Integrand size = 70, antiderivative size = 24 \[ \int \frac {e^{-x^2 \log (3)-\left (x-x^2\right ) \log (3) \log (25)} \left (-3+\left (\left (-6 x-6 x^2\right ) \log (3)+\left (-3+3 x+6 x^2\right ) \log (3) \log (25)\right ) \log (1+x)\right )}{(1+x) \log ^2(1+x)} \, dx=\frac {3^{1-x (x+(1-x) \log (25))}}{\log (1+x)} \]
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Leaf count is larger than twice the leaf count of optimal. \(79\) vs. \(2(24)=48\).
Time = 0.20 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.29, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {2326} \[ \int \frac {e^{-x^2 \log (3)-\left (x-x^2\right ) \log (3) \log (25)} \left (-3+\left (\left (-6 x-6 x^2\right ) \log (3)+\left (-3+3 x+6 x^2\right ) \log (3) \log (25)\right ) \log (1+x)\right )}{(1+x) \log ^2(1+x)} \, dx=\frac {3^{1-x^2} e^{-\left (\left (x-x^2\right ) \log (3) \log (25)\right )} \left (\left (-2 x^2-x+1\right ) \log (3) \log (25)+2 \left (x^2+x\right ) \log (3)\right )}{(x+1) ((1-2 x) \log (3) \log (25)+2 x \log (3)) \log (x+1)} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {3^{1-x^2} e^{-\left (\left (x-x^2\right ) \log (3) \log (25)\right )} \left (2 \left (x+x^2\right ) \log (3)+\left (1-x-2 x^2\right ) \log (3) \log (25)\right )}{(1+x) (2 x \log (3)+(1-2 x) \log (3) \log (25)) \log (1+x)} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(73\) vs. \(2(24)=48\).
Time = 0.11 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.04 \[ \int \frac {e^{-x^2 \log (3)-\left (x-x^2\right ) \log (3) \log (25)} \left (-3+\left (\left (-6 x-6 x^2\right ) \log (3)+\left (-3+3 x+6 x^2\right ) \log (3) \log (25)\right ) \log (1+x)\right )}{(1+x) \log ^2(1+x)} \, dx=\frac {3^{(-1+x) (-1+x (-1+\log (25)))} \left (x^2 \log (9) (-1+\log (25))-\log (3) \log (25)+x (-\log (9)+\log (3) \log (25))\right )}{(1+x) \log (3) (2 x (-1+\log (25))-\log (25)) \log (1+x)} \]
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Time = 0.67 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12
method | result | size |
risch | \(\frac {3 \,9^{x \left (-1+x \right ) \ln \left (5\right )} 3^{-x^{2}}}{\ln \left (1+x \right )}\) | \(27\) |
parallelrisch | \(\frac {3 \,{\mathrm e}^{\ln \left (3\right ) x \left (2 x \ln \left (5\right )+\ln \left (\frac {1}{25}\right )-x \right )}}{\ln \left (1+x \right )}\) | \(30\) |
norman | \(\frac {3 \,{\mathrm e}^{-2 \left (-x^{2}+x \right ) \ln \left (3\right ) \ln \left (5\right )-x^{2} \ln \left (3\right )}}{\ln \left (1+x \right )}\) | \(32\) |
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Time = 0.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.25 \[ \int \frac {e^{-x^2 \log (3)-\left (x-x^2\right ) \log (3) \log (25)} \left (-3+\left (\left (-6 x-6 x^2\right ) \log (3)+\left (-3+3 x+6 x^2\right ) \log (3) \log (25)\right ) \log (1+x)\right )}{(1+x) \log ^2(1+x)} \, dx=\frac {3 \, e^{\left (-x^{2} \log \left (3\right ) + 2 \, {\left (x^{2} - x\right )} \log \left (5\right ) \log \left (3\right )\right )}}{\log \left (x + 1\right )} \]
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Time = 0.15 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \frac {e^{-x^2 \log (3)-\left (x-x^2\right ) \log (3) \log (25)} \left (-3+\left (\left (-6 x-6 x^2\right ) \log (3)+\left (-3+3 x+6 x^2\right ) \log (3) \log (25)\right ) \log (1+x)\right )}{(1+x) \log ^2(1+x)} \, dx=\frac {3 e^{- x^{2} \log {\left (3 \right )} - \left (- 2 x^{2} + 2 x\right ) \log {\left (3 \right )} \log {\left (5 \right )}}}{\log {\left (x + 1 \right )}} \]
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Time = 0.38 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38 \[ \int \frac {e^{-x^2 \log (3)-\left (x-x^2\right ) \log (3) \log (25)} \left (-3+\left (\left (-6 x-6 x^2\right ) \log (3)+\left (-3+3 x+6 x^2\right ) \log (3) \log (25)\right ) \log (1+x)\right )}{(1+x) \log ^2(1+x)} \, dx=\frac {3 \, e^{\left (2 \, x^{2} \log \left (5\right ) \log \left (3\right ) - x^{2} \log \left (3\right ) - 2 \, x \log \left (5\right ) \log \left (3\right )\right )}}{\log \left (x + 1\right )} \]
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Time = 0.32 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38 \[ \int \frac {e^{-x^2 \log (3)-\left (x-x^2\right ) \log (3) \log (25)} \left (-3+\left (\left (-6 x-6 x^2\right ) \log (3)+\left (-3+3 x+6 x^2\right ) \log (3) \log (25)\right ) \log (1+x)\right )}{(1+x) \log ^2(1+x)} \, dx=\frac {3 \, e^{\left (2 \, x^{2} \log \left (5\right ) \log \left (3\right ) - x^{2} \log \left (3\right ) - 2 \, x \log \left (5\right ) \log \left (3\right )\right )}}{\log \left (x + 1\right )} \]
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Time = 12.98 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38 \[ \int \frac {e^{-x^2 \log (3)-\left (x-x^2\right ) \log (3) \log (25)} \left (-3+\left (\left (-6 x-6 x^2\right ) \log (3)+\left (-3+3 x+6 x^2\right ) \log (3) \log (25)\right ) \log (1+x)\right )}{(1+x) \log ^2(1+x)} \, dx=\frac {3\,3^{2\,x^2\,\ln \left (5\right )}}{3^{x^2}\,3^{2\,x\,\ln \left (5\right )}\,\ln \left (x+1\right )} \]
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