Optimal. Leaf size=49 \[ 2 a^3 \sqrt{x}+\frac{2}{3} a^2 c x^{9/2}+\frac{6}{17} a c^2 x^{17/2}+\frac{2}{25} c^3 x^{25/2} \]
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Rubi [A] time = 0.0347239, antiderivative size = 49, 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 \[ 2 a^3 \sqrt{x}+\frac{2}{3} a^2 c x^{9/2}+\frac{6}{17} a c^2 x^{17/2}+\frac{2}{25} c^3 x^{25/2} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)^3/Sqrt[x],x]
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Rubi in Sympy [A] time = 5.7909, size = 48, normalized size = 0.98 \[ 2 a^{3} \sqrt{x} + \frac{2 a^{2} c x^{\frac{9}{2}}}{3} + \frac{6 a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 c^{3} x^{\frac{25}{2}}}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**3/x**(1/2),x)
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Mathematica [A] time = 0.0138767, size = 41, normalized size = 0.84 \[ \frac{2 \sqrt{x} \left (1275 a^3+425 a^2 c x^4+225 a c^2 x^8+51 c^3 x^{12}\right )}{1275} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)^3/Sqrt[x],x]
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Maple [A] time = 0.008, size = 38, normalized size = 0.8 \[{\frac{102\,{c}^{3}{x}^{12}+450\,a{c}^{2}{x}^{8}+850\,{a}^{2}c{x}^{4}+2550\,{a}^{3}}{1275}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^3/x^(1/2),x)
[Out]
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Maxima [A] time = 1.43547, size = 47, normalized size = 0.96 \[ \frac{2}{25} \, c^{3} x^{\frac{25}{2}} + \frac{6}{17} \, a c^{2} x^{\frac{17}{2}} + \frac{2}{3} \, a^{2} c x^{\frac{9}{2}} + 2 \, a^{3} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227382, size = 50, normalized size = 1.02 \[ \frac{2}{1275} \,{\left (51 \, c^{3} x^{12} + 225 \, a c^{2} x^{8} + 425 \, a^{2} c x^{4} + 1275 \, a^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 60.6146, size = 48, normalized size = 0.98 \[ 2 a^{3} \sqrt{x} + \frac{2 a^{2} c x^{\frac{9}{2}}}{3} + \frac{6 a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 c^{3} x^{\frac{25}{2}}}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**3/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215798, size = 47, normalized size = 0.96 \[ \frac{2}{25} \, c^{3} x^{\frac{25}{2}} + \frac{6}{17} \, a c^{2} x^{\frac{17}{2}} + \frac{2}{3} \, a^{2} c x^{\frac{9}{2}} + 2 \, a^{3} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3/sqrt(x),x, algorithm="giac")
[Out]