Optimal. Leaf size=43 \[ -\frac{2 x^{5/2}}{5}-2 \sqrt{x}-\log \left (1-\sqrt{x}\right )+\frac{1}{2} \log (x+1)+\tan ^{-1}\left (\sqrt{x}\right ) \]
[Out]
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Rubi [A] time = 0.193995, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 5, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.294 \[ -\frac{2 x^{5/2}}{5}-2 \sqrt{x}-\log \left (1-\sqrt{x}\right )+\frac{1}{2} \log (x+1)+\tan ^{-1}\left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 + x^(7/2))/(1 - x^2),x]
[Out]
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Rubi in Sympy [A] time = 13.96, size = 41, normalized size = 0.95 \[ - \frac{2 x^{\frac{5}{2}}}{5} - 2 \sqrt{x} - \frac{\log{\left (- x + 1 \right )}}{2} + \frac{\log{\left (x + 1 \right )}}{2} + \operatorname{atan}{\left (\sqrt{x} \right )} + \operatorname{atanh}{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x**(7/2))/(-x**2+1),x)
[Out]
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Mathematica [A] time = 0.0187024, size = 43, normalized size = 1. \[ -\frac{2 x^{5/2}}{5}-2 \sqrt{x}-\log \left (1-\sqrt{x}\right )+\frac{1}{2} \log (x+1)+\tan ^{-1}\left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^(7/2))/(1 - x^2),x]
[Out]
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Maple [A] time = 0.006, size = 34, normalized size = 0.8 \[ -{\frac{2}{5}{x}^{{\frac{5}{2}}}}-2\,\sqrt{x}-{\frac{1}{2}\ln \left ( -1+\sqrt{x} \right ) }+{\frac{1}{2}\ln \left ( 1+\sqrt{x} \right ) }+\arctan \left ( \sqrt{x} \right ) +{\it Artanh} \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x^(7/2))/(-x^2+1),x)
[Out]
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Maxima [A] time = 0.810667, size = 39, normalized size = 0.91 \[ -\frac{2}{5} \, x^{\frac{5}{2}} - 2 \, \sqrt{x} + \arctan \left (\sqrt{x}\right ) + \frac{1}{2} \, \log \left (x + 1\right ) - \log \left (\sqrt{x} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^(7/2) + 1)/(x^2 - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271261, size = 39, normalized size = 0.91 \[ -\frac{2}{5} \,{\left (x^{2} + 5\right )} \sqrt{x} + \arctan \left (\sqrt{x}\right ) + \frac{1}{2} \, \log \left (x + 1\right ) - \log \left (\sqrt{x} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^(7/2) + 1)/(x^2 - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.6502, size = 36, normalized size = 0.84 \[ - \frac{2 x^{\frac{5}{2}}}{5} - 2 \sqrt{x} - \log{\left (\sqrt{x} - 1 \right )} + \frac{\log{\left (x + 1 \right )}}{2} + \operatorname{atan}{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x**(7/2))/(-x**2+1),x)
[Out]
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GIAC/XCAS [A] time = 0.260682, size = 41, normalized size = 0.95 \[ -\frac{2}{5} \, x^{\frac{5}{2}} - 2 \, \sqrt{x} + \arctan \left (\sqrt{x}\right ) + \frac{1}{2} \,{\rm ln}\left (x + 1\right ) -{\rm ln}\left ({\left | \sqrt{x} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^(7/2) + 1)/(x^2 - 1),x, algorithm="giac")
[Out]