Optimal. Leaf size=6 \[ -\cos \left (e^x\right ) \]
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Rubi [A] time = 0.0083315, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {2282, 2638} \[ -\cos \left (e^x\right ) \]
Antiderivative was successfully verified.
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Rule 2282
Rule 2638
Rubi steps
\begin{align*} \int e^x \sin \left (e^x\right ) \, dx &=\operatorname{Subst}\left (\int \sin (x) \, dx,x,e^x\right )\\ &=-\cos \left (e^x\right )\\ \end{align*}
Mathematica [A] time = 0.0093841, size = 6, normalized size = 1. \[ -\cos \left (e^x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 6, normalized size = 1. \begin{align*} -\cos \left ({{\rm e}^{x}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.980391, size = 7, normalized size = 1.17 \begin{align*} -\cos \left (e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.464562, size = 15, normalized size = 2.5 \begin{align*} -\cos \left (e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.298982, size = 5, normalized size = 0.83 \begin{align*} - \cos{\left (e^{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16469, size = 7, normalized size = 1.17 \begin{align*} -\cos \left (e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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