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 = {4380, 8} \[ x \]
Antiderivative was successfully verified.
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Rule 8
Rule 4380
Rubi steps
\begin {align*} \int \frac {1}{\cosh ^2(x)-\sinh ^2(x)} \, 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 = 0.40, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.11, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.10, size = 8, normalized size = 8.00 \[ 2 \arctanh \left (\tanh \left (\frac {x}{2}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.52, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.39, size = 10, normalized size = 10.00 \[ \frac {x}{- \sinh ^{2}{\relax (x )} + \cosh ^{2}{\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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