Optimal. Leaf size=36 \[ \frac{2}{5} a^2 x^{5/2}+\frac{4}{13} a c x^{13/2}+\frac{2}{21} c^2 x^{21/2} \]
[Out]
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Rubi [A] time = 0.0291444, 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 \[ \frac{2}{5} a^2 x^{5/2}+\frac{4}{13} a c x^{13/2}+\frac{2}{21} c^2 x^{21/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(a + c*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 4.50819, size = 34, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a c x^{\frac{13}{2}}}{13} + \frac{2 c^{2} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(c*x**4+a)**2,x)
[Out]
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Mathematica [A] time = 0.012375, size = 30, normalized size = 0.83 \[ \frac{2 x^{5/2} \left (273 a^2+210 a c x^4+65 c^2 x^8\right )}{1365} \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(a + c*x^4)^2,x]
[Out]
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Maple [A] time = 0.008, size = 27, normalized size = 0.8 \[{\frac{130\,{c}^{2}{x}^{8}+420\,ac{x}^{4}+546\,{a}^{2}}{1365}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(c*x^4+a)^2,x)
[Out]
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Maxima [A] time = 1.42541, size = 32, normalized size = 0.89 \[ \frac{2}{21} \, c^{2} x^{\frac{21}{2}} + \frac{4}{13} \, a c x^{\frac{13}{2}} + \frac{2}{5} \, a^{2} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.239145, size = 39, normalized size = 1.08 \[ \frac{2}{1365} \,{\left (65 \, c^{2} x^{10} + 210 \, a c x^{6} + 273 \, a^{2} x^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2*x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 37.8736, size = 34, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a c x^{\frac{13}{2}}}{13} + \frac{2 c^{2} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(c*x**4+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.216725, size = 32, normalized size = 0.89 \[ \frac{2}{21} \, c^{2} x^{\frac{21}{2}} + \frac{4}{13} \, a c x^{\frac{13}{2}} + \frac{2}{5} \, a^{2} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2*x^(3/2),x, algorithm="giac")
[Out]