Optimal. Leaf size=10 \[ \frac{2}{3} \tan ^{-1}\left (x^{3/2}\right ) \]
[Out]
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Rubi [A] time = 0.0201628, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{2}{3} \tan ^{-1}\left (x^{3/2}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]/(1 + x^3),x]
[Out]
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Rubi in Sympy [A] time = 4.16914, size = 8, normalized size = 0.8 \[ \frac{2 \operatorname{atan}{\left (x^{\frac{3}{2}} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(1/2)/(x**3+1),x)
[Out]
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Mathematica [A] time = 0.00759896, size = 10, normalized size = 1. \[ -\frac{2}{3} \tan ^{-1}\left (\frac{1}{x^{3/2}}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]/(1 + x^3),x]
[Out]
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Maple [A] time = 0.008, size = 7, normalized size = 0.7 \[{\frac{2}{3}\arctan \left ({x}^{{\frac{3}{2}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(1/2)/(x^3+1),x)
[Out]
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Maxima [A] time = 1.57841, size = 8, normalized size = 0.8 \[ \frac{2}{3} \, \arctan \left (x^{\frac{3}{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(x^3 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222299, size = 8, normalized size = 0.8 \[ \frac{2}{3} \, \arctan \left (x^{\frac{3}{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(x^3 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.24713, size = 42, normalized size = 4.2 \[ - \frac{2 \operatorname{atan}{\left (\sqrt{x} \right )}}{3} + \frac{2 \operatorname{atan}{\left (2 \sqrt{x} - \sqrt{3} \right )}}{3} + \frac{2 \operatorname{atan}{\left (2 \sqrt{x} + \sqrt{3} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(1/2)/(x**3+1),x)
[Out]
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GIAC/XCAS [A] time = 0.217923, size = 8, normalized size = 0.8 \[ \frac{2}{3} \, \arctan \left (x^{\frac{3}{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(x^3 + 1),x, algorithm="giac")
[Out]