Optimal. Leaf size=12 \[ e^{-x}-\tanh ^{-1}\left (e^x\right ) \]
[Out]
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Rubi [A] time = 0.024791, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ e^{-x}-\tanh ^{-1}\left (e^x\right ) \]
Antiderivative was successfully verified.
[In] Int[(-E^x + E^(3*x))^(-1),x]
[Out]
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Rubi in Sympy [A] time = 4.73425, size = 10, normalized size = 0.83 \[ - \operatorname{atanh}{\left (e^{- x} \right )} + e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-exp(x)+exp(3*x)),x)
[Out]
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Mathematica [B] time = 0.021508, size = 32, normalized size = 2.67 \[ e^{-x}+\frac{1}{2} \log \left (1-e^{-x}\right )-\frac{1}{2} \log \left (e^{-x}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(-E^x + E^(3*x))^(-1),x]
[Out]
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Maple [A] time = 0.013, size = 20, normalized size = 1.7 \[ -{\frac{\ln \left ( 1+{{\rm e}^{x}} \right ) }{2}}+ \left ({{\rm e}^{x}} \right ) ^{-1}+{\frac{\ln \left ( -1+{{\rm e}^{x}} \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-exp(x)+exp(3*x)),x)
[Out]
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Maxima [A] time = 1.34042, size = 26, normalized size = 2.17 \[ e^{\left (-x\right )} - \frac{1}{2} \, \log \left (e^{x} + 1\right ) + \frac{1}{2} \, \log \left (e^{x} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(e^(3*x) - e^x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216942, size = 34, normalized size = 2.83 \[ -\frac{1}{2} \,{\left (e^{x} \log \left (e^{x} + 1\right ) - e^{x} \log \left (e^{x} - 1\right ) - 2\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(e^(3*x) - e^x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.114666, size = 20, normalized size = 1.67 \[ \frac{\log{\left (e^{x} - 1 \right )}}{2} - \frac{\log{\left (e^{x} + 1 \right )}}{2} + e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-exp(x)+exp(3*x)),x)
[Out]
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GIAC/XCAS [A] time = 0.219618, size = 27, normalized size = 2.25 \[ e^{\left (-x\right )} - \frac{1}{2} \,{\rm ln}\left (e^{x} + 1\right ) + \frac{1}{2} \,{\rm ln}\left ({\left | e^{x} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(e^(3*x) - e^x),x, algorithm="giac")
[Out]