Integrand size = 66, antiderivative size = 27 \[ \int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx=3^{4 x^2 (15+\log (x))} \left (\frac {1}{x}\right )^{-1+4 x^2 (15+\log (x))} \]
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Leaf count is larger than twice the leaf count of optimal. \(97\) vs. \(2(27)=54\).
Time = 0.25 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.59, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {2326} \[ \int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx=\frac {3^{60 x^2} \left (\frac {1}{x}\right )^{60 x^2} e^{4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (15 x^2-31 x^2 \log \left (\frac {3}{x}\right )+\left (x^2-2 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right )}{15 x-31 x \log \left (\frac {3}{x}\right )-2 x \log \left (\frac {3}{x}\right ) \log (x)+x \log (x)} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {3^{60 x^2} e^{4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (\frac {1}{x}\right )^{60 x^2} \left (15 x^2-31 x^2 \log \left (\frac {3}{x}\right )+\left (x^2-2 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right )}{15 x-31 x \log \left (\frac {3}{x}\right )+x \log (x)-2 x \log \left (\frac {3}{x}\right ) \log (x)} \\ \end{align*}
\[ \int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx=\int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx \]
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Time = 0.35 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.70
method | result | size |
parallelrisch | \(x \,{\mathrm e}^{4 \left (\ln \left (x \right )+15\right ) x^{2} \ln \left (\frac {3}{x}\right )}\) | \(19\) |
default | \({\mathrm e}^{4 x^{2} \ln \left (\frac {3}{x}\right ) \ln \left (x \right )+60 x^{2} \ln \left (\frac {3}{x}\right )} x\) | \(29\) |
risch | \(x^{-4 x^{2} \left (\ln \left (x \right )-\ln \left (3\right )\right )} {\mathrm e}^{60 x^{2} \left (-\ln \left (x \right )+\ln \left (3\right )\right )} x\) | \(30\) |
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Leaf count of result is larger than twice the leaf count of optimal. 37 vs. \(2 (17) = 34\).
Time = 0.24 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx=x e^{\left (-4 \, x^{2} \log \left (\frac {3}{x}\right )^{2} + 4 \, {\left (x^{2} \log \left (3\right ) + 15 \, x^{2}\right )} \log \left (\frac {3}{x}\right )\right )} \]
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Time = 0.21 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx=x e^{4 x^{2} \left (- \log {\left (x \right )} + \log {\left (3 \right )}\right ) \log {\left (x \right )} + 60 x^{2} \left (- \log {\left (x \right )} + \log {\left (3 \right )}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 36 vs. \(2 (17) = 34\).
Time = 0.35 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx=x e^{\left (4 \, x^{2} \log \left (3\right ) \log \left (x\right ) - 4 \, x^{2} \log \left (x\right )^{2} + 60 \, x^{2} \log \left (3\right ) - 60 \, x^{2} \log \left (x\right )\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 36 vs. \(2 (17) = 34\).
Time = 0.34 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx=x e^{\left (4 \, x^{2} \log \left (3\right ) \log \left (x\right ) - 4 \, x^{2} \log \left (x\right )^{2} + 60 \, x^{2} \log \left (3\right ) - 60 \, x^{2} \log \left (x\right )\right )} \]
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Time = 15.87 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.41 \[ \int e^{60 x^2 \log \left (\frac {3}{x}\right )+4 x^2 \log \left (\frac {3}{x}\right ) \log (x)} \left (1-60 x^2+124 x^2 \log \left (\frac {3}{x}\right )+\left (-4 x^2+8 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx=3^{60\,x^2}\,x\,x^{4\,x^2\,\ln \left (\frac {1}{x}\right )}\,x^{4\,x^2\,\ln \left (3\right )}\,{\left (\frac {1}{x}\right )}^{60\,x^2} \]
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