________________________________
Maple [B] time = 0.009, size = 5225, normalized size = 27.8 \[ \text{output too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(5*x^2+3*x+2)^2/(2*x^2-x+3)^(1/2),x)
[Out]
result too large to display
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (5 \, x^{2} + 3 \, x + 2\right )}^{2} \sqrt{2 \, x^{2} - x + 3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x^2 + 3*x + 2)^2*sqrt(2*x^2 - x + 3)),x, algorithm="maxima")
[Out]
integrate(1/((5*x^2 + 3*x + 2)^2*sqrt(2*x^2 - x + 3)), x)
_______________________________________________________________________________________
Fricas [A] time = 0.362036, size = 1505, normalized size = 8.01 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x^2 + 3*x + 2)^2*sqrt(2*x^2 - x + 3)),x, algorithm="fricas")
[Out]
-1/2641240152695936*930248^(3/4)*sqrt(33574)*sqrt(31)*(4*930248^(1/4)*sqrt(33574
)*sqrt(31)*sqrt(2*x^2 - x + 3)*(2343727*sqrt(2)*(65*x + 4) - 218231000*x - 13429
600)*sqrt((2343727*sqrt(2) - 3357400)/(7868829029800*sqrt(2) - 11129123630529))
+ 8422204*sqrt(16787)*sqrt(2)*(5*x^2 + 3*x + 2)*arctan(520397*(930248^(1/4)*sqrt
(33574)*(2343727*sqrt(2)*(x - 6) - 3357400*x + 20144400)*sqrt((2343727*sqrt(2) -
3357400)/(7868829029800*sqrt(2) - 11129123630529)) + 88*sqrt(16787)*sqrt(2*x^2
- x + 3)*(1816*sqrt(2) - 2119))/(2*930248^(1/4)*sqrt(33574)*sqrt(16787)*sqrt(31)
*(2343727*sqrt(2)*x - 3357400*x)*sqrt(-sqrt(2)*(930248^(1/4)*sqrt(33574)*sqrt(16
787)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(189489825488457357396643*x + 7848927269966315
0388575) - 267979098188120507785218*x - 111000552788794207008068)*sqrt((2343727*
sqrt(2) - 3357400)/(7868829029800*sqrt(2) - 11129123630529)) + 21937161129353338
5864425600*x^2 + 16787*sqrt(2)*(3638234995621319496200*x^2 - 5250243412385936158
3*sqrt(2)*(49*x^2 - 151*x + 200) - 11211703762016719263800*x + 14849938757638038
760000) - 77559535824075985054656248*sqrt(2)*(2*x^2 - x + 3) - 10968580564676669
2932212800*x + 329057416940300078796638400)/(52502434123859361583*sqrt(2)*x^2 -
74249693788190193800*x^2))*sqrt((2343727*sqrt(2) - 3357400)/(7868829029800*sqrt(
2) - 11129123630529)) + 16787*930248^(1/4)*sqrt(33574)*sqrt(31)*(2343727*sqrt(2)
*(19*x - 22) - 63790600*x + 73862800)*sqrt((2343727*sqrt(2) - 3357400)/(78688290
29800*sqrt(2) - 11129123630529)) - 45794936*sqrt(16787)*sqrt(31)*sqrt(2*x^2 - x
+ 3)*(332*sqrt(2) - 537))) + 8422204*sqrt(16787)*sqrt(2)*(5*x^2 + 3*x + 2)*arcta
n(-520397*(930248^(1/4)*sqrt(33574)*(2343727*sqrt(2)*(x - 6) - 3357400*x + 20144
400)*sqrt((2343727*sqrt(2) - 3357400)/(7868829029800*sqrt(2) - 11129123630529))
- 88*sqrt(16787)*sqrt(2*x^2 - x + 3)*(1816*sqrt(2) - 2119))/(2*930248^(1/4)*sqrt
(33574)*sqrt(16787)*sqrt(31)*(2343727*sqrt(2)*x - 3357400*x)*sqrt(sqrt(2)*(93024
8^(1/4)*sqrt(33574)*sqrt(16787)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(189489825488457357
396643*x + 78489272699663150388575) - 267979098188120507785218*x - 1110005527887
94207008068)*sqrt((2343727*sqrt(2) - 3357400)/(7868829029800*sqrt(2) - 111291236
30529)) - 219371611293533385864425600*x^2 - 16787*sqrt(2)*(363823499562131949620
0*x^2 - 52502434123859361583*sqrt(2)*(49*x^2 - 151*x + 200) - 112117037620167192
63800*x + 14849938757638038760000) + 77559535824075985054656248*sqrt(2)*(2*x^2 -
x + 3) + 109685805646766692932212800*x - 329057416940300078796638400)/(52502434
123859361583*sqrt(2)*x^2 - 74249693788190193800*x^2))*sqrt((2343727*sqrt(2) - 33
57400)/(7868829029800*sqrt(2) - 11129123630529)) + 16787*930248^(1/4)*sqrt(33574
)*sqrt(31)*(2343727*sqrt(2)*(19*x - 22) - 63790600*x + 73862800)*sqrt((2343727*s
qrt(2) - 3357400)/(7868829029800*sqrt(2) - 11129123630529)) + 45794936*sqrt(1678
7)*sqrt(31)*sqrt(2*x^2 - x + 3)*(332*sqrt(2) - 537))) - sqrt(16787)*sqrt(31)*(16
787000*x^2 - 2343727*sqrt(2)*(5*x^2 + 3*x + 2) + 10072200*x + 6714800)*log(-4196
7500*sqrt(2)*(930248^(1/4)*sqrt(33574)*sqrt(16787)*sqrt(2*x^2 - x + 3)*(sqrt(2)*
(189489825488457357396643*x + 78489272699663150388575) - 26797909818812050778521
8*x - 111000552788794207008068)*sqrt((2343727*sqrt(2) - 3357400)/(7868829029800*
sqrt(2) - 11129123630529)) + 219371611293533385864425600*x^2 + 16787*sqrt(2)*(36
38234995621319496200*x^2 - 52502434123859361583*sqrt(2)*(49*x^2 - 151*x + 200) -
11211703762016719263800*x + 14849938757638038760000) - 775595358240759850546562
48*sqrt(2)*(2*x^2 - x + 3) - 109685805646766692932212800*x + 3290574169403000787
96638400)/(52502434123859361583*sqrt(2)*x^2 - 74249693788190193800*x^2)) + sqrt(
16787)*sqrt(31)*(16787000*x^2 - 2343727*sqrt(2)*(5*x^2 + 3*x + 2) + 10072200*x +
6714800)*log(41967500*sqrt(2)*(930248^(1/4)*sqrt(33574)*sqrt(16787)*sqrt(2*x^2
- x + 3)*(sqrt(2)*(189489825488457357396643*x + 78489272699663150388575) - 26797
9098188120507785218*x - 111000552788794207008068)*sqrt((2343727*sqrt(2) - 335740
0)/(7868829029800*sqrt(2) - 11129123630529)) - 219371611293533385864425600*x^2 -
16787*sqrt(2)*(3638234995621319496200*x^2 - 52502434123859361583*sqrt(2)*(49*x^
2 - 151*x + 200) - 11211703762016719263800*x + 14849938757638038760000) + 775595
35824075985054656248*sqrt(2)*(2*x^2 - x + 3) + 109685805646766692932212800*x - 3
29057416940300078796638400)/(52502434123859361583*sqrt(2)*x^2 - 7424969378819019
3800*x^2)))/((16787000*x^2 - 2343727*sqrt(2)*(5*x^2 + 3*x + 2) + 10072200*x + 67
14800)*sqrt((2343727*sqrt(2) - 3357400)/(7868829029800*sqrt(2) - 11129123630529)
))
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{2 x^{2} - x + 3} \left (5 x^{2} + 3 x + 2\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(5*x**2+3*x+2)**2/(2*x**2-x+3)**(1/2),x)
[Out]
Integral(1/(sqrt(2*x**2 - x + 3)*(5*x**2 + 3*x + 2)**2), x)
_______________________________________________________________________________________
GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x^2 + 3*x + 2)^2*sqrt(2*x^2 - x + 3)),x, algorithm="giac")
[Out]
Exception raised: RuntimeError