Optimal. Leaf size=65 \[ -\frac{8}{135} \left (2-3 x^2\right )^{3/4} x-\frac{2}{27} \left (2-3 x^2\right )^{3/4} x^3+\frac{32 \sqrt [4]{2} E\left (\left .\frac{1}{2} \sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{135 \sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0565701, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{8}{135} \left (2-3 x^2\right )^{3/4} x-\frac{2}{27} \left (2-3 x^2\right )^{3/4} x^3+\frac{32 \sqrt [4]{2} E\left (\left .\frac{1}{2} \sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{135 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[x^4/(2 - 3*x^2)^(1/4),x]
[Out]
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Rubi in Sympy [A] time = 5.2437, size = 58, normalized size = 0.89 \[ - \frac{2 x^{3} \left (- 3 x^{2} + 2\right )^{\frac{3}{4}}}{27} - \frac{8 x \left (- 3 x^{2} + 2\right )^{\frac{3}{4}}}{135} + \frac{32 \sqrt [4]{2} \sqrt{3} E\left (\frac{\operatorname{asin}{\left (\frac{\sqrt{6} x}{2} \right )}}{2}\middle | 2\right )}{405} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(-3*x**2+2)**(1/4),x)
[Out]
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Mathematica [C] time = 0.0498281, size = 50, normalized size = 0.77 \[ \frac{2}{135} x \left (4\ 2^{3/4} \, _2F_1\left (\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{3 x^2}{2}\right )-\left (2-3 x^2\right )^{3/4} \left (5 x^2+4\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(2 - 3*x^2)^(1/4),x]
[Out]
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Maple [C] time = 0.039, size = 45, normalized size = 0.7 \[{\frac{2\,x \left ( 5\,{x}^{2}+4 \right ) \left ( 3\,{x}^{2}-2 \right ) }{135}{\frac{1}{\sqrt [4]{-3\,{x}^{2}+2}}}}+{\frac{8\,{2}^{3/4}x}{135}{\mbox{$_2$F$_1$}({\frac{1}{4}},{\frac{1}{2}};\,{\frac{3}{2}};\,{\frac{3\,{x}^{2}}{2}})}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(-3*x^2+2)^(1/4),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{{\left (-3 \, x^{2} + 2\right )}^{\frac{1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(-3*x^2 + 2)^(1/4),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x^{4}}{{\left (-3 \, x^{2} + 2\right )}^{\frac{1}{4}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(-3*x^2 + 2)^(1/4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.39721, size = 29, normalized size = 0.45 \[ \frac{2^{\frac{3}{4}} x^{5}{{}_{2}F_{1}\left (\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle |{\frac{3 x^{2} e^{2 i \pi }}{2}} \right )}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(-3*x**2+2)**(1/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{{\left (-3 \, x^{2} + 2\right )}^{\frac{1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(-3*x^2 + 2)^(1/4),x, algorithm="giac")
[Out]