Optimal. Leaf size=16 \[ e^x-\frac{x^{1+e}}{1+e} \]
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Rubi [A] time = 0.004769, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {2194} \[ e^x-\frac{x^{1+e}}{1+e} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin{align*} \int \left (e^x-x^e\right ) \, dx &=-\frac{x^{1+e}}{1+e}+\int e^x \, dx\\ &=e^x-\frac{x^{1+e}}{1+e}\\ \end{align*}
Mathematica [A] time = 0.0053215, size = 16, normalized size = 1. \[ e^x-\frac{x^{1+e}}{1+e} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.036, size = 16, normalized size = 1. \begin{align*}{{\rm e}^{x}}-{\frac{{x}^{1+E}}{1+E}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.86158, size = 43, normalized size = 2.69 \begin{align*} -\frac{x x^{E} -{\left (E + 1\right )} e^{x}}{E + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.080443, size = 10, normalized size = 0.62 \begin{align*} - \frac{x^{1 + e}}{1 + e} + e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16478, size = 20, normalized size = 1.25 \begin{align*} -\frac{x^{E + 1}}{E + 1} + e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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