Optimal. Leaf size=8 \[ e^x-\cos (x) \]
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Rubi [A] time = 0.00333, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {2194, 2638} \[ e^x-\cos (x) \]
Antiderivative was successfully verified.
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Rule 2194
Rule 2638
Rubi steps
\begin{align*} \int \left (e^x+\sin (x)\right ) \, dx &=\int e^x \, dx+\int \sin (x) \, dx\\ &=e^x-\cos (x)\\ \end{align*}
Mathematica [A] time = 0.0028654, size = 8, normalized size = 1. \[ e^x-\cos (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 8, normalized size = 1. \begin{align*}{{\rm e}^{x}}-\cos \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.945783, size = 9, normalized size = 1.12 \begin{align*} -\cos \left (x\right ) + e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.82012, size = 20, normalized size = 2.5 \begin{align*} -\cos \left (x\right ) + e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.071743, size = 5, normalized size = 0.62 \begin{align*} e^{x} - \cos{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06968, size = 9, normalized size = 1.12 \begin{align*} -\cos \left (x\right ) + e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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