Optimal. Leaf size=10 \[ -\frac {\text {csch}(x)}{\coth (x)+1} \]
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Rubi [A] time = 0.02, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {3488} \[ -\frac {\text {csch}(x)}{\coth (x)+1} \]
Antiderivative was successfully verified.
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Rule 3488
Rubi steps
\begin {align*} \int \frac {\text {csch}(x)}{1+\coth (x)} \, dx &=-\frac {\text {csch}(x)}{1+\coth (x)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 0.70 \[ \sinh (x)-\cosh (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 9, normalized size = 0.90 \[ -\frac {1}{\cosh \relax (x) + \sinh \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.11, size = 6, normalized size = 0.60 \[ -e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 11, normalized size = 1.10 \[ -\frac {\mathrm {csch}\relax (x )}{1+\coth \relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 6, normalized size = 0.60 \[ -e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.20, size = 6, normalized size = 0.60 \[ -{\mathrm {e}}^{-x} \]
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 \[ \int \frac {\operatorname {csch}{\relax (x )}}{\coth {\relax (x )} + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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