Integrand size = 48, antiderivative size = 21 \[ \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx=x-\frac {e^{x^2}}{(3-\log (6)) \log (x)} \]
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\[ \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx=\int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{x (-3+\log (6)) \log ^2(x)} \, dx \\ & = \frac {\int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{x \log ^2(x)} \, dx}{-3+\log (6)} \\ & = \frac {\int \left (-3+\log (6)-\frac {e^{x^2}}{x \log ^2(x)}+\frac {2 e^{x^2} x}{\log (x)}\right ) \, dx}{-3+\log (6)} \\ & = x-\frac {2 \int \frac {e^{x^2} x}{\log (x)} \, dx}{3-\log (6)}-\frac {\int \frac {e^{x^2}}{x \log ^2(x)} \, dx}{-3+\log (6)} \\ \end{align*}
Time = 0.16 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86 \[ \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx=x+\frac {e^{x^2}}{(-3+\log (6)) \log (x)} \]
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Time = 0.18 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86
method | result | size |
default | \(x +\frac {{\mathrm e}^{x^{2}}}{\left (\ln \left (6\right )-3\right ) \ln \left (x \right )}\) | \(18\) |
parts | \(x +\frac {{\mathrm e}^{x^{2}}}{\left (\ln \left (6\right )-3\right ) \ln \left (x \right )}\) | \(18\) |
risch | \(x +\frac {{\mathrm e}^{x^{2}}}{\left (\ln \left (2\right )+\ln \left (3\right )-3\right ) \ln \left (x \right )}\) | \(20\) |
norman | \(\frac {x \ln \left (x \right )+\frac {{\mathrm e}^{x^{2}}}{\ln \left (6\right )-3}}{\ln \left (x \right )}\) | \(22\) |
parallelrisch | \(\frac {x \ln \left (x \right ) \ln \left (6\right )-3 x \ln \left (x \right )+{\mathrm e}^{x^{2}}}{\left (\ln \left (6\right )-3\right ) \ln \left (x \right )}\) | \(28\) |
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Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.29 \[ \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx=\frac {{\left (x \log \left (6\right ) - 3 \, x\right )} \log \left (x\right ) + e^{\left (x^{2}\right )}}{{\left (\log \left (6\right ) - 3\right )} \log \left (x\right )} \]
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Time = 0.08 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx=x + \frac {e^{x^{2}}}{- 3 \log {\left (x \right )} + \log {\left (6 \right )} \log {\left (x \right )}} \]
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Time = 0.34 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33 \[ \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx=\frac {x {\left (\log \left (3\right ) + \log \left (2\right ) - 3\right )} \log \left (x\right ) + e^{\left (x^{2}\right )}}{{\left (\log \left (3\right ) + \log \left (2\right ) - 3\right )} \log \left (x\right )} \]
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Time = 0.26 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.38 \[ \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx=\frac {x \log \left (6\right ) \log \left (x\right ) - 3 \, x \log \left (x\right ) + e^{\left (x^{2}\right )}}{\log \left (6\right ) \log \left (x\right ) - 3 \, \log \left (x\right )} \]
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Time = 9.43 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {-e^{x^2}+2 e^{x^2} x^2 \log (x)+(-3 x+x \log (6)) \log ^2(x)}{(-3 x+x \log (6)) \log ^2(x)} \, dx=x+\frac {{\mathrm {e}}^{x^2}}{\ln \left (x\right )\,\left (\ln \left (6\right )-3\right )} \]
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