Optimal. Leaf size=36 \[ -\frac{2 a^2}{3 x^{3/2}}+\frac{4}{5} a c x^{5/2}+\frac{2}{13} c^2 x^{13/2} \]
[Out]
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Rubi [A] time = 0.02622, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2 a^2}{3 x^{3/2}}+\frac{4}{5} a c x^{5/2}+\frac{2}{13} c^2 x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)^2/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 4.53123, size = 34, normalized size = 0.94 \[ - \frac{2 a^{2}}{3 x^{\frac{3}{2}}} + \frac{4 a c x^{\frac{5}{2}}}{5} + \frac{2 c^{2} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**2/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0135442, size = 30, normalized size = 0.83 \[ \frac{2 \left (-65 a^2+78 a c x^4+15 c^2 x^8\right )}{195 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)^2/x^(5/2),x]
[Out]
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Maple [A] time = 0.009, size = 27, normalized size = 0.8 \[ -{\frac{-30\,{c}^{2}{x}^{8}-156\,ac{x}^{4}+130\,{a}^{2}}{195}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^2/x^(5/2),x)
[Out]
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Maxima [A] time = 1.4393, size = 32, normalized size = 0.89 \[ \frac{2}{13} \, c^{2} x^{\frac{13}{2}} + \frac{4}{5} \, a c x^{\frac{5}{2}} - \frac{2 \, a^{2}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227724, size = 35, normalized size = 0.97 \[ \frac{2 \,{\left (15 \, c^{2} x^{8} + 78 \, a c x^{4} - 65 \, a^{2}\right )}}{195 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 22.5508, size = 34, normalized size = 0.94 \[ - \frac{2 a^{2}}{3 x^{\frac{3}{2}}} + \frac{4 a c x^{\frac{5}{2}}}{5} + \frac{2 c^{2} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**2/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212642, size = 32, normalized size = 0.89 \[ \frac{2}{13} \, c^{2} x^{\frac{13}{2}} + \frac{4}{5} \, a c x^{\frac{5}{2}} - \frac{2 \, a^{2}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/x^(5/2),x, algorithm="giac")
[Out]