Optimal. Leaf size=9 \[ y \cosh (y)-\sinh (y) \]
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Rubi [A] time = 0.0115834, 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, Rules used = {3296, 2637} \[ y \cosh (y)-\sinh (y) \]
Antiderivative was successfully verified.
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Rule 3296
Rule 2637
Rubi steps
\begin{align*} \int y \sinh (y) \, dy &=y \cosh (y)-\int \cosh (y) \, dy\\ &=y \cosh (y)-\sinh (y)\\ \end{align*}
Mathematica [A] time = 0.0031957, size = 9, normalized size = 1. \[ y \cosh (y)-\sinh (y) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 10, normalized size = 1.1 \begin{align*} y\cosh \left ( y \right ) -\sinh \left ( y \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.948028, size = 46, normalized size = 5.11 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78134, size = 28, normalized size = 3.11 \begin{align*} y \cosh \left (y\right ) - \sinh \left (y\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.171068, size = 7, normalized size = 0.78 \begin{align*} y \cosh{\left (y \right )} - \sinh{\left (y \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04867, size = 23, normalized size = 2.56 \begin{align*} \frac{1}{2} \,{\left (y + 1\right )} e^{\left (-y\right )} + \frac{1}{2} \,{\left (y - 1\right )} e^{y} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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