Optimal. Leaf size=8 \[ \frac {2 \sinh ^3(x)}{3} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.88, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {4282} \[ \frac {1}{6} \sinh (3 x)-\frac {\sinh (x)}{2} \]
Antiderivative was successfully verified.
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Rule 4282
Rubi steps
\begin {align*} \int \sinh (x) \sinh (2 x) \, dx &=-\frac {\sinh (x)}{2}+\frac {1}{6} \sinh (3 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 1.88 \[ \frac {1}{6} \sinh (3 x)-\frac {\sinh (x)}{2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.40, size = 17, normalized size = 2.12 \[ \frac {1}{6} \, \sinh \relax (x)^{3} + \frac {1}{2} \, {\left (\cosh \relax (x)^{2} - 1\right )} \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 25, normalized size = 3.12 \[ \frac {1}{12} \, {\left (3 \, e^{\left (2 \, x\right )} - 1\right )} e^{\left (-3 \, x\right )} + \frac {1}{12} \, e^{\left (3 \, x\right )} - \frac {1}{4} \, e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 7, normalized size = 0.88 \[ \frac {2 \left (\sinh ^{3}\relax (x )\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.45, size = 27, normalized size = 3.38 \[ -\frac {1}{12} \, {\left (3 \, e^{\left (-2 \, x\right )} - 1\right )} e^{\left (3 \, x\right )} + \frac {1}{4} \, e^{\left (-x\right )} - \frac {1}{12} \, e^{\left (-3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 6, normalized size = 0.75 \[ \frac {2\,{\mathrm {sinh}\relax (x)}^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.44, size = 20, normalized size = 2.50 \[ \frac {2 \sinh {\relax (x )} \cosh {\left (2 x \right )}}{3} - \frac {\sinh {\left (2 x \right )} \cosh {\relax (x )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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