Optimal. Leaf size=30 \[ \sqrt{e^{2 t}-9}-3 \tan ^{-1}\left (\frac{1}{3} \sqrt{e^{2 t}-9}\right ) \]
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Rubi [A] time = 0.0333224, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.364 \[ \sqrt{e^{2 t}-9}-3 \tan ^{-1}\left (\frac{1}{3} \sqrt{e^{2 t}-9}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[-9 + E^(2*t)],t]
[Out]
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Rubi in Sympy [A] time = 2.09252, size = 24, normalized size = 0.8 \[ \sqrt{e^{2 t} - 9} - 3 \operatorname{atan}{\left (\frac{\sqrt{e^{2 t} - 9}}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-9+exp(2*t))**(1/2),t)
[Out]
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Mathematica [A] time = 0.0134914, size = 30, normalized size = 1. \[ \sqrt{e^{2 t}-9}-3 \tan ^{-1}\left (\frac{1}{3} \sqrt{e^{2 t}-9}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[-9 + E^(2*t)],t]
[Out]
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Maple [A] time = 0.009, size = 23, normalized size = 0.8 \[ -3\,\arctan \left ( 1/3\,\sqrt{-9+{{\rm e}^{2\,t}}} \right ) +\sqrt{-9+{{\rm e}^{2\,t}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-9+exp(2*t))^(1/2),t)
[Out]
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Maxima [A] time = 1.53706, size = 30, normalized size = 1. \[ \sqrt{e^{\left (2 \, t\right )} - 9} - 3 \, \arctan \left (\frac{1}{3} \, \sqrt{e^{\left (2 \, t\right )} - 9}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(e^(2*t) - 9),t, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212037, size = 30, normalized size = 1. \[ \sqrt{e^{\left (2 \, t\right )} - 9} - 3 \, \arctan \left (\frac{1}{3} \, \sqrt{e^{\left (2 \, t\right )} - 9}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(e^(2*t) - 9),t, algorithm="fricas")
[Out]
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Sympy [A] time = 1.361, size = 22, normalized size = 0.73 \[ \begin{cases} \sqrt{e^{2 t} - 9} - 3 \operatorname{acos}{\left (3 e^{- t} \right )} & \text{for}\: e^{t} < \log{\left (3 \right )} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-9+exp(2*t))**(1/2),t)
[Out]
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GIAC/XCAS [A] time = 0.208623, size = 30, normalized size = 1. \[ \sqrt{e^{\left (2 \, t\right )} - 9} - 3 \, \arctan \left (\frac{1}{3} \, \sqrt{e^{\left (2 \, t\right )} - 9}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(e^(2*t) - 9),t, algorithm="giac")
[Out]