Optimal. Leaf size=27 \[ -\frac{2 \tanh ^{-1}\left (\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right )}{3 \sqrt{a}} \]
[Out]
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Rubi [A] time = 0.0496006, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{2 \tanh ^{-1}\left (\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right )}{3 \sqrt{a}} \]
Antiderivative was successfully verified.
[In] Int[1/(x*Sqrt[a + b*x^3]),x]
[Out]
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Rubi in Sympy [A] time = 5.23633, size = 26, normalized size = 0.96 \[ - \frac{2 \operatorname{atanh}{\left (\frac{\sqrt{a + b x^{3}}}{\sqrt{a}} \right )}}{3 \sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x**3+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.047194, size = 44, normalized size = 1.63 \[ -\frac{2 \sqrt{\frac{b x^3}{a}+1} \tanh ^{-1}\left (\sqrt{\frac{b x^3}{a}+1}\right )}{3 \sqrt{a+b x^3}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*Sqrt[a + b*x^3]),x]
[Out]
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Maple [A] time = 0.022, size = 20, normalized size = 0.7 \[ -{\frac{2}{3}{\it Artanh} \left ({1\sqrt{b{x}^{3}+a}{\frac{1}{\sqrt{a}}}} \right ){\frac{1}{\sqrt{a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(b*x^3+a)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^3 + a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235079, size = 1, normalized size = 0.04 \[ \left [\frac{\log \left (\frac{{\left (b x^{3} + 2 \, a\right )} \sqrt{a} - 2 \, \sqrt{b x^{3} + a} a}{x^{3}}\right )}{3 \, \sqrt{a}}, \frac{2 \, \arctan \left (\frac{a}{\sqrt{b x^{3} + a} \sqrt{-a}}\right )}{3 \, \sqrt{-a}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^3 + a)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.72377, size = 26, normalized size = 0.96 \[ - \frac{2 \operatorname{asinh}{\left (\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right )}}{3 \sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x**3+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.257831, size = 31, normalized size = 1.15 \[ \frac{2 \, \arctan \left (\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right )}{3 \, \sqrt{-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^3 + a)*x),x, algorithm="giac")
[Out]