Optimal. Leaf size=10 \[ e^{\frac {1}{2} \sin (2 x)} \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, 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 = {4356, 2194} \[ e^{\frac {1}{2} \sin (2 x)} \]
Antiderivative was successfully verified.
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Rule 2194
Rule 4356
Rubi steps
\begin {align*} \int e^{\cos (x) \sin (x)} \cos (2 x) \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int e^{x/2} \, dx,x,\sin (2 x)\right )\\ &=e^{\frac {1}{2} \sin (2 x)}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 7, normalized size = 0.70 \[ e^{\sin (x) \cos (x)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 6, normalized size = 0.60 \[ e^{\left (\cos \relax (x) \sin \relax (x)\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 12, normalized size = 1.20 \[ e^{\left (\frac {\tan \relax (x)}{\tan \relax (x)^{2} + 1}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 7, normalized size = 0.70 \[ {\mathrm e}^{\cos \relax (x ) \sin \relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.95, size = 7, normalized size = 0.70 \[ e^{\left (\frac {1}{2} \, \sin \left (2 \, x\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.99, size = 7, normalized size = 0.70 \[ {\mathrm {e}}^{\frac {\sin \left (2\,x\right )}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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