Optimal. Leaf size=1 \[ x \]
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Rubi [A] time = 0.01, antiderivative size = 1, normalized size of antiderivative = 1.00, 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 8
Rule 4381
Rubi steps
\begin {align*} \int \frac {1}{\left (\sec ^2(x)-\tan ^2(x)\right )^3} \, dx &=\int 1 \, dx\\ &=x\\ \end {align*}
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Mathematica [A] time = 0.00, size = 1, normalized size = 1.00 \[ x \]
Antiderivative was successfully verified.
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fricas [A] time = 1.53, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.07, size = 4, normalized size = 4.00 \[ \arctan \left (\tan \relax (x )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.57, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (- \tan {\relax (x )} + \sec {\relax (x )}\right )^{3} \left (\tan {\relax (x )} + \sec {\relax (x )}\right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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