Optimal. Leaf size=4 \[ e^{\sec (x)} \]
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Rubi [A] time = 0.02, antiderivative size = 4, 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} \[ e^{\sec (x)} \]
Antiderivative was successfully verified.
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Rule 2209
Rule 4339
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*}
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Mathematica [A] time = 0.01, size = 4, normalized size = 1.00 \[ e^{\sec (x)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.92, size = 5, normalized size = 1.25 \[ e^{\frac {1}{\cos \relax (x)}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 5, normalized size = 1.25 \[ e^{\frac {1}{\cos \relax (x)}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 4, normalized size = 1.00 \[ {\mathrm e}^{\sec \relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 3, normalized size = 0.75 \[ e^{\sec \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.09, size = 5, normalized size = 1.25 \[ {\mathrm {e}}^{\frac {1}{\cos \relax (x)}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.61, size = 3, normalized size = 0.75 \[ e^{\sec {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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