Optimal. Leaf size=1 \[ x \]
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Rubi [A] time = 0.012288, antiderivative size = 1, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {4381, 8} \[ x \]
Antiderivative was successfully verified.
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Rule 4381
Rule 8
Rubi steps
\begin{align*} \int \frac{1}{\sec ^2(x)-\tan ^2(x)} \, dx &=\int 1 \, dx\\ &=x\\ \end{align*}
Mathematica [A] time = 0.0005178, size = 1, normalized size = 1. \[ x \]
Antiderivative was successfully verified.
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Maple [C] time = 0.024, size = 4, normalized size = 4. \begin{align*} \arctan \left ( \tan \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.48744, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6008, size = 4, normalized size = 4. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (- \tan{\left (x \right )} + \sec{\left (x \right )}\right ) \left (\tan{\left (x \right )} + \sec{\left (x \right )}\right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11368, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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