Optimal. Leaf size=27 \[ \frac {2}{13} e^{2 t} \sin (3 t)-\frac {3}{13} e^{2 t} \cos (3 t) \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {4432} \[ \frac {2}{13} e^{2 t} \sin (3 t)-\frac {3}{13} e^{2 t} \cos (3 t) \]
Antiderivative was successfully verified.
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Rule 4432
Rubi steps
\begin {align*} \int e^{2 t} \sin (3 t) \, dt &=-\frac {3}{13} e^{2 t} \cos (3 t)+\frac {2}{13} e^{2 t} \sin (3 t)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 22, normalized size = 0.81 \[ \frac {1}{13} e^{2 t} (2 \sin (3 t)-3 \cos (3 t)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 21, normalized size = 0.78 \[ -\frac {3}{13} \, \cos \left (3 \, t\right ) e^{\left (2 \, t\right )} + \frac {2}{13} \, e^{\left (2 \, t\right )} \sin \left (3 \, t\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 19, normalized size = 0.70 \[ -\frac {1}{13} \, {\left (3 \, \cos \left (3 \, t\right ) - 2 \, \sin \left (3 \, t\right )\right )} e^{\left (2 \, t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 22, normalized size = 0.81 \[ -\frac {3 \cos \left (3 t \right ) {\mathrm e}^{2 t}}{13}+\frac {2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 19, normalized size = 0.70 \[ -\frac {1}{13} \, {\left (3 \, \cos \left (3 \, t\right ) - 2 \, \sin \left (3 \, t\right )\right )} e^{\left (2 \, t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 19, normalized size = 0.70 \[ -\frac {{\mathrm {e}}^{2\,t}\,\left (3\,\cos \left (3\,t\right )-2\,\sin \left (3\,t\right )\right )}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 26, normalized size = 0.96 \[ \frac {2 e^{2 t} \sin {\left (3 t \right )}}{13} - \frac {3 e^{2 t} \cos {\left (3 t \right )}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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