Optimal. Leaf size=2 \[ \tan (x) \]
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Rubi [A] time = 0.0055703, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {3767, 8} \[ \tan (x) \]
Antiderivative was successfully verified.
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Rule 3767
Rule 8
Rubi steps
\begin{align*} \int \sec ^2(x) \, dx &=-\operatorname{Subst}(\int 1 \, dx,x,-\tan (x))\\ &=\tan (x)\\ \end{align*}
Mathematica [A] time = 0.0016016, size = 2, normalized size = 1. \[ \tan (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 3, normalized size = 1.5 \begin{align*} \tan \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926789, size = 3, normalized size = 1.5 \begin{align*} \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.90967, size = 20, normalized size = 10. \begin{align*} \frac{\sin \left (x\right )}{\cos \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.058736, size = 5, normalized size = 2.5 \begin{align*} \frac{\sin{\left (x \right )}}{\cos{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06331, size = 3, normalized size = 1.5 \begin{align*} \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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