Optimal. Leaf size=3 \[ \log (\sinh (x)) \]
[Out]
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Rubi [A] time = 0.00608192, antiderivative size = 3, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \log (\sinh (x)) \]
Antiderivative was successfully verified.
[In] Int[Coth[x],x]
[Out]
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Rubi in Sympy [A] time = 35.1172, size = 17, normalized size = 5.67 \[ - \frac{\log{\left (- \tanh ^{2}{\left (x \right )} + 1 \right )}}{2} + \frac{\log{\left (\tanh ^{2}{\left (x \right )} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(coth(x),x)
[Out]
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Mathematica [A] time = 0.00534756, size = 3, normalized size = 1. \[ \log (\sinh (x)) \]
Antiderivative was successfully verified.
[In] Integrate[Coth[x],x]
[Out]
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Maple [A] time = 0.001, size = 4, normalized size = 1.3 \[ \ln \left ( \sinh \left ( x \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(coth(x),x)
[Out]
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Maxima [A] time = 1.46243, size = 4, normalized size = 1.33 \[ \log \left (\sinh \left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(coth(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221777, size = 24, normalized size = 8. \[ -x + \log \left (\frac{2 \, \sinh \left (x\right )}{\cosh \left (x\right ) - \sinh \left (x\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(coth(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.401351, size = 12, normalized size = 4. \[ x - \log{\left (\tanh{\left (x \right )} + 1 \right )} + \log{\left (\tanh{\left (x \right )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(coth(x),x)
[Out]
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GIAC/XCAS [A] time = 0.227696, size = 16, normalized size = 5.33 \[ -x +{\rm ln}\left ({\left | e^{\left (2 \, x\right )} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(coth(x),x, algorithm="giac")
[Out]