Optimal. Leaf size=15 \[ 2 e^{\sin (x)} \sin (x)-2 e^{\sin (x)} \]
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Rubi [A] time = 0.0165931, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {12, 2176, 2194} \[ 2 e^{\sin (x)} \sin (x)-2 e^{\sin (x)} \]
Antiderivative was successfully verified.
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Rule 12
Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{\sin (x)} \sin (2 x) \, dx &=\operatorname{Subst}\left (\int 2 e^x x \, dx,x,\sin (x)\right )\\ &=2 \operatorname{Subst}\left (\int e^x x \, dx,x,\sin (x)\right )\\ &=2 e^{\sin (x)} \sin (x)-2 \operatorname{Subst}\left (\int e^x \, dx,x,\sin (x)\right )\\ &=-2 e^{\sin (x)}+2 e^{\sin (x)} \sin (x)\\ \end{align*}
Mathematica [A] time = 0.0153761, size = 11, normalized size = 0.73 \[ e^{\sin (x)} (2 \sin (x)-2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 14, normalized size = 0.9 \begin{align*} -2\,{{\rm e}^{\sin \left ( x \right ) }}+2\,{{\rm e}^{\sin \left ( x \right ) }}\sin \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.94368, size = 12, normalized size = 0.8 \begin{align*} 2 \,{\left (\sin \left (x\right ) - 1\right )} e^{\sin \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.97079, size = 34, normalized size = 2.27 \begin{align*} 2 \,{\left (\sin \left (x\right ) - 1\right )} e^{\sin \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.2503, size = 15, normalized size = 1. \begin{align*} 2 e^{\sin{\left (x \right )}} \sin{\left (x \right )} - 2 e^{\sin{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.09381, size = 721, normalized size = 48.07 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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