Optimal. Leaf size=33 \[ x \log \left (3 x^2+2\right )-2 x+2 \sqrt{\frac{2}{3}} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x\right ) \]
[Out]
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Rubi [A] time = 0.0243126, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375 \[ x \log \left (3 x^2+2\right )-2 x+2 \sqrt{\frac{2}{3}} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x\right ) \]
Antiderivative was successfully verified.
[In] Int[Log[2 + 3*x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.89674, size = 31, normalized size = 0.94 \[ x \log{\left (3 x^{2} + 2 \right )} - 2 x + \frac{2 \sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x}{2} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(3*x**2+2),x)
[Out]
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Mathematica [A] time = 0.0190889, size = 33, normalized size = 1. \[ x \log \left (3 x^2+2\right )-2 x+2 \sqrt{\frac{2}{3}} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Log[2 + 3*x^2],x]
[Out]
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Maple [A] time = 0., size = 27, normalized size = 0.8 \[ -2\,x+x\ln \left ( 3\,{x}^{2}+2 \right ) +{\frac{2\,\sqrt{6}}{3}\arctan \left ({\frac{x\sqrt{6}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(3*x^2+2),x)
[Out]
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Maxima [A] time = 1.48589, size = 35, normalized size = 1.06 \[ x \log \left (3 \, x^{2} + 2\right ) + \frac{2}{3} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x\right ) - 2 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(3*x^2 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221527, size = 54, normalized size = 1.64 \[ \frac{1}{3} \, \sqrt{3}{\left (\sqrt{3} x \log \left (3 \, x^{2} + 2\right ) - 2 \, \sqrt{3} x + 2 \, \sqrt{2} \arctan \left (\frac{1}{2} \, \sqrt{3} \sqrt{2} x\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(3*x^2 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.139802, size = 31, normalized size = 0.94 \[ x \log{\left (3 x^{2} + 2 \right )} - 2 x + \frac{2 \sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x}{2} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(3*x**2+2),x)
[Out]
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GIAC/XCAS [A] time = 0.205687, size = 35, normalized size = 1.06 \[ x{\rm ln}\left (3 \, x^{2} + 2\right ) + \frac{2}{3} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x\right ) - 2 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(3*x^2 + 2),x, algorithm="giac")
[Out]