Optimal. Leaf size=17 \[ -\frac{F\left (\sin ^{-1}(1-x)|-\frac{1}{3}\right )}{\sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0397019, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13 \[ -\frac{F\left (\sin ^{-1}(1-x)|-\frac{1}{3}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[8*x - 8*x^2 + 4*x^3 - x^4],x]
[Out]
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Rubi in Sympy [A] time = 10.8188, size = 15, normalized size = 0.88 \[ \frac{\sqrt{3} F\left (\operatorname{asin}{\left (x - 1 \right )}\middle | - \frac{1}{3}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**4+4*x**3-8*x**2+8*x)**(1/2),x)
[Out]
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Mathematica [C] time = 0.215032, size = 156, normalized size = 9.18 \[ \frac{\sqrt{\frac{4 i}{x}+\sqrt{3}-i} \sqrt{-\frac{i (x-2)}{\left (\sqrt{3}-i\right ) x}} x \left (-i \sqrt{3} x+x-4\right ) F\left (\sin ^{-1}\left (\frac{\sqrt{\sqrt{3}+i-\frac{4 i}{x}}}{\sqrt{2} \sqrt [4]{3}}\right )|\frac{2 \sqrt{3}}{-i+\sqrt{3}}\right )}{\sqrt{2} \sqrt{-\frac{4 i}{x}+\sqrt{3}+i} \sqrt{-x \left (x^3-4 x^2+8 x-8\right )}} \]
Warning: Unable to verify antiderivative.
[In] Integrate[1/Sqrt[8*x - 8*x^2 + 4*x^3 - x^4],x]
[Out]
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Maple [B] time = 0.038, size = 200, normalized size = 11.8 \[ 2\,{\frac{ \left ( -1+i\sqrt{3} \right ) \left ( x-2 \right ) ^{2}}{ \left ( -i\sqrt{3}-1 \right ) \sqrt{-x \left ( x-2 \right ) \left ( x-i\sqrt{3}-1 \right ) \left ( x-1+i\sqrt{3} \right ) }}\sqrt{{\frac{ \left ( -i\sqrt{3}-1 \right ) x}{ \left ( 1-i\sqrt{3} \right ) \left ( x-2 \right ) }}}\sqrt{{\frac{x-i\sqrt{3}-1}{ \left ( i\sqrt{3}+1 \right ) \left ( x-2 \right ) }}}\sqrt{{\frac{x-1+i\sqrt{3}}{ \left ( 1-i\sqrt{3} \right ) \left ( x-2 \right ) }}}{\it EllipticF} \left ( \sqrt{{\frac{ \left ( -i\sqrt{3}-1 \right ) x}{ \left ( 1-i\sqrt{3} \right ) \left ( x-2 \right ) }}},\sqrt{{\frac{ \left ( 1-i\sqrt{3} \right ) \left ( -1+i\sqrt{3} \right ) }{ \left ( -i\sqrt{3}-1 \right ) \left ( i\sqrt{3}+1 \right ) }}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^4+4*x^3-8*x^2+8*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- x^{4} + 4 x^{3} - 8 x^{2} + 8 x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**4+4*x**3-8*x**2+8*x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x),x, algorithm="giac")
[Out]