Optimal. Leaf size=36 \[ \frac{2}{7} b^2 x^{7/2}+\frac{4}{11} b c x^{11/2}+\frac{2}{15} c^2 x^{15/2} \]
[Out]
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Rubi [A] time = 0.0342171, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{2}{7} b^2 x^{7/2}+\frac{4}{11} b c x^{11/2}+\frac{2}{15} c^2 x^{15/2} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2 + c*x^4)^2/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 6.75102, size = 34, normalized size = 0.94 \[ \frac{2 b^{2} x^{\frac{7}{2}}}{7} + \frac{4 b c x^{\frac{11}{2}}}{11} + \frac{2 c^{2} x^{\frac{15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2)**2/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0118806, size = 30, normalized size = 0.83 \[ \frac{2 x^{7/2} \left (165 b^2+210 b c x^2+77 c^2 x^4\right )}{1155} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2 + c*x^4)^2/x^(3/2),x]
[Out]
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Maple [A] time = 0.007, size = 27, normalized size = 0.8 \[{\frac{154\,{c}^{2}{x}^{4}+420\,bc{x}^{2}+330\,{b}^{2}}{1155}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2)^2/x^(3/2),x)
[Out]
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Maxima [A] time = 0.688772, size = 32, normalized size = 0.89 \[ \frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{11} \, b c x^{\frac{11}{2}} + \frac{2}{7} \, b^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265793, size = 39, normalized size = 1.08 \[ \frac{2}{1155} \,{\left (77 \, c^{2} x^{7} + 210 \, b c x^{5} + 165 \, b^{2} x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 15.8135, size = 34, normalized size = 0.94 \[ \frac{2 b^{2} x^{\frac{7}{2}}}{7} + \frac{4 b c x^{\frac{11}{2}}}{11} + \frac{2 c^{2} x^{\frac{15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2)**2/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.268018, size = 32, normalized size = 0.89 \[ \frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{11} \, b c x^{\frac{11}{2}} + \frac{2}{7} \, b^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2/x^(3/2),x, algorithm="giac")
[Out]