Optimal. Leaf size=36 \[ \frac{2}{5} b^2 x^{5/2}+\frac{4}{9} b c x^{9/2}+\frac{2}{13} c^2 x^{13/2} \]
[Out]
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Rubi [A] time = 0.0348967, 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 \[ \frac{2}{5} b^2 x^{5/2}+\frac{4}{9} b c x^{9/2}+\frac{2}{13} c^2 x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2 + c*x^4)^2/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 6.67276, size = 34, normalized size = 0.94 \[ \frac{2 b^{2} x^{\frac{5}{2}}}{5} + \frac{4 b c x^{\frac{9}{2}}}{9} + \frac{2 c^{2} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2)**2/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0115613, size = 30, normalized size = 0.83 \[ \frac{2}{585} x^{5/2} \left (117 b^2+130 b c x^2+45 c^2 x^4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2 + c*x^4)^2/x^(5/2),x]
[Out]
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Maple [A] time = 0.008, size = 27, normalized size = 0.8 \[{\frac{90\,{c}^{2}{x}^{4}+260\,bc{x}^{2}+234\,{b}^{2}}{585}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2)^2/x^(5/2),x)
[Out]
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Maxima [A] time = 0.687731, size = 32, normalized size = 0.89 \[ \frac{2}{13} \, c^{2} x^{\frac{13}{2}} + \frac{4}{9} \, b c x^{\frac{9}{2}} + \frac{2}{5} \, b^{2} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271015, size = 39, normalized size = 1.08 \[ \frac{2}{585} \,{\left (45 \, c^{2} x^{6} + 130 \, b c x^{4} + 117 \, b^{2} x^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 18.6524, size = 34, normalized size = 0.94 \[ \frac{2 b^{2} x^{\frac{5}{2}}}{5} + \frac{4 b c x^{\frac{9}{2}}}{9} + \frac{2 c^{2} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2)**2/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.268494, size = 32, normalized size = 0.89 \[ \frac{2}{13} \, c^{2} x^{\frac{13}{2}} + \frac{4}{9} \, b c x^{\frac{9}{2}} + \frac{2}{5} \, b^{2} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2/x^(5/2),x, algorithm="giac")
[Out]