Optimal. Leaf size=18 \[ e^x+\frac {1}{6} \left (x+\frac {11 e^2 x}{5}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 5, number of rules used = 4, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.174, Rules used = {6, 12, 14, 2194} \begin {gather*} \frac {1}{30} \left (5+11 e^2\right ) x+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 14
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 e^x x+\left (1+\frac {11 e^2}{5}\right ) x}{6 x} \, dx\\ &=\frac {1}{6} \int \frac {6 e^x x+\left (1+\frac {11 e^2}{5}\right ) x}{x} \, dx\\ &=\frac {1}{6} \int \left (6 e^x+\frac {1}{5} \left (5+11 e^2\right )\right ) \, dx\\ &=\frac {1}{30} \left (5+11 e^2\right ) x+\int e^x \, dx\\ &=e^x+\frac {1}{30} \left (5+11 e^2\right ) x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.94 \begin {gather*} e^x+\frac {x}{6}+\frac {11 e^2 x}{30} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 11, normalized size = 0.61 \begin {gather*} \frac {11}{30} \, x e^{2} + \frac {1}{6} \, x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 12, normalized size = 0.67 \begin {gather*} \frac {1}{30} \, x {\left (11 \, e^{2} + 5\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 12, normalized size = 0.67
method | result | size |
norman | \(\left (\frac {11 \,{\mathrm e}^{2}}{30}+\frac {1}{6}\right ) x +{\mathrm e}^{x}\) | \(12\) |
risch | \(\frac {11 \,{\mathrm e}^{2} x}{30}+\frac {x}{6}+{\mathrm e}^{x}\) | \(12\) |
default | \({\mathrm e}^{x}+\frac {x}{6}-\frac {{\mathrm e}^{\ln \left (-\frac {11 x}{5}\right )+2}}{6}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 11, normalized size = 0.61 \begin {gather*} \frac {11}{30} \, x e^{2} + \frac {1}{6} \, x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.97, size = 11, normalized size = 0.61 \begin {gather*} {\mathrm {e}}^x+x\,\left (\frac {11\,{\mathrm {e}}^2}{30}+\frac {1}{6}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.78 \begin {gather*} x \left (\frac {1}{6} + \frac {11 e^{2}}{30}\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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