Optimal. Leaf size=11 \[ e^x x-e^x \]
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Rubi [A] time = 0.007018, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4, Rules used = {2176, 2194} \[ e^x x-e^x \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^x x \, dx &=e^x x-\int e^x \, dx\\ &=-e^x+e^x x\\ \end{align*}
Mathematica [A] time = 0.0009849, size = 7, normalized size = 0.64 \[ e^x (x-1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 7, normalized size = 0.6 \begin{align*} \left ( -1+x \right ){{\rm e}^{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.928983, size = 8, normalized size = 0.73 \begin{align*}{\left (x - 1\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.93113, size = 18, normalized size = 1.64 \begin{align*}{\left (x - 1\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.073761, size = 5, normalized size = 0.45 \begin{align*} \left (x - 1\right ) e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09205, size = 8, normalized size = 0.73 \begin{align*}{\left (x - 1\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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