Optimal. Leaf size=16 \[ \frac{x^2}{2}-x \tanh (x)+\log (\cosh (x)) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0307238, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \frac{x^2}{2}-x \tanh (x)+\log (\cosh (x)) \]
Antiderivative was successfully verified.
[In] Int[x*Tanh[x]^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - x \tanh{\left (x \right )} - \frac{\log{\left (- \tanh ^{2}{\left (x \right )} + 1 \right )}}{2} + \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*tanh(x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00775351, size = 16, normalized size = 1. \[ \frac{x^2}{2}-x \tanh (x)+\log (\cosh (x)) \]
Antiderivative was successfully verified.
[In] Integrate[x*Tanh[x]^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.025, size = 28, normalized size = 1.8 \[{\frac{{x}^{2}}{2}}-2\,x+2\,{\frac{x}{1+{{\rm e}^{2\,x}}}}+\ln \left ( 1+{{\rm e}^{2\,x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*tanh(x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.63203, size = 66, normalized size = 4.12 \[ -\frac{x e^{\left (2 \, x\right )}}{e^{\left (2 \, x\right )} + 1} + \frac{x^{2} +{\left (x^{2} - 2 \, x\right )} e^{\left (2 \, x\right )}}{2 \,{\left (e^{\left (2 \, x\right )} + 1\right )}} + \log \left (e^{\left (2 \, x\right )} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*tanh(x)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.214682, size = 126, normalized size = 7.88 \[ \frac{{\left (x^{2} - 4 \, x\right )} \cosh \left (x\right )^{2} + 2 \,{\left (x^{2} - 4 \, x\right )} \cosh \left (x\right ) \sinh \left (x\right ) +{\left (x^{2} - 4 \, x\right )} \sinh \left (x\right )^{2} + x^{2} + 2 \,{\left (\cosh \left (x\right )^{2} + 2 \, \cosh \left (x\right ) \sinh \left (x\right ) + \sinh \left (x\right )^{2} + 1\right )} \log \left (\frac{2 \, \cosh \left (x\right )}{\cosh \left (x\right ) - \sinh \left (x\right )}\right )}{2 \,{\left (\cosh \left (x\right )^{2} + 2 \, \cosh \left (x\right ) \sinh \left (x\right ) + \sinh \left (x\right )^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*tanh(x)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.207648, size = 17, normalized size = 1.06 \[ \frac{x^{2}}{2} - x \tanh{\left (x \right )} + x - \log{\left (\tanh{\left (x \right )} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*tanh(x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.228031, size = 69, normalized size = 4.31 \[ \frac{x^{2} e^{\left (2 \, x\right )} + x^{2} - 4 \, x e^{\left (2 \, x\right )} + 2 \, e^{\left (2 \, x\right )}{\rm ln}\left (e^{\left (2 \, x\right )} + 1\right ) + 2 \,{\rm ln}\left (e^{\left (2 \, x\right )} + 1\right )}{2 \,{\left (e^{\left (2 \, x\right )} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*tanh(x)^2,x, algorithm="giac")
[Out]