Optimal. Leaf size=4 \[ \sin \left (e^x\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2282, 2637} \[ \sin \left (e^x\right ) \]
Antiderivative was successfully verified.
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Rule 2282
Rule 2637
Rubi steps
\begin {align*} \int e^x \cos \left (e^x\right ) \, dx &=\operatorname {Subst}\left (\int \cos (x) \, dx,x,e^x\right )\\ &=\sin \left (e^x\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 4, normalized size = 1.00 \[ \sin \left (e^x\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 3, normalized size = 0.75 \[ \sin \left (e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 3, normalized size = 0.75 \[ \sin \left (e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 4, normalized size = 1.00 \[ \sin \left ({\mathrm e}^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 3, normalized size = 0.75 \[ \sin \left (e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 3, normalized size = 0.75 \[ \sin \left ({\mathrm {e}}^x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 3, normalized size = 0.75 \[ \sin {\left (e^{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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