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 = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 0.63 \[ \frac {1}{2} e^x (\sin (x)+\cos (x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 13, normalized size = 0.68 \[ \frac {1}{2} \, \cos \relax (x) e^{x} + \frac {1}{2} \, e^{x} \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 9, normalized size = 0.47 \[ \frac {1}{2} \, {\left (\cos \relax (x) + \sin \relax (x)\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 0.74 \[ \frac {\cos \relax (x ) {\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{x} \sin \relax (x )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 9, normalized size = 0.47 \[ \frac {1}{2} \, {\left (\cos \relax (x) + \sin \relax (x)\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 9, normalized size = 0.47 \[ \frac {{\mathrm {e}}^x\,\left (\cos \relax (x)+\sin \relax (x)\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 15, normalized size = 0.79 \[ \frac {e^{x} \sin {\relax (x )}}{2} + \frac {e^{x} \cos {\relax (x )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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