Integrand size = 93, antiderivative size = 27 \[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx=2+e^{\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}+\log (x) \]
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\[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx=\int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{(-3+x) x \log (3-x)} \, dx \\ & = \int \left (\frac {1}{x}-\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (e^3+x-(-3+x) \log (3-x)\right )}{(-3+x) \log ^2(3-x)}\right ) \, dx \\ & = \log (x)-\int \frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (e^3+x-(-3+x) \log (3-x)\right )}{(-3+x) \log ^2(3-x)} \, dx \\ & = \log (x)-\int \left (\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (e^3+x\right )}{(-3+x) \log ^2(3-x)}-\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}}{\log (3-x)}\right ) \, dx \\ & = \log (x)-\int \frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (e^3+x\right )}{(-3+x) \log ^2(3-x)} \, dx+\int \frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}}{\log (3-x)} \, dx \\ & = \log (x)-\int \left (\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}}{\log ^2(3-x)}+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (3+e^3\right )}{(-3+x) \log ^2(3-x)}\right ) \, dx+\int \frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}}{\log (3-x)} \, dx \\ & = \log (x)-\left (3+e^3\right ) \int \frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}}{(-3+x) \log ^2(3-x)} \, dx-\int \frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}}{\log ^2(3-x)} \, dx+\int \frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}}{\log (3-x)} \, dx \\ \end{align*}
Time = 1.91 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx=e^{\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}}+\log (x) \]
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Time = 23.72 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.81
method | result | size |
default | \(\ln \left (x \right )+{\mathrm e}^{\frac {\left ({\mathrm e}^{3}+x \right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{5}}}}{\ln \left (-x +3\right )}}\) | \(22\) |
norman | \(\ln \left (x \right )+{\mathrm e}^{\frac {\left ({\mathrm e}^{3}+x \right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{5}}}}{\ln \left (-x +3\right )}}\) | \(22\) |
risch | \(\ln \left (x \right )+{\mathrm e}^{\frac {\left ({\mathrm e}^{3}+x \right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{5}}}}{\ln \left (-x +3\right )}}\) | \(22\) |
parts | \(\ln \left (x \right )+{\mathrm e}^{\frac {\left ({\mathrm e}^{3}+x \right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{5}}}}{\ln \left (-x +3\right )}}\) | \(22\) |
parallelrisch | \(\ln \left (x \right )+{\mathrm e}^{\left ({\mathrm e}^{3}+x \right ) {\mathrm e}^{-\ln \left (\ln \left (-x +3\right )\right )+{\mathrm e}^{{\mathrm e}^{5}}}}\) | \(24\) |
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Leaf count of result is larger than twice the leaf count of optimal. 67 vs. \(2 (24) = 48\).
Time = 0.25 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.48 \[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx={\left (e^{\left (e^{\left (e^{5}\right )}\right )} \log \left (x\right ) + e^{\left (\frac {{\left (x + e^{3}\right )} e^{\left (e^{\left (e^{5}\right )}\right )} + e^{\left (e^{5}\right )} \log \left (-x + 3\right ) - \log \left (-x + 3\right ) \log \left (\log \left (-x + 3\right )\right )}{\log \left (-x + 3\right )}\right )} \log \left (-x + 3\right )\right )} e^{\left (-e^{\left (e^{5}\right )}\right )} \]
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Exception generated. \[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx=\text {Exception raised: TypeError} \]
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Exception generated. \[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx=\text {Exception raised: RuntimeError} \]
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\[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx=\int { -\frac {{\left (x^{2} + x e^{3} - {\left (x^{2} - 3 \, x\right )} \log \left (-x + 3\right )\right )} e^{\left ({\left (x + e^{3}\right )} e^{\left (e^{\left (e^{5}\right )} - \log \left (\log \left (-x + 3\right )\right )\right )} + e^{\left (e^{5}\right )} - \log \left (\log \left (-x + 3\right )\right )\right )} - {\left (x - 3\right )} \log \left (-x + 3\right )}{{\left (x^{2} - 3 \, x\right )} \log \left (-x + 3\right )} \,d x } \]
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Time = 13.74 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.30 \[ \int \frac {(-3+x) \log (3-x)+\frac {e^{e^{e^5}+\frac {e^{e^{e^5}} \left (e^3+x\right )}{\log (3-x)}} \left (-e^3 x-x^2+\left (-3 x+x^2\right ) \log (3-x)\right )}{\log (3-x)}}{\left (-3 x+x^2\right ) \log (3-x)} \, dx=\ln \left (x\right )+{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^5}}\,{\mathrm {e}}^3}{\ln \left (3-x\right )}}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^5}}}{\ln \left (3-x\right )}} \]
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