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 = 0.0355204, antiderivative size = 30, normalized size of antiderivative = 1., 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 4574
Rule 2638
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*}
Mathematica [A] time = 0.0608572, size = 30, normalized size = 1. \[ \frac{1}{6} e^{3 x-1} \sin (1)-\frac{1}{12} \cos \left (2 e^{3 x-1}+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.051, size = 25, normalized size = 0.8 \begin{align*} -{\frac{\cos \left ( 1+2\,{{\rm e}^{-1+3\,x}} \right ) }{12}}+{\frac{{{\rm e}^{-1+3\,x}}\sin \left ( 1 \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.986635, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{6} \, e^{\left (3 \, x - 1\right )} \sin \left (1\right ) - \frac{1}{12} \, \cos \left (2 \, e^{\left (3 \, x - 1\right )} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.483324, size = 140, normalized size = 4.67 \begin{align*} -\frac{1}{6} \, \cos \left (1\right ) \cos \left (e^{\left (3 \, x - 1\right )}\right )^{2} + \frac{1}{6} \, \cos \left (e^{\left (3 \, x - 1\right )}\right ) \sin \left (1\right ) \sin \left (e^{\left (3 \, x - 1\right )}\right ) + \frac{1}{6} \, e^{\left (3 \, x - 1\right )} \sin \left (1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12193, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{6} \, e^{\left (3 \, x - 1\right )} \sin \left (1\right ) - \frac{1}{12} \, \cos \left (2 \, e^{\left (3 \, x - 1\right )} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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