Optimal. Leaf size=6 \[ -\tanh ^{-1}\left (e^x\right ) \]
[Out]
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Rubi [A] time = 0.0290647, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\tanh ^{-1}\left (e^x\right ) \]
Antiderivative was successfully verified.
[In] Int[E^x/(-1 + E^(2*x)),x]
[Out]
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Rubi in Sympy [A] time = 2.87644, size = 5, normalized size = 0.83 \[ - \operatorname{atanh}{\left (e^{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x)/(-1+exp(2*x)),x)
[Out]
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Mathematica [B] time = 0.00452744, size = 23, normalized size = 3.83 \[ \frac{1}{2} \log \left (1-e^x\right )-\frac{1}{2} \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^x/(-1 + E^(2*x)),x]
[Out]
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Maple [A] time = 0.003, size = 6, normalized size = 1. \[ -{\it Artanh} \left ({{\rm e}^{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x)/(-1+exp(2*x)),x)
[Out]
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Maxima [A] time = 1.34911, size = 20, normalized size = 3.33 \[ -\frac{1}{2} \, \log \left (e^{x} + 1\right ) + \frac{1}{2} \, \log \left (e^{x} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^x/(e^(2*x) - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216822, size = 20, normalized size = 3.33 \[ -\frac{1}{2} \, \log \left (e^{x} + 1\right ) + \frac{1}{2} \, \log \left (e^{x} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^x/(e^(2*x) - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.099362, size = 15, normalized size = 2.5 \[ \frac{\log{\left (e^{x} - 1 \right )}}{2} - \frac{\log{\left (e^{x} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x)/(-1+exp(2*x)),x)
[Out]
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GIAC/XCAS [A] time = 0.225082, size = 22, normalized size = 3.67 \[ -\frac{1}{2} \,{\rm ln}\left (e^{x} + 1\right ) + \frac{1}{2} \,{\rm ln}\left ({\left | e^{x} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^x/(e^(2*x) - 1),x, algorithm="giac")
[Out]