Optimal. Leaf size=62 \[ -\frac{2 a^2}{\sqrt{x}}+\frac{2}{7} x^{7/2} \left (2 a c+b^2\right )+\frac{4}{3} a b x^{3/2}+\frac{4}{11} b c x^{11/2}+\frac{2}{15} c^2 x^{15/2} \]
[Out]
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Rubi [A] time = 0.054175, antiderivative size = 62, 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 \[ -\frac{2 a^2}{\sqrt{x}}+\frac{2}{7} x^{7/2} \left (2 a c+b^2\right )+\frac{4}{3} a b x^{3/2}+\frac{4}{11} b c x^{11/2}+\frac{2}{15} c^2 x^{15/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)^2/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 9.17958, size = 63, normalized size = 1.02 \[ - \frac{2 a^{2}}{\sqrt{x}} + \frac{4 a b x^{\frac{3}{2}}}{3} + \frac{4 b c x^{\frac{11}{2}}}{11} + \frac{2 c^{2} x^{\frac{15}{2}}}{15} + x^{\frac{7}{2}} \left (\frac{4 a c}{7} + \frac{2 b^{2}}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)**2/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0298845, size = 50, normalized size = 0.81 \[ \frac{2 \left (-1155 a^2+165 x^4 \left (2 a c+b^2\right )+770 a b x^2+210 b c x^6+77 c^2 x^8\right )}{1155 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)^2/x^(3/2),x]
[Out]
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Maple [A] time = 0.009, size = 49, normalized size = 0.8 \[ -{\frac{-154\,{c}^{2}{x}^{8}-420\,bc{x}^{6}-660\,{x}^{4}ac-330\,{b}^{2}{x}^{4}-1540\,ab{x}^{2}+2310\,{a}^{2}}{1155}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)^2/x^(3/2),x)
[Out]
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Maxima [A] time = 0.758327, size = 59, normalized size = 0.95 \[ \frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{11} \, b c x^{\frac{11}{2}} + \frac{2}{7} \,{\left (b^{2} + 2 \, a c\right )} x^{\frac{7}{2}} + \frac{4}{3} \, a b x^{\frac{3}{2}} - \frac{2 \, a^{2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.27402, size = 62, normalized size = 1. \[ \frac{2 \,{\left (77 \, c^{2} x^{8} + 210 \, b c x^{6} + 165 \,{\left (b^{2} + 2 \, a c\right )} x^{4} + 770 \, a b x^{2} - 1155 \, a^{2}\right )}}{1155 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 15.9796, size = 68, normalized size = 1.1 \[ - \frac{2 a^{2}}{\sqrt{x}} + \frac{4 a b x^{\frac{3}{2}}}{3} + \frac{4 a c x^{\frac{7}{2}}}{7} + \frac{2 b^{2} x^{\frac{7}{2}}}{7} + \frac{4 b c x^{\frac{11}{2}}}{11} + \frac{2 c^{2} x^{\frac{15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)**2/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.261894, size = 62, normalized size = 1. \[ \frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{11} \, b c x^{\frac{11}{2}} + \frac{2}{7} \, b^{2} x^{\frac{7}{2}} + \frac{4}{7} \, a c x^{\frac{7}{2}} + \frac{4}{3} \, a b x^{\frac{3}{2}} - \frac{2 \, a^{2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^(3/2),x, algorithm="giac")
[Out]