Optimal. Leaf size=22 \[ 7+x+\left (\frac {4}{3} \left (-4+e^{\frac {1}{x}}\right )-x\right ) x+\log (5) \]
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Rubi [A]
time = 0.03, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps
used = 4, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 14, 2326}
\begin {gather*} -x^2+\frac {4}{3} e^{\frac {1}{x}} x-\frac {13 x}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {-13 x-6 x^2+e^{\frac {1}{x}} (-4+4 x)}{x} \, dx\\ &=\frac {1}{3} \int \left (-13+\frac {4 e^{\frac {1}{x}} (-1+x)}{x}-6 x\right ) \, dx\\ &=-\frac {13 x}{3}-x^2+\frac {4}{3} \int \frac {e^{\frac {1}{x}} (-1+x)}{x} \, dx\\ &=-\frac {13 x}{3}+\frac {4}{3} e^{\frac {1}{x}} x-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 0.95 \begin {gather*} \frac {1}{3} \left (-13 x+4 e^{\frac {1}{x}} x-3 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.10, size = 17, normalized size = 0.77
method | result | size |
derivativedivides | \(-x^{2}-\frac {13 x}{3}+\frac {4 x \,{\mathrm e}^{\frac {1}{x}}}{3}\) | \(17\) |
default | \(-x^{2}-\frac {13 x}{3}+\frac {4 x \,{\mathrm e}^{\frac {1}{x}}}{3}\) | \(17\) |
norman | \(-x^{2}-\frac {13 x}{3}+\frac {4 x \,{\mathrm e}^{\frac {1}{x}}}{3}\) | \(17\) |
risch | \(-x^{2}-\frac {13 x}{3}+\frac {4 x \,{\mathrm e}^{\frac {1}{x}}}{3}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.29, size = 24, normalized size = 1.09 \begin {gather*} -x^{2} - \frac {13}{3} \, x + \frac {4}{3} \, {\rm Ei}\left (\frac {1}{x}\right ) - \frac {4}{3} \, \Gamma \left (-1, -\frac {1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 16, normalized size = 0.73 \begin {gather*} -x^{2} + \frac {4}{3} \, x e^{\frac {1}{x}} - \frac {13}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 17, normalized size = 0.77 \begin {gather*} - x^{2} + \frac {4 x e^{\frac {1}{x}}}{3} - \frac {13 x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 21, normalized size = 0.95 \begin {gather*} \frac {1}{3} \, x^{2} {\left (\frac {4 \, e^{\frac {1}{x}}}{x} - \frac {13}{x} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.06, size = 14, normalized size = 0.64 \begin {gather*} -\frac {x\,\left (3\,x-4\,{\mathrm {e}}^{1/x}+13\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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