Optimal. Leaf size=10 \[ x-\log \left (e^x+1\right ) \]
[Out]
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Rubi [A] time = 0.0134802, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.571 \[ x-\log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 + E^x)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.18841, size = 10, normalized size = 1. \[ - \log{\left (e^{x} + 1 \right )} + \log{\left (e^{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+exp(x)),x)
[Out]
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Mathematica [A] time = 0.00310863, size = 10, normalized size = 1. \[ x-\log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + E^x)^(-1),x]
[Out]
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Maple [A] time = 0.008, size = 12, normalized size = 1.2 \[ -\ln \left ( 1+{{\rm e}^{x}} \right ) +\ln \left ({{\rm e}^{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+exp(x)),x)
[Out]
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Maxima [A] time = 1.34933, size = 12, normalized size = 1.2 \[ x - \log \left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(e^x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218086, size = 12, normalized size = 1.2 \[ x - \log \left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(e^x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.055553, size = 7, normalized size = 0.7 \[ x - \log{\left (e^{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+exp(x)),x)
[Out]
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GIAC/XCAS [A] time = 0.219186, size = 12, normalized size = 1.2 \[ x -{\rm ln}\left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(e^x + 1),x, algorithm="giac")
[Out]