Optimal. Leaf size=2 \[ \tan (x) \]
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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 = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {3767, 8} \[ \tan (x) \]
Antiderivative was successfully verified.
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Rule 8
Rule 3767
Rubi steps
\begin {align*} \int \sec ^2(x) \, dx &=-\operatorname {Subst}(\int 1 \, dx,x,-\tan (x))\\ &=\tan (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 2, normalized size = 1.00 \[ \tan (x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.43, size = 7, normalized size = 3.50 \[ \frac {\sin \relax (x)}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.11, size = 2, normalized size = 1.00 \[ \tan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 3, normalized size = 1.50 \[ \tan \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 2, normalized size = 1.00 \[ \tan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 2, normalized size = 1.00 \[ \mathrm {tan}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.06, size = 5, normalized size = 2.50 \[ \frac {\sin {\relax (x )}}{\cos {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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