Optimal. Leaf size=9 \[ \frac {2^{\sec (x)}}{\log (2)} \]
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Rubi [A] time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, 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 2209
Rule 4339
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*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 1.00 \[ \frac {2^{\sec (x)}}{\log (2)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 11, normalized size = 1.22 \[ \frac {2^{\left (\frac {1}{\cos \relax (x)}\right )}}{\log \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 11, normalized size = 1.22 \[ \frac {2^{\left (\frac {1}{\cos \relax (x)}\right )}}{\log \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 1.11 \[ \frac {2^{\sec \relax (x )}}{\ln \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 9, normalized size = 1.00 \[ \frac {2^{\sec \relax (x)}}{\log \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.12, size = 11, normalized size = 1.22 \[ \frac {2^{\frac {1}{\cos \relax (x)}}}{\ln \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.65, size = 7, normalized size = 0.78 \[ \frac {2^{\sec {\relax (x )}}}{\log {\relax (2 )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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