Optimal. Leaf size=4 \[ e^{\sec (x)} \]
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Rubi [A] time = 0.0217493, 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 = {4339, 2209} \[ e^{\sec (x)} \]
Antiderivative was successfully verified.
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Rule 4339
Rule 2209
Rubi steps
\begin{align*} \int e^{\sec (x)} \sec (x) \tan (x) \, dx &=-\operatorname{Subst}\left (\int \frac{e^{\frac{1}{x}}}{x^2} \, dx,x,\cos (x)\right )\\ &=e^{\sec (x)}\\ \end{align*}
Mathematica [A] time = 0.0073632, size = 4, normalized size = 1. \[ e^{\sec (x)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 4, normalized size = 1. \begin{align*}{{\rm e}^{\sec \left ( x \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955632, size = 4, normalized size = 1. \begin{align*} e^{\sec \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.29366, size = 19, normalized size = 4.75 \begin{align*} e^{\frac{1}{\cos \left (x\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.828806, size = 3, normalized size = 0.75 \begin{align*} e^{\sec{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11965, size = 7, normalized size = 1.75 \begin{align*} e^{\frac{1}{\cos \left (x\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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