Optimal. Leaf size=28 \[ \frac {4}{5} \left (\frac {e^{-16+\frac {\log ^2(-2+x)}{x}}}{x^2}-x^2\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(90\) vs. \(2(28)=56\).
time = 0.71, antiderivative size = 90, normalized size of antiderivative = 3.21, number of steps
used = 4, number of rules used = 3, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1607, 6874,
2326} \begin {gather*} \frac {4 e^{\frac {\log ^2(x-2)}{x}-16} \left (-x \log ^2(x-2)+2 \log ^2(x-2)+2 x \log (x-2)\right )}{5 (2-x) x^4 \left (\frac {\log ^2(x-2)}{x^2}+\frac {2 \log (x-2)}{(2-x) x}\right )}-\frac {4 x^2}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 2326
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16 x^5-8 x^6+e^{\frac {-16 x+\log ^2(-2+x)}{x}} \left (16 x-8 x^2+8 x \log (-2+x)+(8-4 x) \log ^2(-2+x)\right )}{x^4 (-10+5 x)} \, dx\\ &=\int \left (-\frac {8 x}{5}-\frac {4 e^{-16+\frac {\log ^2(-2+x)}{x}} \left (-4 x+2 x^2-2 x \log (-2+x)-2 \log ^2(-2+x)+x \log ^2(-2+x)\right )}{5 (-2+x) x^4}\right ) \, dx\\ &=-\frac {4 x^2}{5}-\frac {4}{5} \int \frac {e^{-16+\frac {\log ^2(-2+x)}{x}} \left (-4 x+2 x^2-2 x \log (-2+x)-2 \log ^2(-2+x)+x \log ^2(-2+x)\right )}{(-2+x) x^4} \, dx\\ &=-\frac {4 x^2}{5}+\frac {4 e^{-16+\frac {\log ^2(-2+x)}{x}} \left (2 x \log (-2+x)+2 \log ^2(-2+x)-x \log ^2(-2+x)\right )}{5 (2-x) x^4 \left (\frac {2 \log (-2+x)}{(2-x) x}+\frac {\log ^2(-2+x)}{x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.14, size = 29, normalized size = 1.04 \begin {gather*} \frac {1}{5} \left (\frac {4 e^{-16+\frac {\log ^2(-2+x)}{x}}}{x^2}-4 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 27, normalized size = 0.96
method | result | size |
risch | \(-\frac {4 x^{2}}{5}+\frac {4 \,{\mathrm e}^{\frac {\ln \left (x -2\right )^{2}-16 x}{x}}}{5 x^{2}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.88, size = 24, normalized size = 0.86 \begin {gather*} -\frac {4}{5} \, x^{2} + \frac {4 \, e^{\left (\frac {\log \left (x - 2\right )^{2}}{x} - 16\right )}}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 26, normalized size = 0.93 \begin {gather*} -\frac {4 \, {\left (x^{4} - e^{\left (\frac {\log \left (x - 2\right )^{2} - 16 \, x}{x}\right )}\right )}}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 26, normalized size = 0.93 \begin {gather*} - \frac {4 x^{2}}{5} + \frac {4 e^{\frac {- 16 x + \log {\left (x - 2 \right )}^{2}}{x}}}{5 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 26, normalized size = 0.93 \begin {gather*} -\frac {4 \, {\left (x^{4} - e^{\left (\frac {\log \left (x - 2\right )^{2} - 16 \, x}{x}\right )}\right )}}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.59, size = 24, normalized size = 0.86 \begin {gather*} \frac {4\,{\mathrm {e}}^{\frac {{\ln \left (x-2\right )}^2}{x}}\,{\mathrm {e}}^{-16}}{5\,x^2}-\frac {4\,x^2}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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