Optimal. Leaf size=27 \[ \frac {3}{10} e^{-x} \sin (3 x)-\frac {1}{10} e^{-x} \cos (3 x) \]
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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 = {4433} \[ \frac {3}{10} e^{-x} \sin (3 x)-\frac {1}{10} e^{-x} \cos (3 x) \]
Antiderivative was successfully verified.
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Rule 4433
Rubi steps
\begin {align*} \int e^{-x} \cos (3 x) \, dx &=-\frac {1}{10} e^{-x} \cos (3 x)+\frac {3}{10} e^{-x} \sin (3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 20, normalized size = 0.74 \[ -\frac {1}{10} e^{-x} (\cos (3 x)-3 \sin (3 x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 21, normalized size = 0.78 \[ -\frac {1}{10} \, \cos \left (3 \, x\right ) e^{\left (-x\right )} + \frac {3}{10} \, e^{\left (-x\right )} \sin \left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 17, normalized size = 0.63 \[ -\frac {1}{10} \, {\left (\cos \left (3 \, x\right ) - 3 \, \sin \left (3 \, x\right )\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 22, normalized size = 0.81 \[ -\frac {\cos \left (3 x \right ) {\mathrm e}^{-x}}{10}+\frac {3 \,{\mathrm e}^{-x} \sin \left (3 x \right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.83, size = 17, normalized size = 0.63 \[ -\frac {1}{10} \, {\left (\cos \left (3 \, x\right ) - 3 \, \sin \left (3 \, x\right )\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 17, normalized size = 0.63 \[ -\frac {{\mathrm {e}}^{-x}\,\left (\cos \left (3\,x\right )-3\,\sin \left (3\,x\right )\right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.44, size = 20, normalized size = 0.74 \[ \frac {3 e^{- x} \sin {\left (3 x \right )}}{10} - \frac {e^{- x} \cos {\left (3 x \right )}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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