Optimal. Leaf size=4 \[ x+\tan (x) \]
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Rubi [A] time = 0.0182728, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {3012, 8} \[ x+\tan (x) \]
Antiderivative was successfully verified.
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Rule 3012
Rule 8
Rubi steps
\begin{align*} \int \left (1+\cos ^2(x)\right ) \sec ^2(x) \, dx &=\tan (x)+\int 1 \, dx\\ &=x+\tan (x)\\ \end{align*}
Mathematica [A] time = 0.0023942, size = 4, normalized size = 1. \[ x+\tan (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.032, size = 5, normalized size = 1.3 \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 = 1.46473, size = 5, normalized size = 1.25 \begin{align*} x + \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.95409, size = 38, normalized size = 9.5 \begin{align*} \frac{x \cos \left (x\right ) + \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 [A] time = 23.6743, size = 3, normalized size = 0.75 \begin{align*} x + \tan{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.12031, size = 20, normalized size = 5. \begin{align*} -\pi \left \lfloor \frac{x}{\pi } + \frac{1}{2} \right \rfloor + x + \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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