Optimal. Leaf size=12 \[ e^x-3 \log \left (e^x+1\right ) \]
[Out]
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Rubi [A] time = 0.0578177, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ e^x-3 \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(E^x*(-2 + E^x))/(1 + E^x),x]
[Out]
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Rubi in Sympy [A] time = 20.9066, size = 20, normalized size = 1.67 \[ - 3 x + e^{x} - 3 \log{\left (e^{x} + 1 \right )} + 3 \log{\left (e^{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x)*(-2+exp(x))/(1+exp(x)),x)
[Out]
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Mathematica [A] time = 0.00665981, size = 12, normalized size = 1. \[ e^x-3 \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(E^x*(-2 + E^x))/(1 + E^x),x]
[Out]
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Maple [A] time = 0.004, size = 11, normalized size = 0.9 \[{{\rm e}^{x}}-3\,\ln \left ( 1+{{\rm e}^{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x)*(-2+exp(x))/(1+exp(x)),x)
[Out]
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Maxima [A] time = 0.82933, size = 14, normalized size = 1.17 \[ e^{x} - 3 \, \log \left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^x - 2)*e^x/(e^x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259894, size = 14, normalized size = 1.17 \[ e^{x} - 3 \, \log \left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^x - 2)*e^x/(e^x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.073321, size = 10, normalized size = 0.83 \[ e^{x} - 3 \log{\left (e^{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x)*(-2+exp(x))/(1+exp(x)),x)
[Out]
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GIAC/XCAS [A] time = 0.230626, size = 14, normalized size = 1.17 \[ e^{x} - 3 \,{\rm ln}\left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^x - 2)*e^x/(e^x + 1),x, algorithm="giac")
[Out]