Optimal. Leaf size=6 \[ \tan (x)-x \]
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Rubi [A] time = 0.00, antiderivative size = 6, 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 = {3473, 8} \[ \tan (x)-x \]
Antiderivative was successfully verified.
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Rule 8
Rule 3473
Rubi steps
\begin {align*} \int \tan ^2(x) \, dx &=\tan (x)-\int 1 \, dx\\ &=-x+\tan (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 6, normalized size = 1.00 \[ \tan (x)-x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 6, normalized size = 1.00 \[ -x + \tan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 6, normalized size = 1.00 \[ -x + \tan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 7, normalized size = 1.17 \[ -x +\tan \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.22, size = 6, normalized size = 1.00 \[ -x + \tan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 6, normalized size = 1.00 \[ \mathrm {tan}\relax (x)-x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 7, normalized size = 1.17 \[ - x + \frac {\sin {\relax (x )}}{\cos {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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