Optimal. Leaf size=34 \[ -2 \text{PolyLog}\left (2,-e^x\right )-\frac{x^2}{e^x+1}+x^2-2 x \log \left (e^x+1\right ) \]
[Out]
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Rubi [A] time = 0.37813, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 7, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.438 \[ -2 \text{PolyLog}\left (2,-e^x\right )-\frac{x^2}{e^x+1}+x^2-2 x \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
[In] Int[x^2/(2 + E^(-x) + E^x),x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(2+exp(-x)+exp(x)),x)
[Out]
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Mathematica [A] time = 0.0565122, size = 33, normalized size = 0.97 \[ x \left (\frac{e^x x}{e^x+1}-2 \log \left (e^x+1\right )\right )-2 \text{PolyLog}\left (2,-e^x\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(2 + E^(-x) + E^x),x]
[Out]
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Maple [A] time = 0.031, size = 32, normalized size = 0.9 \[{x}^{2}-{\frac{{x}^{2}}{1+{{\rm e}^{x}}}}-2\,x\ln \left ( 1+{{\rm e}^{x}} \right ) -2\,{\it polylog} \left ( 2,-{{\rm e}^{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(2+exp(-x)+exp(x)),x)
[Out]
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Maxima [A] time = 0.81497, size = 41, normalized size = 1.21 \[ x^{2} - 2 \, x \log \left (e^{x} + 1\right ) - \frac{x^{2}}{e^{x} + 1} - 2 \,{\rm Li}_2\left (-e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(e^(-x) + e^x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.257606, size = 51, normalized size = 1.5 \[ \frac{x^{2} e^{x} - 2 \,{\left (e^{x} + 1\right )}{\rm Li}_2\left (-e^{x}\right ) - 2 \,{\left (x e^{x} + x\right )} \log \left (e^{x} + 1\right )}{e^{x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(e^(-x) + e^x + 2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{x^{2}}{e^{x} + 1} + 2 \int \frac{x}{e^{x} + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(2+exp(-x)+exp(x)),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2}}{e^{\left (-x\right )} + e^{x} + 2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(e^(-x) + e^x + 2),x, algorithm="giac")
[Out]