Optimal. Leaf size=4 \[ e^{\tan (x)} \]
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Rubi [A] time = 0.0123224, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {4342, 2194} \[ e^{\tan (x)} \]
Antiderivative was successfully verified.
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Rule 4342
Rule 2194
Rubi steps
\begin{align*} \int e^{\tan (x)} \sec ^2(x) \, dx &=\operatorname{Subst}\left (\int e^x \, dx,x,\tan (x)\right )\\ &=e^{\tan (x)}\\ \end{align*}
Mathematica [A] time = 0.0600031, size = 4, normalized size = 1. \[ e^{\tan (x)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.012, size = 4, normalized size = 1. \begin{align*}{{\rm e}^{\tan \left ( x \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.961285, size = 4, normalized size = 1. \begin{align*} e^{\tan \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.98432, size = 26, normalized size = 6.5 \begin{align*} e^{\frac{\sin \left (x\right )}{\cos \left (x\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.72, size = 3, normalized size = 0.75 \begin{align*} e^{\tan{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1086, size = 4, normalized size = 1. \begin{align*} e^{\tan \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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