Optimal. Leaf size=27 \[ \frac{2^{3/4} F\left (\left .\frac{1}{2} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{\sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0138725, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{2^{3/4} F\left (\left .\frac{1}{2} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x^2)^(-3/4),x]
[Out]
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Rubi in Sympy [A] time = 1.07586, size = 24, normalized size = 0.89 \[ \frac{2^{\frac{3}{4}} \sqrt{3} F\left (\frac{\operatorname{atan}{\left (\frac{\sqrt{6} x}{2} \right )}}{2}\middle | 2\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3*x**2+2)**(3/4),x)
[Out]
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Mathematica [C] time = 0.0123072, size = 24, normalized size = 0.89 \[ \frac{x \, _2F_1\left (\frac{1}{2},\frac{3}{4};\frac{3}{2};-\frac{3 x^2}{2}\right )}{2^{3/4}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x^2)^(-3/4),x]
[Out]
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Maple [C] time = 0.014, size = 18, normalized size = 0.7 \[{\frac{\sqrt [4]{2}x}{2}{\mbox{$_2$F$_1$}({\frac{1}{2}},{\frac{3}{4}};\,{\frac{3}{2}};\,-{\frac{3\,{x}^{2}}{2}})}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3*x^2+2)^(3/4),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (3 \, x^{2} + 2\right )}^{\frac{3}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + 2)^(-3/4),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{{\left (3 \, x^{2} + 2\right )}^{\frac{3}{4}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + 2)^(-3/4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.00819, size = 26, normalized size = 0.96 \[ \frac{\sqrt [4]{2} x{{}_{2}F_{1}\left (\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle |{\frac{3 x^{2} e^{i \pi }}{2}} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x**2+2)**(3/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (3 \, x^{2} + 2\right )}^{\frac{3}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + 2)^(-3/4),x, algorithm="giac")
[Out]