Optimal. Leaf size=18 \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} e^x\right )}{\sqrt{6}} \]
[Out]
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Rubi [A] time = 0.0357168, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} e^x\right )}{\sqrt{6}} \]
Antiderivative was successfully verified.
[In] Int[E^x/(2 + 3*E^(2*x)),x]
[Out]
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Rubi in Sympy [A] time = 3.15427, size = 17, normalized size = 0.94 \[ \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} e^{x}}{2} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x)/(2+3*exp(2*x)),x)
[Out]
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Mathematica [A] time = 0.0131084, size = 18, normalized size = 1. \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} e^x\right )}{\sqrt{6}} \]
Antiderivative was successfully verified.
[In] Integrate[E^x/(2 + 3*E^(2*x)),x]
[Out]
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Maple [A] time = 0.005, size = 14, normalized size = 0.8 \[{\frac{\sqrt{6}}{6}\arctan \left ({\frac{{{\rm e}^{x}}\sqrt{6}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x)/(2+3*exp(2*x)),x)
[Out]
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Maxima [A] time = 1.54985, size = 18, normalized size = 1. \[ \frac{1}{6} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^x/(3*e^(2*x) + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207156, size = 18, normalized size = 1. \[ \frac{1}{6} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^x/(3*e^(2*x) + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.113463, size = 15, normalized size = 0.83 \[ \operatorname{RootSum}{\left (24 z^{2} + 1, \left ( i \mapsto i \log{\left (4 i + e^{x} \right )} \right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x)/(2+3*exp(2*x)),x)
[Out]
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GIAC/XCAS [A] time = 0.207173, size = 18, normalized size = 1. \[ \frac{1}{6} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^x/(3*e^(2*x) + 2),x, algorithm="giac")
[Out]