Optimal. Leaf size=4 \[ \sec \left (e^x\right ) \]
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Rubi [A] time = 0.0200626, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {2282, 2606, 8} \[ \sec \left (e^x\right ) \]
Antiderivative was successfully verified.
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Rule 2282
Rule 2606
Rule 8
Rubi steps
\begin{align*} \int e^x \sec \left (e^x\right ) \tan \left (e^x\right ) \, dx &=\operatorname{Subst}\left (\int \sec (x) \tan (x) \, dx,x,e^x\right )\\ &=\operatorname{Subst}\left (\int 1 \, dx,x,\sec \left (e^x\right )\right )\\ &=\sec \left (e^x\right )\\ \end{align*}
Mathematica [A] time = 0.0102617, size = 4, normalized size = 1. \[ \sec \left (e^x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 4, normalized size = 1. \begin{align*} \sec \left ({{\rm e}^{x}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01238, size = 7, normalized size = 1.75 \begin{align*} \frac{1}{\cos \left (e^{x}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.464941, size = 16, normalized size = 4. \begin{align*} \frac{1}{\cos \left (e^{x}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.05962, size = 3, normalized size = 0.75 \begin{align*} \sec{\left (e^{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18569, size = 7, normalized size = 1.75 \begin{align*} \frac{1}{\cos \left (e^{x}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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