Optimal. Leaf size=37 \[ \frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3} \]
[Out]
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Rubi [A] time = 0.0247574, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.263 \[ \frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a*x^6]/(x - x^5),x]
[Out]
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Rubi in Sympy [A] time = 14.9667, size = 32, normalized size = 0.86 \[ - \frac{\sqrt{a x^{6}} \operatorname{atan}{\left (x \right )}}{2 x^{3}} + \frac{\sqrt{a x^{6}} \operatorname{atanh}{\left (x \right )}}{2 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*x**6)**(1/2)/(-x**5+x),x)
[Out]
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Mathematica [A] time = 0.00652605, size = 33, normalized size = 0.89 \[ -\frac{\sqrt{a x^6} \left (\log (1-x)-\log (x+1)+2 \tan ^{-1}(x)\right )}{4 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a*x^6]/(x - x^5),x]
[Out]
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Maple [A] time = 0.01, size = 28, normalized size = 0.8 \[ -{\frac{\ln \left ( -1+x \right ) -\ln \left ( 1+x \right ) +2\,\arctan \left ( x \right ) }{4\,{x}^{3}}\sqrt{a{x}^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*x^6)^(1/2)/(-x^5+x),x)
[Out]
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Maxima [A] time = 0.769744, size = 35, normalized size = 0.95 \[ -\frac{1}{2} \, \sqrt{a} \arctan \left (x\right ) + \frac{1}{4} \, \sqrt{a} \log \left (x + 1\right ) - \frac{1}{4} \, \sqrt{a} \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(a*x^6)/(x^5 - x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.298899, size = 39, normalized size = 1.05 \[ -\frac{\sqrt{a x^{6}}{\left (2 \, \arctan \left (x\right ) - \log \left (\frac{x + 1}{x - 1}\right )\right )}}{4 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(a*x^6)/(x^5 - x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \int \frac{\sqrt{a x^{6}}}{x^{5} - x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x**6)**(1/2)/(-x**5+x),x)
[Out]
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GIAC/XCAS [A] time = 0.259908, size = 39, normalized size = 1.05 \[ -\frac{1}{4} \,{\left (2 \, \arctan \left (x\right ){\rm sign}\left (x\right ) -{\rm ln}\left ({\left | x + 1 \right |}\right ){\rm sign}\left (x\right ) +{\rm ln}\left ({\left | x - 1 \right |}\right ){\rm sign}\left (x\right )\right )} \sqrt{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(a*x^6)/(x^5 - x),x, algorithm="giac")
[Out]