Optimal. Leaf size=32 \[ \frac{1}{8 \left (3 x^4+2\right )}-\frac{1}{16} \log \left (3 x^4+2\right )+\frac{\log (x)}{4} \]
[Out]
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Rubi [A] time = 0.0453793, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{8 \left (3 x^4+2\right )}-\frac{1}{16} \log \left (3 x^4+2\right )+\frac{\log (x)}{4} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(2 + 3*x^4)^2),x]
[Out]
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Rubi in Sympy [A] time = 5.38617, size = 24, normalized size = 0.75 \[ \frac{\log{\left (x^{4} \right )}}{16} - \frac{\log{\left (3 x^{4} + 2 \right )}}{16} + \frac{1}{8 \left (3 x^{4} + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(3*x**4+2)**2,x)
[Out]
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Mathematica [A] time = 0.015962, size = 32, normalized size = 1. \[ \frac{1}{8 \left (3 x^4+2\right )}-\frac{1}{16} \log \left (3 x^4+2\right )+\frac{\log (x)}{4} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(2 + 3*x^4)^2),x]
[Out]
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Maple [A] time = 0.019, size = 27, normalized size = 0.8 \[{\frac{1}{24\,{x}^{4}+16}}+{\frac{\ln \left ( x \right ) }{4}}-{\frac{\ln \left ( 3\,{x}^{4}+2 \right ) }{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(3*x^4+2)^2,x)
[Out]
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Maxima [A] time = 1.42523, size = 38, normalized size = 1.19 \[ \frac{1}{8 \,{\left (3 \, x^{4} + 2\right )}} - \frac{1}{16} \, \log \left (3 \, x^{4} + 2\right ) + \frac{1}{16} \, \log \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^4 + 2)^2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229597, size = 54, normalized size = 1.69 \[ -\frac{{\left (3 \, x^{4} + 2\right )} \log \left (3 \, x^{4} + 2\right ) - 4 \,{\left (3 \, x^{4} + 2\right )} \log \left (x\right ) - 2}{16 \,{\left (3 \, x^{4} + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^4 + 2)^2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.335434, size = 22, normalized size = 0.69 \[ \frac{\log{\left (x \right )}}{4} - \frac{\log{\left (3 x^{4} + 2 \right )}}{16} + \frac{1}{24 x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(3*x**4+2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.226198, size = 47, normalized size = 1.47 \[ \frac{3 \, x^{4} + 4}{16 \,{\left (3 \, x^{4} + 2\right )}} - \frac{1}{16} \,{\rm ln}\left (3 \, x^{4} + 2\right ) + \frac{1}{16} \,{\rm ln}\left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^4 + 2)^2*x),x, algorithm="giac")
[Out]