Optimal. Leaf size=9 \[ y \cosh (y)-\sinh (y) \]
[Out]
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Rubi [A] time = 0.0191523, 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 \[ y \cosh (y)-\sinh (y) \]
Antiderivative was successfully verified.
[In] Int[y*Sinh[y],y]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ y \cosh{\left (y \right )} - \int \cosh{\left (y \right )}\, dy \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(y*sinh(y),y)
[Out]
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Mathematica [A] time = 0.00513669, size = 9, normalized size = 1. \[ y \cosh (y)-\sinh (y) \]
Antiderivative was successfully verified.
[In] Integrate[y*Sinh[y],y]
[Out]
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Maple [A] time = 0.003, size = 10, normalized size = 1.1 \[ y\cosh \left ( y \right ) -\sinh \left ( y \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(y*sinh(y),y)
[Out]
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Maxima [A] time = 1.35613, size = 46, normalized size = 5.11 \[ \frac{1}{2} \, y^{2} \sinh \left (y\right ) + \frac{1}{4} \,{\left (y^{2} + 2 \, y + 2\right )} e^{\left (-y\right )} - \frac{1}{4} \,{\left (y^{2} - 2 \, y + 2\right )} e^{y} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(y*sinh(y),y, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210783, size = 12, normalized size = 1.33 \[ y \cosh \left (y\right ) - \sinh \left (y\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(y*sinh(y),y, algorithm="fricas")
[Out]
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Sympy [A] time = 0.177784, size = 7, normalized size = 0.78 \[ y \cosh{\left (y \right )} - \sinh{\left (y \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(y*sinh(y),y)
[Out]
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GIAC/XCAS [A] time = 0.198044, size = 23, normalized size = 2.56 \[ \frac{1}{2} \,{\left (y + 1\right )} e^{\left (-y\right )} + \frac{1}{2} \,{\left (y - 1\right )} e^{y} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(y*sinh(y),y, algorithm="giac")
[Out]