Optimal. Leaf size=6 \[ \tan (x)-x \]
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Rubi [A] time = 0.004091, antiderivative size = 6, 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 = {3473, 8} \[ \tan (x)-x \]
Antiderivative was successfully verified.
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Rule 3473
Rule 8
Rubi steps
\begin{align*} \int \tan ^2(x) \, dx &=\tan (x)-\int 1 \, dx\\ &=-x+\tan (x)\\ \end{align*}
Mathematica [A] time = 0.0020183, size = 6, normalized size = 1. \[ \tan (x)-x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 7, normalized size = 1.2 \begin{align*} -x+\tan \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.40741, size = 8, normalized size = 1.33 \begin{align*} -x + \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.97729, size = 18, normalized size = 3. \begin{align*} -x + \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.061568, size = 7, normalized size = 1.17 \begin{align*} - x + \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 = 1.06425, size = 8, normalized size = 1.33 \begin{align*} -x + \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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