Optimal. Leaf size=10 \[ e^x-\tan ^{-1}\left (e^x\right ) \]
[Out]
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Rubi [A] time = 0.039652, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ e^x-\tan ^{-1}\left (e^x\right ) \]
Antiderivative was successfully verified.
[In] Int[E^(3*x)/(1 + E^(2*x)),x]
[Out]
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Rubi in Sympy [A] time = 7.6365, size = 7, normalized size = 0.7 \[ e^{x} - \operatorname{atan}{\left (e^{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(3*x)/(1+exp(2*x)),x)
[Out]
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Mathematica [A] time = 0.00637822, size = 10, normalized size = 1. \[ e^x-\tan ^{-1}\left (e^x\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^(3*x)/(1 + E^(2*x)),x]
[Out]
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Maple [A] time = 0.005, size = 9, normalized size = 0.9 \[{{\rm e}^{x}}-\arctan \left ({{\rm e}^{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(3*x)/(1+exp(2*x)),x)
[Out]
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Maxima [A] time = 0.856133, size = 11, normalized size = 1.1 \[ -\arctan \left (e^{x}\right ) + e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(3*x)/(e^(2*x) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.298067, size = 11, normalized size = 1.1 \[ -\arctan \left (e^{x}\right ) + e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(3*x)/(e^(2*x) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.109671, size = 19, normalized size = 1.9 \[ e^{x} + \operatorname{RootSum}{\left (4 z^{2} + 1, \left ( i \mapsto i \log{\left (- 2 i + e^{x} \right )} \right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(3*x)/(1+exp(2*x)),x)
[Out]
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GIAC/XCAS [A] time = 0.242792, size = 11, normalized size = 1.1 \[ -\arctan \left (e^{x}\right ) + e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(3*x)/(e^(2*x) + 1),x, algorithm="giac")
[Out]