Optimal. Leaf size=9 \[ x \cosh (x)-\sinh (x) \]
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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} \[ x \cosh (x)-\sinh (x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 3296
Rubi steps
\begin {align*} \int x \sinh (x) \, dx &=x \cosh (x)-\int \cosh (x) \, dx\\ &=x \cosh (x)-\sinh (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 1.00 \[ x \cosh (x)-\sinh (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 9, normalized size = 1.00 \[ x \cosh \relax (x) - \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 17, normalized size = 1.89 \[ \frac {1}{2} \, {\left (x + 1\right )} e^{\left (-x\right )} + \frac {1}{2} \, {\left (x - 1\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 10, normalized size = 1.11 \[ x \cosh \relax (x )-\sinh \relax (x ) \]
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 \[ \frac {1}{2} \, x^{2} \sinh \relax (x) + \frac {1}{4} \, {\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} - \frac {1}{4} \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 9, normalized size = 1.00 \[ x\,\mathrm {cosh}\relax (x)-\mathrm {sinh}\relax (x) \]
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 \[ x \cosh {\relax (x )} - \sinh {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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