Optimal. Leaf size=2 \[ \sec (x) \]
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Rubi [A]
time = 0.00, 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 = {2686, 8}
\begin {gather*} \sec (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 2686
Rubi steps
\begin {align*} \int \sec (x) \tan (x) \, dx &=\text {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 \begin {gather*} \sec (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 3, normalized size = 1.50
method | result | size |
derivativedivides | \(\sec \left (x \right )\) | \(3\) |
default | \(\sec \left (x \right )\) | \(3\) |
risch | \(\frac {2 \,{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.97, size = 4, normalized size = 2.00 \begin {gather*} \frac {1}{\cos \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.05, size = 4, normalized size = 2.00 \begin {gather*} \frac {1}{\cos \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 3, normalized size = 1.50 \begin {gather*} \frac {1}{\cos {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.24, size = 4, normalized size = 2.00 \begin {gather*} \frac {1}{\cos \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.26, size = 12, normalized size = 6.00 \begin {gather*} -\frac {2}{{\mathrm {tan}\left (\frac {x}{2}\right )}^2-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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