Optimal. Leaf size=4 \[ x+\tan (x) \]
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Rubi [A] time = 0.02, antiderivative size = 4, normalized size of antiderivative = 1.00, 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 8
Rule 3012
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*}
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Mathematica [A] time = 0.00, size = 4, normalized size = 1.00 \[ x+\tan (x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 12, normalized size = 3.00 \[ \frac {x \cos \relax (x) + \sin \relax (x)}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.19, size = 15, normalized size = 3.75 \[ -\pi \left \lfloor \frac {x}{\pi } + \frac {1}{2} \right \rfloor + x + \tan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 5, normalized size = 1.25 \[ x +\tan \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 4, 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 = 2.88, size = 4, normalized size = 1.00 \[ x+\mathrm {tan}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.38, size = 3, normalized size = 0.75 \[ x + \tan {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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