Optimal. Leaf size=1 \[ x \]
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Rubi [A] time = 0.02, 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 = {4382, 8} \[ x \]
Antiderivative was successfully verified.
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Rule 8
Rule 4382
Rubi steps
\begin {align*} \int \frac {1}{\left (\coth ^2(x)-\text {csch}^2(x)\right )^2} \, 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 = 0.38, 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 = 0.13, 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 = 0.32, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, 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 \[ \int \frac {1}{\left (\coth {\relax (x )} - \operatorname {csch}{\relax (x )}\right )^{2} \left (\coth {\relax (x )} + \operatorname {csch}{\relax (x )}\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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