Optimal. Leaf size=9 \[ x \sinh (x)-\cosh (x) \]
[Out]
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Rubi [A] time = 0.0177194, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ x \sinh (x)-\cosh (x) \]
Antiderivative was successfully verified.
[In] Int[x*Cosh[x],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ x \sinh{\left (x \right )} - \int \sinh{\left (x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*cosh(x),x)
[Out]
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Mathematica [A] time = 0.00497574, size = 9, normalized size = 1. \[ x \sinh (x)-\cosh (x) \]
Antiderivative was successfully verified.
[In] Integrate[x*Cosh[x],x]
[Out]
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Maple [A] time = 0.004, size = 10, normalized size = 1.1 \[ -\cosh \left ( x \right ) +x\sinh \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*cosh(x),x)
[Out]
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Maxima [A] time = 1.36487, size = 46, normalized size = 5.11 \[ \frac{1}{2} \, x^{2} \cosh \left (x\right ) - \frac{1}{4} \,{\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} - \frac{1}{4} \,{\left (x^{2} - 2 \, x + 2\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cosh(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217322, size = 12, normalized size = 1.33 \[ x \sinh \left (x\right ) - \cosh \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cosh(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.169484, size = 7, normalized size = 0.78 \[ x \sinh{\left (x \right )} - \cosh{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cosh(x),x)
[Out]
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GIAC/XCAS [A] time = 0.228665, size = 23, normalized size = 2.56 \[ -\frac{1}{2} \,{\left (x + 1\right )} e^{\left (-x\right )} + \frac{1}{2} \,{\left (x - 1\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cosh(x),x, algorithm="giac")
[Out]