Optimal. Leaf size=14 \[ x-\frac{1}{3} \tanh ^3(x)-\tanh (x) \]
[Out]
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Rubi [A] time = 0.0179731, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ x-\frac{1}{3} \tanh ^3(x)-\tanh (x) \]
Antiderivative was successfully verified.
[In] Int[Tanh[x]^4,x]
[Out]
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Rubi in Sympy [A] time = 40.0089, size = 14, normalized size = 1. \[ - \frac{\tanh ^{3}{\left (x \right )}}{3} - \tanh{\left (x \right )} + \operatorname{atanh}{\left (\tanh{\left (x \right )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(tanh(x)**4,x)
[Out]
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Mathematica [A] time = 0.00551939, size = 18, normalized size = 1.29 \[ x-\frac{4 \tanh (x)}{3}+\frac{1}{3} \tanh (x) \text{sech}^2(x) \]
Antiderivative was successfully verified.
[In] Integrate[Tanh[x]^4,x]
[Out]
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Maple [B] time = 0.017, size = 26, normalized size = 1.9 \[ -{\frac{ \left ( \tanh \left ( x \right ) \right ) ^{3}}{3}}-\tanh \left ( x \right ) -{\frac{\ln \left ( -1+\tanh \left ( x \right ) \right ) }{2}}+{\frac{\ln \left ( 1+\tanh \left ( x \right ) \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(tanh(x)^4,x)
[Out]
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Maxima [A] time = 1.3713, size = 51, normalized size = 3.64 \[ x - \frac{4 \,{\left (3 \, e^{\left (-2 \, x\right )} + 3 \, e^{\left (-4 \, x\right )} + 2\right )}}{3 \,{\left (3 \, e^{\left (-2 \, x\right )} + 3 \, e^{\left (-4 \, x\right )} + e^{\left (-6 \, x\right )} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tanh(x)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2035, size = 92, normalized size = 6.57 \[ \frac{{\left (3 \, x + 4\right )} \cosh \left (x\right )^{3} + 3 \,{\left (3 \, x + 4\right )} \cosh \left (x\right ) \sinh \left (x\right )^{2} - 12 \, \cosh \left (x\right )^{2} \sinh \left (x\right ) - 4 \, \sinh \left (x\right )^{3} + 3 \,{\left (3 \, x + 4\right )} \cosh \left (x\right )}{3 \,{\left (\cosh \left (x\right )^{3} + 3 \, \cosh \left (x\right ) \sinh \left (x\right )^{2} + 3 \, \cosh \left (x\right )\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tanh(x)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.271181, size = 10, normalized size = 0.71 \[ x - \frac{\tanh ^{3}{\left (x \right )}}{3} - \tanh{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tanh(x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.20209, size = 35, normalized size = 2.5 \[ x + \frac{4 \,{\left (3 \, e^{\left (4 \, x\right )} + 3 \, e^{\left (2 \, x\right )} + 2\right )}}{3 \,{\left (e^{\left (2 \, x\right )} + 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tanh(x)^4,x, algorithm="giac")
[Out]