Optimal. Leaf size=9 \[ y \cosh (y)-\sinh (y) \]
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Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {3296, 2637} \[ y \cosh (y)-\sinh (y) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 3296
Rubi steps
\begin {align*} \int y \sinh (y) \, dy &=y \cosh (y)-\int \cosh (y) \, dy\\ &=y \cosh (y)-\sinh (y)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 1.00 \[ y \cosh (y)-\sinh (y) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 9, normalized size = 1.00 \[ y \cosh \relax (y) - \sinh \relax (y) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.81, size = 17, normalized size = 1.89 \[ \frac {1}{2} \, {\left (y + 1\right )} e^{\left (-y\right )} + \frac {1}{2} \, {\left (y - 1\right )} e^{y} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 1.11 \[ y \cosh \relax (y )-\sinh \relax (y ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.43, size = 34, normalized size = 3.78 \[ \frac {1}{2} \, y^{2} \sinh \relax (y) + \frac {1}{4} \, {\left (y^{2} + 2 \, y + 2\right )} e^{\left (-y\right )} - \frac {1}{4} \, {\left (y^{2} - 2 \, y + 2\right )} e^{y} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 9, normalized size = 1.00 \[ y\,\mathrm {cosh}\relax (y)-\mathrm {sinh}\relax (y) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 7, normalized size = 0.78 \[ y \cosh {\relax (y )} - \sinh {\relax (y )} \]
Verification of antiderivative is not currently implemented for this CAS.
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