Optimal. Leaf size=25 \[ \frac {1}{4} \left (5-\frac {256 x}{9 \left (-3+e^{\frac {2 (7+x)}{x}}\right )}\right ) \]
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Rubi [A] time = 0.29, antiderivative size = 20, normalized size of antiderivative = 0.80, number of steps used = 3, number of rules used = 3, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {6741, 12, 6687} \begin {gather*} \frac {64 x}{9 \left (3-e^{\frac {14}{x}+2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6687
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {2 (7+x)}{x}} (-896-64 x)+192 x}{9 \left (3-e^{2+\frac {14}{x}}\right )^2 x} \, dx\\ &=\frac {1}{9} \int \frac {e^{\frac {2 (7+x)}{x}} (-896-64 x)+192 x}{\left (3-e^{2+\frac {14}{x}}\right )^2 x} \, dx\\ &=\frac {64 x}{9 \left (3-e^{2+\frac {14}{x}}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 18, normalized size = 0.72 \begin {gather*} -\frac {64 x}{9 \left (-3+e^{2+\frac {14}{x}}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 16, normalized size = 0.64 \begin {gather*} -\frac {64 \, x}{9 \, {\left (e^{\left (\frac {2 \, {\left (x + 7\right )}}{x}\right )} - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 22, normalized size = 0.88 \begin {gather*} -\frac {64}{9 \, {\left (\frac {e^{\left (\frac {14}{x} + 2\right )}}{x} - \frac {3}{x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 17, normalized size = 0.68
method | result | size |
risch | \(-\frac {64 x}{9 \left ({\mathrm e}^{\frac {14+2 x}{x}}-3\right )}\) | \(17\) |
norman | \(-\frac {64 x}{9 \left ({\mathrm e}^{\frac {14+2 x}{x}}-3\right )}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 15, normalized size = 0.60 \begin {gather*} -\frac {64 \, x}{9 \, {\left (e^{\left (\frac {14}{x} + 2\right )} - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.84, size = 17, normalized size = 0.68 \begin {gather*} -\frac {64\,x}{9\,\left ({\mathrm {e}}^{\frac {14}{x}+2}-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 0.60 \begin {gather*} - \frac {64 x}{9 e^{\frac {2 \left (x + 7\right )}{x}} - 27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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