Optimal. Leaf size=9 \[ \frac{2^{\sec (x)}}{\log (2)} \]
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Rubi [A] time = 0.0216664, antiderivative size = 9, 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} \[ \frac{2^{\sec (x)}}{\log (2)} \]
Antiderivative was successfully verified.
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Rule 4339
Rule 2209
Rubi steps
\begin{align*} \int 2^{\sec (x)} \sec (x) \tan (x) \, dx &=-\operatorname{Subst}\left (\int \frac{2^{\frac{1}{x}}}{x^2} \, dx,x,\cos (x)\right )\\ &=\frac{2^{\sec (x)}}{\log (2)}\\ \end{align*}
Mathematica [A] time = 0.0081172, size = 9, normalized size = 1. \[ \frac{2^{\sec (x)}}{\log (2)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 10, normalized size = 1.1 \begin{align*}{\frac{{2}^{\sec \left ( x \right ) }}{\ln \left ( 2 \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.956561, size = 12, normalized size = 1.33 \begin{align*} \frac{2^{\sec \left (x\right )}}{\log \left (2\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.31062, size = 28, normalized size = 3.11 \begin{align*} \frac{2^{\left (\frac{1}{\cos \left (x\right )}\right )}}{\log \left (2\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.927133, size = 7, normalized size = 0.78 \begin{align*} \frac{2^{\sec{\left (x \right )}}}{\log{\left (2 \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0824, size = 15, normalized size = 1.67 \begin{align*} \frac{2^{\left (\frac{1}{\cos \left (x\right )}\right )}}{\log \left (2\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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