Optimal. Leaf size=20 \[ e^x x-e^x+\frac{e^{2 x}}{2} \]
[Out]
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Rubi [A] time = 0.1087, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 13, number of rules used = 7, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.438 \[ e^x x-e^x+\frac{e^{2 x}}{2} \]
Antiderivative was successfully verified.
[In] Int[(x + Cosh[x] + Sinh[x])/(Cosh[x] - Sinh[x]),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\left (x + e^{x}\right )^{2}}{2} - e^{x} - \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x+cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x)
[Out]
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Mathematica [A] time = 0.0641025, size = 23, normalized size = 1.15 \[ (x-1) \sinh (x)+\frac{1}{2} \cosh (2 x)+(x+\sinh (x)-1) \cosh (x) \]
Antiderivative was successfully verified.
[In] Integrate[(x + Cosh[x] + Sinh[x])/(Cosh[x] - Sinh[x]),x]
[Out]
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Maple [A] time = 0.112, size = 14, normalized size = 0.7 \[ \left ( -1+x \right ){{\rm e}^{x}}+{\frac{{{\rm e}^{2\,x}}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x+cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x)
[Out]
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Maxima [A] time = 1.3682, size = 18, normalized size = 0.9 \[{\left (x - 1\right )} e^{x} + \frac{1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + cosh(x) + sinh(x))/(cosh(x) - sinh(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215303, size = 27, normalized size = 1.35 \[ \frac{2 \, x + \cosh \left (x\right ) + \sinh \left (x\right ) - 2}{2 \,{\left (\cosh \left (x\right ) - \sinh \left (x\right )\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + cosh(x) + sinh(x))/(cosh(x) - sinh(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.662627, size = 26, normalized size = 1.3 \[ \frac{x}{- \sinh{\left (x \right )} + \cosh{\left (x \right )}} + \frac{\sinh{\left (x \right )}}{- \sinh{\left (x \right )} + \cosh{\left (x \right )}} - \frac{1}{- \sinh{\left (x \right )} + \cosh{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x+cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x)
[Out]
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GIAC/XCAS [A] time = 0.218583, size = 15, normalized size = 0.75 \[ \frac{1}{2} \,{\left (2 \, x + e^{x} - 2\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + cosh(x) + sinh(x))/(cosh(x) - sinh(x)),x, algorithm="giac")
[Out]