Optimal. Leaf size=15 \[ x-(1-x) \tanh \left (\frac{x}{2}\right ) \]
[Out]
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Rubi [A] time = 0.20023, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ x-(1-x) \tanh \left (\frac{x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[(x + Cosh[x] + Sinh[x])/(1 + Cosh[x]),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x + e^{x}}{\cosh{\left (x \right )} + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x+cosh(x)+sinh(x))/(1+cosh(x)),x)
[Out]
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Mathematica [A] time = 0.0392386, size = 20, normalized size = 1.33 \[ \frac{\sinh (x) \left (x+x \coth \left (\frac{x}{2}\right )-1\right )}{\cosh (x)+1} \]
Antiderivative was successfully verified.
[In] Integrate[(x + Cosh[x] + Sinh[x])/(1 + Cosh[x]),x]
[Out]
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Maple [A] time = 0.032, size = 16, normalized size = 1.1 \[ 2\,x-2\,{\frac{-1+x}{1+{{\rm e}^{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x+cosh(x)+sinh(x))/(1+cosh(x)),x)
[Out]
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Maxima [A] time = 1.3595, size = 47, normalized size = 3.13 \[ x + \frac{2 \, x e^{x}}{e^{x} + 1} - \frac{2}{e^{\left (-x\right )} + 1} + \log \left (\cosh \left (x\right ) + 1\right ) - 2 \, \log \left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + cosh(x) + sinh(x))/(cosh(x) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203108, size = 27, normalized size = 1.8 \[ \frac{2 \,{\left (x \cosh \left (x\right ) + x \sinh \left (x\right ) + 1\right )}}{\cosh \left (x\right ) + \sinh \left (x\right ) + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + cosh(x) + sinh(x))/(cosh(x) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.651869, size = 12, normalized size = 0.8 \[ x \tanh{\left (\frac{x}{2} \right )} + x - \tanh{\left (\frac{x}{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x+cosh(x)+sinh(x))/(1+cosh(x)),x)
[Out]
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GIAC/XCAS [A] time = 0.21597, size = 19, normalized size = 1.27 \[ \frac{2 \,{\left (x e^{x} + 1\right )}}{e^{x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + cosh(x) + sinh(x))/(cosh(x) + 1),x, algorithm="giac")
[Out]