3.30 \(\int \frac{2+x}{\left (2+4 x-3 x^2\right ) \left (1+3 x+2 x^2\right )^{5/2}} \, dx\)

Optimal. Leaf size=197 \[ \frac{2 (22 x+21)}{15 \left (2 x^2+3 x+1\right )^{3/2}}+\frac{2 (230 x+273)}{15 \sqrt{2 x^2+3 x+1}}-\frac{1}{50} \sqrt{\frac{1}{3} \left (4885115+1544809 \sqrt{10}\right )} \tanh ^{-1}\left (\frac{\left (17-4 \sqrt{10}\right ) x+3 \left (4-\sqrt{10}\right )}{2 \sqrt{55-17 \sqrt{10}} \sqrt{2 x^2+3 x+1}}\right )+\frac{1}{50} \sqrt{\frac{1}{3} \left (4885115-1544809 \sqrt{10}\right )} \tanh ^{-1}\left (\frac{\left (17+4 \sqrt{10}\right ) x+3 \left (4+\sqrt{10}\right )}{2 \sqrt{55+17 \sqrt{10}} \sqrt{2 x^2+3 x+1}}\right ) \]

[Out]

(2*(21 + 22*x))/(15*(1 + 3*x + 2*x^2)^(3/2)) + (2*(273 + 230*x))/(15*Sqrt[1 + 3*
x + 2*x^2]) - (Sqrt[(4885115 + 1544809*Sqrt[10])/3]*ArcTanh[(3*(4 - Sqrt[10]) +
(17 - 4*Sqrt[10])*x)/(2*Sqrt[55 - 17*Sqrt[10]]*Sqrt[1 + 3*x + 2*x^2])])/50 + (Sq
rt[(4885115 - 1544809*Sqrt[10])/3]*ArcTanh[(3*(4 + Sqrt[10]) + (17 + 4*Sqrt[10])
*x)/(2*Sqrt[55 + 17*Sqrt[10]]*Sqrt[1 + 3*x + 2*x^2])])/50

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Rubi [A]  time = 0.816461, antiderivative size = 197, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 5, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{2 (22 x+21)}{15 \left (2 x^2+3 x+1\right )^{3/2}}+\frac{2 (230 x+273)}{15 \sqrt{2 x^2+3 x+1}}-\frac{1}{50} \sqrt{\frac{1}{3} \left (4885115+1544809 \sqrt{10}\right )} \tanh ^{-1}\left (\frac{\left (17-4 \sqrt{10}\right ) x+3 \left (4-\sqrt{10}\right )}{2 \sqrt{55-17 \sqrt{10}} \sqrt{2 x^2+3 x+1}}\right )+\frac{1}{50} \sqrt{\frac{1}{3} \left (4885115-1544809 \sqrt{10}\right )} \tanh ^{-1}\left (\frac{\left (17+4 \sqrt{10}\right ) x+3 \left (4+\sqrt{10}\right )}{2 \sqrt{55+17 \sqrt{10}} \sqrt{2 x^2+3 x+1}}\right ) \]

Antiderivative was successfully verified.

[In]  Int[(2 + x)/((2 + 4*x - 3*x^2)*(1 + 3*x + 2*x^2)^(5/2)),x]

[Out]

(2*(21 + 22*x))/(15*(1 + 3*x + 2*x^2)^(3/2)) + (2*(273 + 230*x))/(15*Sqrt[1 + 3*
x + 2*x^2]) - (Sqrt[(4885115 + 1544809*Sqrt[10])/3]*ArcTanh[(3*(4 - Sqrt[10]) +
(17 - 4*Sqrt[10])*x)/(2*Sqrt[55 - 17*Sqrt[10]]*Sqrt[1 + 3*x + 2*x^2])])/50 + (Sq
rt[(4885115 - 1544809*Sqrt[10])/3]*ArcTanh[(3*(4 + Sqrt[10]) + (17 + 4*Sqrt[10])
*x)/(2*Sqrt[55 + 17*Sqrt[10]]*Sqrt[1 + 3*x + 2*x^2])])/50

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Rubi in Sympy [A]  time = 79.2848, size = 194, normalized size = 0.98 \[ \frac{2 \left (66 x + 63\right )}{45 \left (2 x^{2} + 3 x + 1\right )^{\frac{3}{2}}} + \frac{4 \left (5175 x + \frac{12285}{2}\right )}{675 \sqrt{2 x^{2} + 3 x + 1}} + \frac{\sqrt{10} \left (\frac{27135 \sqrt{10}}{2} + 42930\right ) \operatorname{atanh}{\left (\frac{x \left (-34 + 8 \sqrt{10}\right ) - 24 + 6 \sqrt{10}}{4 \sqrt{- 17 \sqrt{10} + 55} \sqrt{2 x^{2} + 3 x + 1}} \right )}}{6750 \sqrt{- 17 \sqrt{10} + 55}} - \frac{\sqrt{10} \left (- \frac{27135 \sqrt{10}}{2} + 42930\right ) \operatorname{atanh}{\left (\frac{x \left (-34 - 8 \sqrt{10}\right ) - 24 - 6 \sqrt{10}}{4 \sqrt{17 \sqrt{10} + 55} \sqrt{2 x^{2} + 3 x + 1}} \right )}}{6750 \sqrt{17 \sqrt{10} + 55}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+x)/(-3*x**2+4*x+2)/(2*x**2+3*x+1)**(5/2),x)

[Out]

2*(66*x + 63)/(45*(2*x**2 + 3*x + 1)**(3/2)) + 4*(5175*x + 12285/2)/(675*sqrt(2*
x**2 + 3*x + 1)) + sqrt(10)*(27135*sqrt(10)/2 + 42930)*atanh((x*(-34 + 8*sqrt(10
)) - 24 + 6*sqrt(10))/(4*sqrt(-17*sqrt(10) + 55)*sqrt(2*x**2 + 3*x + 1)))/(6750*
sqrt(-17*sqrt(10) + 55)) - sqrt(10)*(-27135*sqrt(10)/2 + 42930)*atanh((x*(-34 -
8*sqrt(10)) - 24 - 6*sqrt(10))/(4*sqrt(17*sqrt(10) + 55)*sqrt(2*x**2 + 3*x + 1))
)/(6750*sqrt(17*sqrt(10) + 55))

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Mathematica [A]  time = 3.36487, size = 283, normalized size = 1.44 \[ \frac{1}{300} \left (\frac{40 (22 x+21)}{\left (2 x^2+3 x+1\right )^{3/2}}+\frac{40 (230 x+273)}{\sqrt{2 x^2+3 x+1}}-9 \sqrt{\frac{10}{55-17 \sqrt{10}}} \left (212+67 \sqrt{10}\right ) \log \left (-2 \sqrt{550-170 \sqrt{10}} \sqrt{2 x^2+3 x+1}-17 \sqrt{10} x+40 x-12 \sqrt{10}+30\right )-9 \sqrt{\frac{10}{55+17 \sqrt{10}}} \left (67 \sqrt{10}-212\right ) \log \left (2 \sqrt{550+170 \sqrt{10}} \sqrt{2 x^2+3 x+1}+17 \sqrt{10} x+40 x+12 \sqrt{10}+30\right )+9 \sqrt{\frac{10}{55-17 \sqrt{10}}} \left (212+67 \sqrt{10}\right ) \log \left (-3 x-\sqrt{10}+2\right )+9 \sqrt{\frac{10}{55+17 \sqrt{10}}} \left (67 \sqrt{10}-212\right ) \log \left (-3 x+\sqrt{10}+2\right )\right ) \]

Warning: Unable to verify antiderivative.

[In]  Integrate[(2 + x)/((2 + 4*x - 3*x^2)*(1 + 3*x + 2*x^2)^(5/2)),x]

[Out]

((40*(21 + 22*x))/(1 + 3*x + 2*x^2)^(3/2) + (40*(273 + 230*x))/Sqrt[1 + 3*x + 2*
x^2] + 9*Sqrt[10/(55 - 17*Sqrt[10])]*(212 + 67*Sqrt[10])*Log[2 - Sqrt[10] - 3*x]
+ 9*Sqrt[10/(55 + 17*Sqrt[10])]*(-212 + 67*Sqrt[10])*Log[2 + Sqrt[10] - 3*x] -
9*Sqrt[10/(55 - 17*Sqrt[10])]*(212 + 67*Sqrt[10])*Log[30 - 12*Sqrt[10] + 40*x -
17*Sqrt[10]*x - 2*Sqrt[550 - 170*Sqrt[10]]*Sqrt[1 + 3*x + 2*x^2]] - 9*Sqrt[10/(5
5 + 17*Sqrt[10])]*(-212 + 67*Sqrt[10])*Log[30 + 12*Sqrt[10] + 40*x + 17*Sqrt[10]
*x + 2*Sqrt[550 + 170*Sqrt[10]]*Sqrt[1 + 3*x + 2*x^2]])/300

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Maple [B]  time = 0.023, size = 878, normalized size = 4.5 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(5/2),x)

[Out]

-1/20*(-8+10^(1/2))*10^(1/2)*(1/9/(55/9-17/9*10^(1/2))/(2*(x-2/3+1/3*10^(1/2))^2
+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(3/2)-1/6*(17/3-4/
3*10^(1/2))/(55/9-17/9*10^(1/2))*(2/3*(3+4*x)/(440/9-136/9*10^(1/2)-(17/3-4/3*10
^(1/2))^2)/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55
/9-17/9*10^(1/2))^(3/2)+32/3/(440/9-136/9*10^(1/2)-(17/3-4/3*10^(1/2))^2)^2*(3+4
*x)/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9
*10^(1/2))^(1/2))+1/3/(55/9-17/9*10^(1/2))*(1/(55/9-17/9*10^(1/2))/(2*(x-2/3+1/3
*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(1/2)-
(17/3-4/3*10^(1/2))/(55/9-17/9*10^(1/2))*(3+4*x)/(440/9-136/9*10^(1/2)-(17/3-4/3
*10^(1/2))^2)/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))
+55/9-17/9*10^(1/2))^(1/2)-3/(55/9-17/9*10^(1/2))/(55-17*10^(1/2))^(1/2)*arctanh
(9/2*(110/9-34/9*10^(1/2)+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(55-17*10^(1
/2))^(1/2)/(18*(x-2/3+1/3*10^(1/2))^2+9*(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))
+55-17*10^(1/2))^(1/2))))-1/20*(8+10^(1/2))*10^(1/2)*(1/9/(55/9+17/9*10^(1/2))/(
2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(
1/2))^(3/2)-1/6*(17/3+4/3*10^(1/2))/(55/9+17/9*10^(1/2))*(2/3*(3+4*x)/(440/9+136
/9*10^(1/2)-(17/3+4/3*10^(1/2))^2)/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))
*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(3/2)+32/3/(440/9+136/9*10^(1/2)-(17/3
+4/3*10^(1/2))^2)^2*(3+4*x)/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3
-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(1/2))+1/3/(55/9+17/9*10^(1/2))*(1/(55/9+17/9
*10^(1/2))/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55
/9+17/9*10^(1/2))^(1/2)-(17/3+4/3*10^(1/2))/(55/9+17/9*10^(1/2))*(3+4*x)/(440/9+
136/9*10^(1/2)-(17/3+4/3*10^(1/2))^2)/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/
2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(1/2)-3/(55/9+17/9*10^(1/2))/(55+17
*10^(1/2))^(1/2)*arctanh(9/2*(110/9+34/9*10^(1/2)+(17/3+4/3*10^(1/2))*(x-2/3-1/3
*10^(1/2)))/(55+17*10^(1/2))^(1/2)/(18*(x-2/3-1/3*10^(1/2))^2+9*(17/3+4/3*10^(1/
2))*(x-2/3-1/3*10^(1/2))+55+17*10^(1/2))^(1/2))))

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Maxima [A]  time = 0.837167, size = 1723, normalized size = 8.75 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(x + 2)/((3*x^2 - 4*x - 2)*(2*x^2 + 3*x + 1)^(5/2)),x, algorithm="maxima")

[Out]

-1/300*sqrt(10)*(980*sqrt(10)*x/(17*sqrt(10)*(2*x^2 + 3*x + 1)^(3/2) + 55*(2*x^2
+ 3*x + 1)^(3/2)) - 980*sqrt(10)*x/(17*sqrt(10)*(2*x^2 + 3*x + 1)^(3/2) - 55*(2
*x^2 + 3*x + 1)^(3/2)) + 5292*sqrt(10)*x/(374*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 1
183*sqrt(2*x^2 + 3*x + 1)) - 5292*sqrt(10)*x/(374*sqrt(10)*sqrt(2*x^2 + 3*x + 1)
- 1183*sqrt(2*x^2 + 3*x + 1)) - 15680*sqrt(10)*x/(17*sqrt(10)*sqrt(2*x^2 + 3*x
+ 1) + 55*sqrt(2*x^2 + 3*x + 1)) + 15680*sqrt(10)*x/(17*sqrt(10)*sqrt(2*x^2 + 3*
x + 1) - 55*sqrt(2*x^2 + 3*x + 1)) + 3520*x/(17*sqrt(10)*(2*x^2 + 3*x + 1)^(3/2)
+ 55*(2*x^2 + 3*x + 1)^(3/2)) + 3520*x/(17*sqrt(10)*(2*x^2 + 3*x + 1)^(3/2) - 5
5*(2*x^2 + 3*x + 1)^(3/2)) + 19008*x/(374*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 1183*
sqrt(2*x^2 + 3*x + 1)) + 19008*x/(374*sqrt(10)*sqrt(2*x^2 + 3*x + 1) - 1183*sqrt
(2*x^2 + 3*x + 1)) - 56320*x/(17*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 55*sqrt(2*x^2
+ 3*x + 1)) - 56320*x/(17*sqrt(10)*sqrt(2*x^2 + 3*x + 1) - 55*sqrt(2*x^2 + 3*x +
1)) + 750*sqrt(10)/(17*sqrt(10)*(2*x^2 + 3*x + 1)^(3/2) + 55*(2*x^2 + 3*x + 1)^
(3/2)) - 750*sqrt(10)/(17*sqrt(10)*(2*x^2 + 3*x + 1)^(3/2) - 55*(2*x^2 + 3*x + 1
)^(3/2)) + 4050*sqrt(10)/(374*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 1183*sqrt(2*x^2 +
3*x + 1)) - 4050*sqrt(10)/(374*sqrt(10)*sqrt(2*x^2 + 3*x + 1) - 1183*sqrt(2*x^2
+ 3*x + 1)) - 11760*sqrt(10)/(17*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 55*sqrt(2*x^2
+ 3*x + 1)) + 11760*sqrt(10)/(17*sqrt(10)*sqrt(2*x^2 + 3*x + 1) - 55*sqrt(2*x^2
+ 3*x + 1)) + 2760/(17*sqrt(10)*(2*x^2 + 3*x + 1)^(3/2) + 55*(2*x^2 + 3*x + 1)^
(3/2)) + 2760/(17*sqrt(10)*(2*x^2 + 3*x + 1)^(3/2) - 55*(2*x^2 + 3*x + 1)^(3/2))
+ 14904/(374*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 1183*sqrt(2*x^2 + 3*x + 1)) + 149
04/(374*sqrt(10)*sqrt(2*x^2 + 3*x + 1) - 1183*sqrt(2*x^2 + 3*x + 1)) - 42240/(17
*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 55*sqrt(2*x^2 + 3*x + 1)) - 42240/(17*sqrt(10)
*sqrt(2*x^2 + 3*x + 1) - 55*sqrt(2*x^2 + 3*x + 1)) - 1215*sqrt(10)*log(2/9*sqrt(
10) + 2/3*sqrt(2*x^2 + 3*x + 1)*sqrt(17*sqrt(10) + 55)/abs(6*x - 2*sqrt(10) - 4)
+ 34/9*sqrt(10)/abs(6*x - 2*sqrt(10) - 4) + 110/9/abs(6*x - 2*sqrt(10) - 4) + 1
7/18)/(17*sqrt(10) + 55)^(5/2) - 5*sqrt(10)*log(-2/9*sqrt(10) + 2*sqrt(2*x^2 + 3
*x + 1)*sqrt(-17/9*sqrt(10) + 55/9)/abs(6*x + 2*sqrt(10) - 4) - 34/9*sqrt(10)/ab
s(6*x + 2*sqrt(10) - 4) + 110/9/abs(6*x + 2*sqrt(10) - 4) + 17/18)/(-17/9*sqrt(1
0) + 55/9)^(5/2) - 9720*log(2/9*sqrt(10) + 2/3*sqrt(2*x^2 + 3*x + 1)*sqrt(17*sqr
t(10) + 55)/abs(6*x - 2*sqrt(10) - 4) + 34/9*sqrt(10)/abs(6*x - 2*sqrt(10) - 4)
+ 110/9/abs(6*x - 2*sqrt(10) - 4) + 17/18)/(17*sqrt(10) + 55)^(5/2) + 40*log(-2/
9*sqrt(10) + 2*sqrt(2*x^2 + 3*x + 1)*sqrt(-17/9*sqrt(10) + 55/9)/abs(6*x + 2*sqr
t(10) - 4) - 34/9*sqrt(10)/abs(6*x + 2*sqrt(10) - 4) + 110/9/abs(6*x + 2*sqrt(10
) - 4) + 17/18)/(-17/9*sqrt(10) + 55/9)^(5/2))

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Fricas [A]  time = 0.289555, size = 1088, normalized size = 5.52 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(x + 2)/((3*x^2 - 4*x - 2)*(2*x^2 + 3*x + 1)^(5/2)),x, algorithm="fricas")

[Out]

1/150*(735600*x^6 + 2817840*x^5 + 4240620*x^4 + 3131360*x^3 + 1134240*x^2 + 3*(s
qrt(1/6)*(198*x^5 + 717*x^4 + 1017*x^3 + 706*x^2 + 240*x + 32)*sqrt(2*x^2 + 3*x
+ 1)*sqrt(sqrt(10)*(977023*sqrt(10) + 3089618)) - 2*sqrt(1/6)*(140*x^6 + 612*x^5
+ 1095*x^4 + 1026*x^3 + 531*x^2 + 144*x + 16)*sqrt(sqrt(10)*(977023*sqrt(10) +
3089618)))*log(-(sqrt(1/6)*(1412*sqrt(10)*x - 4465*x)*sqrt(sqrt(10)*(977023*sqrt
(10) + 3089618)) + 81*sqrt(10)*(x + 1) - 81*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 405
*x)/x) - 3*(sqrt(1/6)*(198*x^5 + 717*x^4 + 1017*x^3 + 706*x^2 + 240*x + 32)*sqrt
(2*x^2 + 3*x + 1)*sqrt(sqrt(10)*(977023*sqrt(10) + 3089618)) - 2*sqrt(1/6)*(140*
x^6 + 612*x^5 + 1095*x^4 + 1026*x^3 + 531*x^2 + 144*x + 16)*sqrt(sqrt(10)*(97702
3*sqrt(10) + 3089618)))*log((sqrt(1/6)*(1412*sqrt(10)*x - 4465*x)*sqrt(sqrt(10)*
(977023*sqrt(10) + 3089618)) - 81*sqrt(10)*(x + 1) + 81*sqrt(10)*sqrt(2*x^2 + 3*
x + 1) - 405*x)/x) + 3*(sqrt(1/6)*(198*x^5 + 717*x^4 + 1017*x^3 + 706*x^2 + 240*
x + 32)*sqrt(2*x^2 + 3*x + 1)*sqrt(sqrt(10)*(977023*sqrt(10) - 3089618)) - 2*sqr
t(1/6)*(140*x^6 + 612*x^5 + 1095*x^4 + 1026*x^3 + 531*x^2 + 144*x + 16)*sqrt(sqr
t(10)*(977023*sqrt(10) - 3089618)))*log(-(sqrt(1/6)*(1412*sqrt(10)*x + 4465*x)*s
qrt(sqrt(10)*(977023*sqrt(10) - 3089618)) + 81*sqrt(10)*(x + 1) - 81*sqrt(10)*sq
rt(2*x^2 + 3*x + 1) - 405*x)/x) - 3*(sqrt(1/6)*(198*x^5 + 717*x^4 + 1017*x^3 + 7
06*x^2 + 240*x + 32)*sqrt(2*x^2 + 3*x + 1)*sqrt(sqrt(10)*(977023*sqrt(10) - 3089
618)) - 2*sqrt(1/6)*(140*x^6 + 612*x^5 + 1095*x^4 + 1026*x^3 + 531*x^2 + 144*x +
16)*sqrt(sqrt(10)*(977023*sqrt(10) - 3089618)))*log((sqrt(1/6)*(1412*sqrt(10)*x
+ 4465*x)*sqrt(sqrt(10)*(977023*sqrt(10) - 3089618)) - 81*sqrt(10)*(x + 1) + 81
*sqrt(10)*sqrt(2*x^2 + 3*x + 1) + 405*x)/x) - 40*(13006*x^5 + 40059*x^4 + 45326*
x^3 + 22308*x^2 + 4032*x)*sqrt(2*x^2 + 3*x + 1) + 161280*x)/(280*x^6 + 1224*x^5
+ 2190*x^4 + 2052*x^3 + 1062*x^2 - (198*x^5 + 717*x^4 + 1017*x^3 + 706*x^2 + 240
*x + 32)*sqrt(2*x^2 + 3*x + 1) + 288*x + 32)

_______________________________________________________________________________________

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((2+x)/(-3*x**2+4*x+2)/(2*x**2+3*x+1)**(5/2),x)

[Out]

Timed out

_______________________________________________________________________________________

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(-(x + 2)/((3*x^2 - 4*x - 2)*(2*x^2 + 3*x + 1)^(5/2)),x, algorithm="giac")

[Out]

Exception raised: RuntimeError