Optimal. Leaf size=4 \[ x+\coth (x) \]
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Rubi [A] time = 0.02, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {3012, 8} \[ x+\coth (x) \]
Antiderivative was successfully verified.
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Rule 8
Rule 3012
Rubi steps
\begin {align*} \int \text {csch}^2(x) \left (-1+\sinh ^2(x)\right ) \, dx &=\coth (x)+\int 1 \, dx\\ &=x+\coth (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 4, normalized size = 1.00 \[ x+\coth (x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.42, size = 14, normalized size = 3.50 \[ \frac {{\left (x - 1\right )} \sinh \relax (x) + \cosh \relax (x)}{\sinh \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 12, normalized size = 3.00 \[ x + \frac {2}{e^{\left (2 \, x\right )} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.38, size = 5, normalized size = 1.25 \[ x +\coth \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.31, size = 12, normalized size = 3.00 \[ x - \frac {2}{e^{\left (-2 \, x\right )} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.72, size = 12, normalized size = 3.00 \[ x+\frac {2}{{\mathrm {e}}^{2\,x}-1} \]
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 \[ \int \left (\sinh {\relax (x )} - 1\right ) \left (\sinh {\relax (x )} + 1\right ) \operatorname {csch}^{2}{\relax (x )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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