Optimal. Leaf size=36 \[ \frac{2}{7} a^2 x^{7/2}+\frac{4}{15} a c x^{15/2}+\frac{2}{23} c^2 x^{23/2} \]
[Out]
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Rubi [A] time = 0.0264287, 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 \[ \frac{2}{7} a^2 x^{7/2}+\frac{4}{15} a c x^{15/2}+\frac{2}{23} c^2 x^{23/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + c*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 4.51766, size = 34, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a c x^{\frac{15}{2}}}{15} + \frac{2 c^{2} x^{\frac{23}{2}}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(c*x**4+a)**2,x)
[Out]
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Mathematica [A] time = 0.012895, size = 30, normalized size = 0.83 \[ \frac{2 x^{7/2} \left (345 a^2+322 a c x^4+105 c^2 x^8\right )}{2415} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + c*x^4)^2,x]
[Out]
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \[{\frac{210\,{c}^{2}{x}^{8}+644\,ac{x}^{4}+690\,{a}^{2}}{2415}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(c*x^4+a)^2,x)
[Out]
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Maxima [A] time = 1.43973, size = 32, normalized size = 0.89 \[ \frac{2}{23} \, c^{2} x^{\frac{23}{2}} + \frac{4}{15} \, a c x^{\frac{15}{2}} + \frac{2}{7} \, a^{2} x^{\frac{7}{2}} \]
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 = 0.226314, size = 39, normalized size = 1.08 \[ \frac{2}{2415} \,{\left (105 \, c^{2} x^{11} + 322 \, a c x^{7} + 345 \, a^{2} x^{3}\right )} \sqrt{x} \]
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 = 70.4942, size = 34, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a c x^{\frac{15}{2}}}{15} + \frac{2 c^{2} x^{\frac{23}{2}}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(c*x**4+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217067, size = 32, normalized size = 0.89 \[ \frac{2}{23} \, c^{2} x^{\frac{23}{2}} + \frac{4}{15} \, a c x^{\frac{15}{2}} + \frac{2}{7} \, a^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2*x^(5/2),x, algorithm="giac")
[Out]