Optimal. Leaf size=30 \[ \frac {1}{6} e^{3 x-1} \sin (1)-\frac {1}{12} \cos \left (2 e^{3 x-1}+1\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {2282, 4574, 2638} \[ \frac {1}{6} e^{3 x-1} \sin (1)-\frac {1}{12} \cos \left (2 e^{3 x-1}+1\right ) \]
Antiderivative was successfully verified.
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Rule 2282
Rule 2638
Rule 4574
Rubi steps
\begin {align*} \int e^{-1+3 x} \cos \left (e^{-1+3 x}\right ) \sin \left (1+e^{-1+3 x}\right ) \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \cos (x) \sin (1+x) \, dx,x,e^{-1+3 x}\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (\frac {\sin (1)}{2}+\frac {1}{2} \sin (1+2 x)\right ) \, dx,x,e^{-1+3 x}\right )\\ &=\frac {1}{6} e^{-1+3 x} \sin (1)+\frac {1}{6} \operatorname {Subst}\left (\int \sin (1+2 x) \, dx,x,e^{-1+3 x}\right )\\ &=-\frac {1}{12} \cos \left (1+2 e^{-1+3 x}\right )+\frac {1}{6} e^{-1+3 x} \sin (1)\\ \end {align*}
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Mathematica [A] time = 0.06, size = 30, normalized size = 1.00 \[ \frac {1}{6} e^{3 x-1} \sin (1)-\frac {1}{12} \cos \left (2 e^{3 x-1}+1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 42, normalized size = 1.40 \[ -\frac {1}{6} \, \cos \relax (1) \cos \left (e^{\left (3 \, x - 1\right )}\right )^{2} + \frac {1}{6} \, \cos \left (e^{\left (3 \, x - 1\right )}\right ) \sin \relax (1) \sin \left (e^{\left (3 \, x - 1\right )}\right ) + \frac {1}{6} \, e^{\left (3 \, x - 1\right )} \sin \relax (1) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 24, normalized size = 0.80 \[ \frac {1}{6} \, e^{\left (3 \, x - 1\right )} \sin \relax (1) - \frac {1}{12} \, \cos \left (2 \, e^{\left (3 \, x - 1\right )} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 25, normalized size = 0.83 \[ -\frac {\cos \left (1+2 \,{\mathrm e}^{-1+3 x}\right )}{12}+\frac {{\mathrm e}^{-1+3 x} \sin \relax (1)}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 24, normalized size = 0.80 \[ \frac {1}{6} \, e^{\left (3 \, x - 1\right )} \sin \relax (1) - \frac {1}{12} \, \cos \left (2 \, e^{\left (3 \, x - 1\right )} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 24, normalized size = 0.80 \[ \frac {{\mathrm {e}}^{3\,x-1}\,\sin \relax (1)}{6}-\frac {\cos \left (2\,{\mathrm {e}}^{3\,x-1}+1\right )}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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