Optimal. Leaf size=64 \[ \frac{2}{7} a^2 x^{7/2}+\frac{2}{15} x^{15/2} \left (2 a c+b^2\right )+\frac{4}{11} a b x^{11/2}+\frac{4}{19} b c x^{19/2}+\frac{2}{23} c^2 x^{23/2} \]
[Out]
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Rubi [A] time = 0.0581908, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{2}{7} a^2 x^{7/2}+\frac{2}{15} x^{15/2} \left (2 a c+b^2\right )+\frac{4}{11} a b x^{11/2}+\frac{4}{19} b c x^{19/2}+\frac{2}{23} c^2 x^{23/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + b*x^2 + c*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 9.14314, size = 65, normalized size = 1.02 \[ \frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{11}{2}}}{11} + \frac{4 b c x^{\frac{19}{2}}}{19} + \frac{2 c^{2} x^{\frac{23}{2}}}{23} + x^{\frac{15}{2}} \left (\frac{4 a c}{15} + \frac{2 b^{2}}{15}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(c*x**4+b*x**2+a)**2,x)
[Out]
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Mathematica [A] time = 0.029601, size = 64, normalized size = 1. \[ \frac{2}{7} a^2 x^{7/2}+\frac{2}{15} x^{15/2} \left (2 a c+b^2\right )+\frac{4}{11} a b x^{11/2}+\frac{4}{19} b c x^{19/2}+\frac{2}{23} c^2 x^{23/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + b*x^2 + c*x^4)^2,x]
[Out]
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Maple [A] time = 0.009, size = 49, normalized size = 0.8 \[{\frac{43890\,{c}^{2}{x}^{8}+106260\,bc{x}^{6}+134596\,{x}^{4}ac+67298\,{b}^{2}{x}^{4}+183540\,ab{x}^{2}+144210\,{a}^{2}}{504735}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(c*x^4+b*x^2+a)^2,x)
[Out]
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Maxima [A] time = 0.75981, size = 59, normalized size = 0.92 \[ \frac{2}{23} \, c^{2} x^{\frac{23}{2}} + \frac{4}{19} \, b c x^{\frac{19}{2}} + \frac{2}{15} \,{\left (b^{2} + 2 \, a c\right )} x^{\frac{15}{2}} + \frac{4}{11} \, a b x^{\frac{11}{2}} + \frac{2}{7} \, a^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271702, size = 66, normalized size = 1.03 \[ \frac{2}{504735} \,{\left (21945 \, c^{2} x^{11} + 53130 \, b c x^{9} + 33649 \,{\left (b^{2} + 2 \, a c\right )} x^{7} + 91770 \, a b x^{5} + 72105 \, a^{2} x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 62.8919, size = 70, normalized size = 1.09 \[ \frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{11}{2}}}{11} + \frac{4 a c x^{\frac{15}{2}}}{15} + \frac{2 b^{2} x^{\frac{15}{2}}}{15} + \frac{4 b c x^{\frac{19}{2}}}{19} + \frac{2 c^{2} x^{\frac{23}{2}}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(c*x**4+b*x**2+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.261276, size = 62, normalized size = 0.97 \[ \frac{2}{23} \, c^{2} x^{\frac{23}{2}} + \frac{4}{19} \, b c x^{\frac{19}{2}} + \frac{2}{15} \, b^{2} x^{\frac{15}{2}} + \frac{4}{15} \, a c x^{\frac{15}{2}} + \frac{4}{11} \, a b x^{\frac{11}{2}} + \frac{2}{7} \, a^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2*x^(5/2),x, algorithm="giac")
[Out]