Optimal. Leaf size=31 \[ -\frac{1}{4 x^2}-\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x^2\right ) \]
[Out]
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Rubi [A] time = 0.0347719, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{1}{4 x^2}-\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*(2 + 3*x^4)),x]
[Out]
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Rubi in Sympy [A] time = 5.17499, size = 26, normalized size = 0.84 \[ - \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x^{2}}{2} \right )}}{8} - \frac{1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(3*x**4+2),x)
[Out]
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Mathematica [A] time = 0.0357927, size = 48, normalized size = 1.55 \[ \frac{\sqrt{6} x^2 \tan ^{-1}\left (1-\sqrt [4]{6} x\right )+\sqrt{6} x^2 \tan ^{-1}\left (\sqrt [4]{6} x+1\right )-2}{8 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*(2 + 3*x^4)),x]
[Out]
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Maple [A] time = 0.006, size = 21, normalized size = 0.7 \[ -{\frac{1}{4\,{x}^{2}}}-{\frac{\sqrt{6}}{8}\arctan \left ({\frac{{x}^{2}\sqrt{6}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(3*x^4+2),x)
[Out]
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Maxima [A] time = 1.59174, size = 27, normalized size = 0.87 \[ -\frac{1}{8} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x^{2}\right ) - \frac{1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^4 + 2)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221196, size = 42, normalized size = 1.35 \[ -\frac{\sqrt{2}{\left (\sqrt{3} x^{2} \arctan \left (\frac{1}{2} \, \sqrt{3} \sqrt{2} x^{2}\right ) + \sqrt{2}\right )}}{8 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^4 + 2)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.279784, size = 26, normalized size = 0.84 \[ - \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x^{2}}{2} \right )}}{8} - \frac{1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(3*x**4+2),x)
[Out]
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GIAC/XCAS [A] time = 0.219831, size = 27, normalized size = 0.87 \[ -\frac{1}{8} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x^{2}\right ) - \frac{1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^4 + 2)*x^3),x, algorithm="giac")
[Out]