3.90 \(\int \frac{1}{\left (3-x+2 x^2\right )^{3/2} \left (2+3 x+5 x^2\right )} \, dx\)
Optimal. Leaf size=176 \[ \frac{13-6 x}{253 \sqrt{2 x^2-x+3}}+\frac{1}{22} \sqrt{\frac{1}{682} \left (247+500 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (247+500 \sqrt{2}\right )}} \left (\left (69+65 \sqrt{2}\right ) x+4 \sqrt{2}+61\right )}{\sqrt{2 x^2-x+3}}\right )-\frac{1}{22} \sqrt{\frac{1}{682} \left (500 \sqrt{2}-247\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (500 \sqrt{2}-247\right )}} \left (\left (69-65 \sqrt{2}\right ) x-4 \sqrt{2}+61\right )}{\sqrt{2 x^2-x+3}}\right ) \]
[Out]
(13 - 6*x)/(253*Sqrt[3 - x + 2*x^2]) + (Sqrt[(247 + 500*Sqrt[2])/682]*ArcTan[(Sq
rt[11/(31*(247 + 500*Sqrt[2]))]*(61 + 4*Sqrt[2] + (69 + 65*Sqrt[2])*x))/Sqrt[3 -
x + 2*x^2]])/22 - (Sqrt[(-247 + 500*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-247 +
500*Sqrt[2]))]*(61 - 4*Sqrt[2] + (69 - 65*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/22
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Rubi [A] time = 0.832572, antiderivative size = 176, 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
\[ \frac{13-6 x}{253 \sqrt{2 x^2-x+3}}+\frac{1}{22} \sqrt{\frac{1}{682} \left (247+500 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (247+500 \sqrt{2}\right )}} \left (\left (69+65 \sqrt{2}\right ) x+4 \sqrt{2}+61\right )}{\sqrt{2 x^2-x+3}}\right )-\frac{1}{22} \sqrt{\frac{1}{682} \left (500 \sqrt{2}-247\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (500 \sqrt{2}-247\right )}} \left (\left (69-65 \sqrt{2}\right ) x-4 \sqrt{2}+61\right )}{\sqrt{2 x^2-x+3}}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)),x]
[Out]
(13 - 6*x)/(253*Sqrt[3 - x + 2*x^2]) + (Sqrt[(247 + 500*Sqrt[2])/682]*ArcTan[(Sq
rt[11/(31*(247 + 500*Sqrt[2]))]*(61 + 4*Sqrt[2] + (69 + 65*Sqrt[2])*x))/Sqrt[3 -
x + 2*x^2]])/22 - (Sqrt[(-247 + 500*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-247 +
500*Sqrt[2]))]*(61 - 4*Sqrt[2] + (69 - 65*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/22
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Rubi in Sympy [A] time = 79.3106, size = 207, normalized size = 1.18 \[ \frac{- 66 x + 143}{2783 \sqrt{2 x^{2} - x + 3}} + \frac{\sqrt{682} \left (8349 + 22264 \sqrt{2}\right ) \left (5566 \sqrt{2} + \frac{169763}{2}\right ) \operatorname{atan}{\left (\frac{2 \sqrt{341} \left (x \left (\frac{192027}{2} + \frac{180895 \sqrt{2}}{2}\right ) + 5566 \sqrt{2} + \frac{169763}{2}\right )}{86273 \sqrt{247 + 500 \sqrt{2}} \sqrt{2 x^{2} - x + 3}} \right )}}{58103657678 \sqrt{247 + 500 \sqrt{2}}} + \frac{\sqrt{682} \left (- 22264 \sqrt{2} + 8349\right ) \left (- 5566 \sqrt{2} + \frac{169763}{2}\right ) \operatorname{atanh}{\left (\frac{2 \sqrt{341} \left (x \left (- \frac{180895 \sqrt{2}}{2} + \frac{192027}{2}\right ) - 5566 \sqrt{2} + \frac{169763}{2}\right )}{86273 \sqrt{-247 + 500 \sqrt{2}} \sqrt{2 x^{2} - x + 3}} \right )}}{58103657678 \sqrt{-247 + 500 \sqrt{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(2*x**2-x+3)**(3/2)/(5*x**2+3*x+2),x)
[Out]
(-66*x + 143)/(2783*sqrt(2*x**2 - x + 3)) + sqrt(682)*(8349 + 22264*sqrt(2))*(55
66*sqrt(2) + 169763/2)*atan(2*sqrt(341)*(x*(192027/2 + 180895*sqrt(2)/2) + 5566*
sqrt(2) + 169763/2)/(86273*sqrt(247 + 500*sqrt(2))*sqrt(2*x**2 - x + 3)))/(58103
657678*sqrt(247 + 500*sqrt(2))) + sqrt(682)*(-22264*sqrt(2) + 8349)*(-5566*sqrt(
2) + 169763/2)*atanh(2*sqrt(341)*(x*(-180895*sqrt(2)/2 + 192027/2) - 5566*sqrt(2
) + 169763/2)/(86273*sqrt(-247 + 500*sqrt(2))*sqrt(2*x**2 - x + 3)))/(5810365767
8*sqrt(-247 + 500*sqrt(2)))
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Mathematica [C] time = 6.39428, size = 1129, normalized size = 6.41 \[ \frac{13-6 x}{253 \sqrt{2 x^2-x+3}}-\frac{5 \left (-13 i+\sqrt{31}\right ) \tan ^{-1}\left (\frac{4439 i \sqrt{31} x^4+17732 x^4-2200 i \sqrt{22 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x^3+5120 i \sqrt{31} x^3-17050 x^3+4980 i \sqrt{22 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x^2+6405 i \sqrt{31} x^2+21142 x^2+2900 i \sqrt{22 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x-4266 i \sqrt{31} x-7502 x+2520 i \sqrt{22 \left (-13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3}+602 i \sqrt{31}-14322}{1364 \sqrt{31} x^4+24293 i x^4-3410 \sqrt{31} x^3-85640 i x^3+4774 \sqrt{31} x^2+88855 i x^2-4774 \sqrt{31} x+58298 i x+2046 \sqrt{31}+82294 i}\right )}{22 \sqrt{682 \left (-13+i \sqrt{31}\right )}}+\frac{5 i \left (13 i+\sqrt{31}\right ) \tan ^{-1}\left (\frac{31 \left (44 \sqrt{31} x^4+797 i x^4-110 \sqrt{31} x^3-1160 i x^3+154 \sqrt{31} x^2+1295 i x^2-154 \sqrt{31} x+42 i x+66 \sqrt{31}-74 i\right )}{4439 i \sqrt{31} x^4-17732 x^4+400 i \sqrt{682 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x^3+5120 i \sqrt{31} x^3+17050 x^3+140 i \sqrt{682 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x^2+6405 i \sqrt{31} x^2-21142 x^2+100 i \sqrt{682 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3} x-4266 i \sqrt{31} x+7502 x-40 i \sqrt{682 \left (13+i \sqrt{31}\right )} \sqrt{2 x^2-x+3}+602 i \sqrt{31}+14322}\right )}{22 \sqrt{682 \left (13+i \sqrt{31}\right )}}+\frac{5 \left (13 i+\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 )}{44 \sqrt{682 \left (13+i \sqrt{31}\right )}}-\frac{5 i \left (-13 i+\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 )}{44 \sqrt{682 \left (-13+i \sqrt{31}\right )}}+\frac{5 i \left (-13 i+\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 )}{44 \sqrt{682 \left (-13+i \sqrt{31}\right )}}-\frac{5 \left (13 i+\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 )}{44 \sqrt{682 \left (13+i \sqrt{31}\right )}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)),x]
[Out]
(13 - 6*x)/(253*Sqrt[3 - x + 2*x^2]) - (5*(-13*I + Sqrt[31])*ArcTan[(-14322 + (6
02*I)*Sqrt[31] - 7502*x - (4266*I)*Sqrt[31]*x + 21142*x^2 + (6405*I)*Sqrt[31]*x^
2 - 17050*x^3 + (5120*I)*Sqrt[31]*x^3 + 17732*x^4 + (4439*I)*Sqrt[31]*x^4 + (252
0*I)*Sqrt[22*(-13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2] + (2900*I)*Sqrt[22*(-13 + I
*Sqrt[31])]*x*Sqrt[3 - x + 2*x^2] + (4980*I)*Sqrt[22*(-13 + I*Sqrt[31])]*x^2*Sqr
t[3 - x + 2*x^2] - (2200*I)*Sqrt[22*(-13 + I*Sqrt[31])]*x^3*Sqrt[3 - x + 2*x^2])
/(82294*I + 2046*Sqrt[31] + (58298*I)*x - 4774*Sqrt[31]*x + (88855*I)*x^2 + 4774
*Sqrt[31]*x^2 - (85640*I)*x^3 - 3410*Sqrt[31]*x^3 + (24293*I)*x^4 + 1364*Sqrt[31
]*x^4)])/(22*Sqrt[682*(-13 + I*Sqrt[31])]) + (((5*I)/22)*(13*I + Sqrt[31])*ArcTa
n[(31*(-74*I + 66*Sqrt[31] + (42*I)*x - 154*Sqrt[31]*x + (1295*I)*x^2 + 154*Sqrt
[31]*x^2 - (1160*I)*x^3 - 110*Sqrt[31]*x^3 + (797*I)*x^4 + 44*Sqrt[31]*x^4))/(14
322 + (602*I)*Sqrt[31] + 7502*x - (4266*I)*Sqrt[31]*x - 21142*x^2 + (6405*I)*Sqr
t[31]*x^2 + 17050*x^3 + (5120*I)*Sqrt[31]*x^3 - 17732*x^4 + (4439*I)*Sqrt[31]*x^
4 - (40*I)*Sqrt[682*(13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2] + (100*I)*Sqrt[682*(1
3 + I*Sqrt[31])]*x*Sqrt[3 - x + 2*x^2] + (140*I)*Sqrt[682*(13 + I*Sqrt[31])]*x^2
*Sqrt[3 - x + 2*x^2] + (400*I)*Sqrt[682*(13 + I*Sqrt[31])]*x^3*Sqrt[3 - x + 2*x^
2])])/Sqrt[682*(13 + I*Sqrt[31])] - (((5*I)/44)*(-13*I + Sqrt[31])*Log[(-3*I + S
qrt[31] - (10*I)*x)^2*(3*I + Sqrt[31] + (10*I)*x)^2])/Sqrt[682*(-13 + I*Sqrt[31]
)] + (5*(13*I + Sqrt[31])*Log[(-3*I + Sqrt[31] - (10*I)*x)^2*(3*I + Sqrt[31] + (
10*I)*x)^2])/(44*Sqrt[682*(13 + I*Sqrt[31])]) + (((5*I)/44)*(-13*I + Sqrt[31])*L
og[(2 + 3*x + 5*x^2)*(-142*I + 66*Sqrt[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*Sqrt[3 - x + 2*x^2])])/Sqrt[682*(-13 + I*Sqrt
[31])] - (5*(13*I + Sqrt[31])*Log[(2 + 3*x + 5*x^2)*(-1858*I + 66*Sqrt[31] + (10
41*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])])/(44*Sqrt[682*(13 + I*Sqrt[31])])
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Maple [B] time = 0.037, size = 718, normalized size = 4.1 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2*x^2-x+3)^(3/2)/(5*x^2+3*x+2),x)
[Out]
1/465124*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1
-x)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(2197*2^(1/2)*arctan(1/11692487*(-775687+549362
*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+24*2^(1/
2)-41))^(1/2)*(6485*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+10368*(2^(1/2)-1+x)^
2/(2^(1/2)+1-x)^2+22379*2^(1/2)+32016)/(23*(2^(1/2)-1+x)^4/(2^(1/2)+1-x)^4+82*(2
^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+23)*(8+3*2^(1/2))*(2^(1/2)-1+x)/(2^(1/2)+1-x))*(-8
866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)+3070*arctan(1/11692487*(-
775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(2^(1/2)-1+x)^2/(2^(1/2)+1-
x)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+10368*(
2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+22379*2^(1/2)+32016)/(23*(2^(1/2)-1+x)^4/(2^(1/2)
+1-x)^4+82*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+23)*(8+3*2^(1/2))*(2^(1/2)-1+x)/(2^(1
/2)+1-x))*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)+1712502*arct
anh(31/2*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1
-x)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-6617446*arctanh(31/
2*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8
-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)
^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))/(1+(2^(1/2)-1+x)/(2^(1
/2)+1-x))^2)^(1/2)/(1+(2^(1/2)-1+x)/(2^(1/2)+1-x))/(8+3*2^(1/2))/(-8866+6820*2^(
1/2))^(1/2)-3/506*(4*x-1)/(2*x^2-x+3)^(1/2)+1/22/(2*x^2-x+3)^(1/2)
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (5 \, x^{2} + 3 \, x + 2\right )}{\left (2 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x^2 + 3*x + 2)*(2*x^2 - x + 3)^(3/2)),x, algorithm="maxima")
[Out]
integrate(1/((5*x^2 + 3*x + 2)*(2*x^2 - x + 3)^(3/2)), x)
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Fricas [A] time = 0.33274, size = 1463, normalized size = 8.31 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x^2 + 3*x + 2)*(2*x^2 - x + 3)^(3/2)),x, algorithm="fricas")
[Out]
1/213957040*sqrt(341)*sqrt(31)*sqrt(10)*(8*sqrt(341)*sqrt(31)*sqrt(10)*sqrt(2*x^
2 - x + 3)*(500*sqrt(2)*(6*x - 13) - 1482*x + 3211)*sqrt((247*sqrt(2) - 1000)/(2
47000*sqrt(2) - 561009)) + 23*50^(1/4)*sqrt(31)*(494*x^2 - 500*sqrt(2)*(2*x^2 -
x + 3) - 247*x + 741)*log(-25000*(sqrt(341)*50^(1/4)*sqrt(10)*sqrt(2*x^2 - x + 3
)*(sqrt(2)*(24886429777*x + 2962665725) - 27849095502*x - 21923764052)*sqrt((247
*sqrt(2) - 1000)/(247000*sqrt(2) - 561009)) + 167341615000*x^2 + 220*sqrt(2)*(13
66054000*x^2 - 385569223*sqrt(2)*(2*x^2 - x + 3) - 683027000*x + 2049081000) - 1
927846115*sqrt(2)*(49*x^2 - 151*x + 200) - 515685385000*x + 683027000000)/(38556
9223*sqrt(2)*x^2 - 683027000*x^2)) - 23*50^(1/4)*sqrt(31)*(494*x^2 - 500*sqrt(2)
*(2*x^2 - x + 3) - 247*x + 741)*log(25000*(sqrt(341)*50^(1/4)*sqrt(10)*sqrt(2*x^
2 - x + 3)*(sqrt(2)*(24886429777*x + 2962665725) - 27849095502*x - 21923764052)*
sqrt((247*sqrt(2) - 1000)/(247000*sqrt(2) - 561009)) - 167341615000*x^2 - 220*sq
rt(2)*(1366054000*x^2 - 385569223*sqrt(2)*(2*x^2 - x + 3) - 683027000*x + 204908
1000) + 1927846115*sqrt(2)*(49*x^2 - 151*x + 200) + 515685385000*x - 68302700000
0)/(385569223*sqrt(2)*x^2 - 683027000*x^2)) - 339388*50^(1/4)*(2*x^2 - x + 3)*ar
ctan(31*(sqrt(341)*sqrt(10)*(500*sqrt(2)*(x - 6) - 247*x + 1482)*sqrt((247*sqrt(
2) - 1000)/(247000*sqrt(2) - 561009)) + 22*50^(1/4)*sqrt(2*x^2 - x + 3)*(61*sqrt
(2) - 8))/(sqrt(341)*sqrt(31)*sqrt(10)*(500*sqrt(2)*(19*x - 22) - 4693*x + 5434)
*sqrt((247*sqrt(2) - 1000)/(247000*sqrt(2) - 561009)) + 4*sqrt(341)*sqrt(31)*(50
0*sqrt(2)*x - 247*x)*sqrt(-(sqrt(341)*50^(1/4)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqr
t(2)*(24886429777*x + 2962665725) - 27849095502*x - 21923764052)*sqrt((247*sqrt(
2) - 1000)/(247000*sqrt(2) - 561009)) + 167341615000*x^2 + 220*sqrt(2)*(13660540
00*x^2 - 385569223*sqrt(2)*(2*x^2 - x + 3) - 683027000*x + 2049081000) - 1927846
115*sqrt(2)*(49*x^2 - 151*x + 200) - 515685385000*x + 683027000000)/(385569223*s
qrt(2)*x^2 - 683027000*x^2))*sqrt((247*sqrt(2) - 1000)/(247000*sqrt(2) - 561009)
) - 682*50^(1/4)*sqrt(31)*sqrt(2*x^2 - x + 3)*(3*sqrt(2) - 16))) - 339388*50^(1/
4)*(2*x^2 - x + 3)*arctan(-31*(sqrt(341)*sqrt(10)*(500*sqrt(2)*(x - 6) - 247*x +
1482)*sqrt((247*sqrt(2) - 1000)/(247000*sqrt(2) - 561009)) - 22*50^(1/4)*sqrt(2
*x^2 - x + 3)*(61*sqrt(2) - 8))/(sqrt(341)*sqrt(31)*sqrt(10)*(500*sqrt(2)*(19*x
- 22) - 4693*x + 5434)*sqrt((247*sqrt(2) - 1000)/(247000*sqrt(2) - 561009)) + 4*
sqrt(341)*sqrt(31)*(500*sqrt(2)*x - 247*x)*sqrt((sqrt(341)*50^(1/4)*sqrt(10)*sqr
t(2*x^2 - x + 3)*(sqrt(2)*(24886429777*x + 2962665725) - 27849095502*x - 2192376
4052)*sqrt((247*sqrt(2) - 1000)/(247000*sqrt(2) - 561009)) - 167341615000*x^2 -
220*sqrt(2)*(1366054000*x^2 - 385569223*sqrt(2)*(2*x^2 - x + 3) - 683027000*x +
2049081000) + 1927846115*sqrt(2)*(49*x^2 - 151*x + 200) + 515685385000*x - 68302
7000000)/(385569223*sqrt(2)*x^2 - 683027000*x^2))*sqrt((247*sqrt(2) - 1000)/(247
000*sqrt(2) - 561009)) + 682*50^(1/4)*sqrt(31)*sqrt(2*x^2 - x + 3)*(3*sqrt(2) -
16))))/((494*x^2 - 500*sqrt(2)*(2*x^2 - x + 3) - 247*x + 741)*sqrt((247*sqrt(2)
- 1000)/(247000*sqrt(2) - 561009)))
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (2 x^{2} - x + 3\right )^{\frac{3}{2}} \left (5 x^{2} + 3 x + 2\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(2*x**2-x+3)**(3/2)/(5*x**2+3*x+2),x)
[Out]
Integral(1/((2*x**2 - x + 3)**(3/2)*(5*x**2 + 3*x + 2)), x)
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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*x^2 - x + 3)^(3/2)),x, algorithm="giac")
[Out]
Exception raised: RuntimeError