Optimal. Leaf size=4 \[ \text{Si}\left (e^x\right ) \]
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Rubi [A] time = 0.0117071, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {2282, 3299} \[ \text{Si}\left (e^x\right ) \]
Antiderivative was successfully verified.
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Rule 2282
Rule 3299
Rubi steps
\begin{align*} \int \sin \left (e^x\right ) \, dx &=\operatorname{Subst}\left (\int \frac{\sin (x)}{x} \, dx,x,e^x\right )\\ &=\text{Si}\left (e^x\right )\\ \end{align*}
Mathematica [A] time = 0.005286, size = 4, normalized size = 1. \[ \text{Si}\left (e^x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 4, normalized size = 1. \begin{align*}{\it Si} \left ({{\rm e}^{x}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] time = 1.06478, size = 20, normalized size = 5. \begin{align*} -\frac{1}{2} i \,{\rm Ei}\left (i \, e^{x}\right ) + \frac{1}{2} i \,{\rm Ei}\left (-i \, e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.9311, size = 26, normalized size = 6.5 \begin{align*} \operatorname{Si}\left (e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.64135, size = 3, normalized size = 0.75 \begin{align*} \operatorname{Si}{\left (e^{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06027, size = 4, normalized size = 1. \begin{align*} \operatorname{Si}\left (e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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