Optimal. Leaf size=27 \[ \frac{2 \tanh ^{-1}\left (\frac{\sqrt{a+\frac{b}{x^5}}}{\sqrt{a}}\right )}{5 \sqrt{a}} \]
[Out]
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Rubi [A] time = 0.0624642, 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 \[ \frac{2 \tanh ^{-1}\left (\frac{\sqrt{a+\frac{b}{x^5}}}{\sqrt{a}}\right )}{5 \sqrt{a}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[a + b/x^5]*x),x]
[Out]
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Rubi in Sympy [A] time = 5.12292, size = 24, normalized size = 0.89 \[ \frac{2 \operatorname{atanh}{\left (\frac{\sqrt{a + \frac{b}{x^{5}}}}{\sqrt{a}} \right )}}{5 \sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(a+b/x**5)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0519659, size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{a+\frac{b}{x^5}} x} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[1/(Sqrt[a + b/x^5]*x),x]
[Out]
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Maple [F] time = 0.053, size = 0, normalized size = 0. \[ \int{\frac{1}{x}{\frac{1}{\sqrt{a+{\frac{b}{{x}^{5}}}}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(a+b/x^5)^(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(a + b/x^5)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.725371, size = 1, normalized size = 0.04 \[ \left [\frac{\log \left (-{\left (8 \, a^{2} x^{10} + 8 \, a b x^{5} + b^{2}\right )} \sqrt{a} - 4 \,{\left (2 \, a^{2} x^{10} + a b x^{5}\right )} \sqrt{\frac{a x^{5} + b}{x^{5}}}\right )}{10 \, \sqrt{a}}, -\frac{\sqrt{-a} \arctan \left (\frac{2 \, \sqrt{-a} x^{5} \sqrt{\frac{a x^{5} + b}{x^{5}}}}{2 \, a x^{5} + b}\right )}{5 \, a}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^5)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.4739, size = 24, normalized size = 0.89 \[ \frac{2 \operatorname{asinh}{\left (\frac{\sqrt{a} x^{\frac{5}{2}}}{\sqrt{b}} \right )}}{5 \sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(a+b/x**5)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{a + \frac{b}{x^{5}}} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^5)*x),x, algorithm="giac")
[Out]