Optimal. Leaf size=85 \[ -\frac{63 \left (2-3 x^2\right )^{3/4}}{160 x}-\frac{\left (2-3 x^2\right )^{3/4}}{10 x^5}-\frac{7 \left (2-3 x^2\right )^{3/4}}{40 x^3}-\frac{63 \sqrt{3} E\left (\left .\frac{1}{2} \sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{80\ 2^{3/4}} \]
[Out]
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Rubi [A] time = 0.0747803, antiderivative size = 85, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{63 \left (2-3 x^2\right )^{3/4}}{160 x}-\frac{\left (2-3 x^2\right )^{3/4}}{10 x^5}-\frac{7 \left (2-3 x^2\right )^{3/4}}{40 x^3}-\frac{63 \sqrt{3} E\left (\left .\frac{1}{2} \sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{80\ 2^{3/4}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^6*(2 - 3*x^2)^(1/4)),x]
[Out]
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Rubi in Sympy [A] time = 6.77728, size = 75, normalized size = 0.88 \[ - \frac{63 \sqrt [4]{2} \sqrt{3} E\left (\frac{\operatorname{asin}{\left (\frac{\sqrt{6} x}{2} \right )}}{2}\middle | 2\right )}{160} - \frac{63 \left (- 3 x^{2} + 2\right )^{\frac{3}{4}}}{160 x} - \frac{7 \left (- 3 x^{2} + 2\right )^{\frac{3}{4}}}{40 x^{3}} - \frac{\left (- 3 x^{2} + 2\right )^{\frac{3}{4}}}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**6/(-3*x**2+2)**(1/4),x)
[Out]
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Mathematica [C] time = 0.0473031, size = 62, normalized size = 0.73 \[ \left (-\frac{1}{10 x^5}-\frac{7}{40 x^3}-\frac{63}{160 x}\right ) \left (2-3 x^2\right )^{3/4}-\frac{189 x \, _2F_1\left (\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{3 x^2}{2}\right )}{320 \sqrt [4]{2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^6*(2 - 3*x^2)^(1/4)),x]
[Out]
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Maple [C] time = 0.045, size = 50, normalized size = 0.6 \[{\frac{189\,{x}^{6}-42\,{x}^{4}-8\,{x}^{2}-32}{160\,{x}^{5}}{\frac{1}{\sqrt [4]{-3\,{x}^{2}+2}}}}-{\frac{189\,{2}^{3/4}x}{640}{\mbox{$_2$F$_1$}({\frac{1}{4}},{\frac{1}{2}};\,{\frac{3}{2}};\,{\frac{3\,{x}^{2}}{2}})}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^6/(-3*x^2+2)^(1/4),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (-3 \, x^{2} + 2\right )}^{\frac{1}{4}} x^{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-3*x^2 + 2)^(1/4)*x^6),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{{\left (-3 \, x^{2} + 2\right )}^{\frac{1}{4}} x^{6}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-3*x^2 + 2)^(1/4)*x^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.6624, size = 34, normalized size = 0.4 \[ - \frac{2^{\frac{3}{4}}{{}_{2}F_{1}\left (\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle |{\frac{3 x^{2} e^{2 i \pi }}{2}} \right )}}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**6/(-3*x**2+2)**(1/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (-3 \, x^{2} + 2\right )}^{\frac{1}{4}} x^{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-3*x^2 + 2)^(1/4)*x^6),x, algorithm="giac")
[Out]