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 = {4467, 8}
\begin {gather*} x \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 4467
Rubi steps
\begin {align*} \int \frac {1}{\left (\coth ^2(x)-\text {csch}^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 \begin {gather*} x \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 3 vs. order
1.
time = 0.79, size = 8, normalized size = 8.00
method | result | size |
risch | \(x\) | \(2\) |
default | \(2 \arctanh \left (\tanh \left (\frac {x}{2}\right )\right )\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
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 \begin {gather*} \int \frac {1}{\left (\coth {\left (x \right )} - \operatorname {csch}{\left (x \right )}\right )^{3} \left (\coth {\left (x \right )} + \operatorname {csch}{\left (x \right )}\right )^{3}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.54, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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