Optimal. Leaf size=19 \[ \frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x \cos (x) \]
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Rubi [A] time = 0.0070147, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {4433} \[ \frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x \cos (x) \]
Antiderivative was successfully verified.
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Rule 4433
Rubi steps
\begin{align*} \int e^x \cos (x) \, dx &=\frac{1}{2} e^x \cos (x)+\frac{1}{2} e^x \sin (x)\\ \end{align*}
Mathematica [A] time = 0.0081464, size = 12, normalized size = 0.63 \[ \frac{1}{2} e^x (\sin (x)+\cos (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 14, normalized size = 0.7 \begin{align*}{\frac{{{\rm e}^{x}}\cos \left ( x \right ) }{2}}+{\frac{{{\rm e}^{x}}\sin \left ( x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0471, size = 12, normalized size = 0.63 \begin{align*} \frac{1}{2} \,{\left (\cos \left (x\right ) + \sin \left (x\right )\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.496677, size = 45, normalized size = 2.37 \begin{align*} \frac{1}{2} \, \cos \left (x\right ) e^{x} + \frac{1}{2} \, e^{x} \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.285548, size = 15, normalized size = 0.79 \begin{align*} \frac{e^{x} \sin{\left (x \right )}}{2} + \frac{e^{x} \cos{\left (x \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09889, size = 12, normalized size = 0.63 \begin{align*} \frac{1}{2} \,{\left (\cos \left (x\right ) + \sin \left (x\right )\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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