Optimal. Leaf size=13 \[ e^x \sin \left (e^x\right )+\cos \left (e^x\right ) \]
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Rubi [A] time = 0.0165981, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.3, Rules used = {2282, 3296, 2638} \[ e^x \sin \left (e^x\right )+\cos \left (e^x\right ) \]
Antiderivative was successfully verified.
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Rule 2282
Rule 3296
Rule 2638
Rubi steps
\begin{align*} \int e^{2 x} \cos \left (e^x\right ) \, dx &=\operatorname{Subst}\left (\int x \cos (x) \, dx,x,e^x\right )\\ &=e^x \sin \left (e^x\right )-\operatorname{Subst}\left (\int \sin (x) \, dx,x,e^x\right )\\ &=\cos \left (e^x\right )+e^x \sin \left (e^x\right )\\ \end{align*}
Mathematica [A] time = 0.0166958, size = 13, normalized size = 1. \[ e^x \sin \left (e^x\right )+\cos \left (e^x\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.02, size = 24, normalized size = 1.9 \begin{align*}{ \left ( 2\,{{\rm e}^{x}}\tan \left ( 1/2\,{{\rm e}^{x}} \right ) +2 \right ) \left ( 1+ \left ( \tan \left ({\frac{{{\rm e}^{x}}}{2}} \right ) \right ) ^{2} \right ) ^{-1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00955, size = 14, normalized size = 1.08 \begin{align*} e^{x} \sin \left (e^{x}\right ) + \cos \left (e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.47621, size = 34, normalized size = 2.62 \begin{align*} e^{x} \sin \left (e^{x}\right ) + \cos \left (e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 11.9689, size = 12, normalized size = 0.92 \begin{align*} e^{x} \sin{\left (e^{x} \right )} + \cos{\left (e^{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12902, size = 14, normalized size = 1.08 \begin{align*} e^{x} \sin \left (e^{x}\right ) + \cos \left (e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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