Optimal. Leaf size=20 \[ \frac{e^{2 x}}{2}-\frac{1}{2} \tan ^{-1}\left (e^{2 x}\right ) \]
[Out]
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Rubi [A] time = 0.0396088, antiderivative size = 20, 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 \[ \frac{e^{2 x}}{2}-\frac{1}{2} \tan ^{-1}\left (e^{2 x}\right ) \]
Antiderivative was successfully verified.
[In] Int[E^(6*x)/(1 + E^(4*x)),x]
[Out]
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Rubi in Sympy [A] time = 4.07059, size = 14, normalized size = 0.7 \[ \frac{e^{2 x}}{2} - \frac{\operatorname{atan}{\left (e^{2 x} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(6*x)/(1+exp(4*x)),x)
[Out]
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Mathematica [A] time = 0.00885969, size = 20, normalized size = 1. \[ \frac{e^{2 x}}{2}-\frac{1}{2} \tan ^{-1}\left (e^{2 x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^(6*x)/(1 + E^(4*x)),x]
[Out]
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Maple [A] time = 0.006, size = 15, normalized size = 0.8 \[{\frac{ \left ({{\rm e}^{x}} \right ) ^{2}}{2}}-{\frac{\arctan \left ( \left ({{\rm e}^{x}} \right ) ^{2} \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(6*x)/(1+exp(4*x)),x)
[Out]
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Maxima [A] time = 1.48415, size = 19, normalized size = 0.95 \[ -\frac{1}{2} \, \arctan \left (e^{\left (2 \, x\right )}\right ) + \frac{1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(6*x)/(e^(4*x) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222383, size = 19, normalized size = 0.95 \[ -\frac{1}{2} \, \arctan \left (e^{\left (2 \, x\right )}\right ) + \frac{1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(6*x)/(e^(4*x) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.120295, size = 24, normalized size = 1.2 \[ \frac{e^{2 x}}{2} + \operatorname{RootSum}{\left (16 z^{2} + 1, \left ( i \mapsto i \log{\left (- 4 i + e^{2 x} \right )} \right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(6*x)/(1+exp(4*x)),x)
[Out]
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GIAC/XCAS [A] time = 0.201267, size = 19, normalized size = 0.95 \[ -\frac{1}{2} \, \arctan \left (e^{\left (2 \, x\right )}\right ) + \frac{1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(6*x)/(e^(4*x) + 1),x, algorithm="giac")
[Out]