Optimal. Leaf size=10 \[ \frac{1}{2} \sin \left (e^{2 x}\right ) \]
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Rubi [A] time = 0.0106718, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {2282, 2637} \[ \frac{1}{2} \sin \left (e^{2 x}\right ) \]
Antiderivative was successfully verified.
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Rule 2282
Rule 2637
Rubi steps
\begin{align*} \int e^{2 x} \cos \left (e^{2 x}\right ) \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \cos (x) \, dx,x,e^{2 x}\right )\\ &=\frac{1}{2} \sin \left (e^{2 x}\right )\\ \end{align*}
Mathematica [A] time = 0.0102269, size = 10, normalized size = 1. \[ \frac{1}{2} \sin \left (e^{2 x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 8, normalized size = 0.8 \begin{align*}{\frac{\sin \left ({{\rm e}^{2\,x}} \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00125, size = 9, normalized size = 0.9 \begin{align*} \frac{1}{2} \, \sin \left (e^{\left (2 \, x\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.457448, size = 24, normalized size = 2.4 \begin{align*} \frac{1}{2} \, \sin \left (e^{\left (2 \, x\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.502239, size = 7, normalized size = 0.7 \begin{align*} \frac{\sin{\left (e^{2 x} \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11665, size = 9, normalized size = 0.9 \begin{align*} \frac{1}{2} \, \sin \left (e^{\left (2 \, x\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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