Optimal. Leaf size=2 \[ \sec (x) \]
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Rubi [A] time = 0.01, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {2606, 8} \[ \sec (x) \]
Antiderivative was successfully verified.
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Rule 8
Rule 2606
Rubi steps
\begin {align*} \int \sec (x) \tan (x) \, dx &=\operatorname {Subst}(\int 1 \, dx,x,\sec (x))\\ &=\sec (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 2, normalized size = 1.00 \[ \sec (x) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sec (x) \tan (x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.15, size = 4, normalized size = 2.00 \[ \frac {1}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 4, normalized size = 2.00 \[ \frac {1}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 3, normalized size = 1.50
method | result | size |
derivativedivides | \(\sec \relax (x )\) | \(3\) |
default | \(\sec \relax (x )\) | \(3\) |
risch | \(\frac {2 \,{\mathrm e}^{i x}}{1+{\mathrm e}^{2 i x}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 4, normalized size = 2.00 \[ \frac {1}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 12, normalized size = 6.00 \[ -\frac {2}{{\mathrm {tan}\left (\frac {x}{2}\right )}^2-1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 3, normalized size = 1.50 \[ \frac {1}{\cos {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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