Integrand size = 147, antiderivative size = 30 \[ \int \frac {e^{5 e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)}+5 x^2} \left (2-x-20 x^2+10 x^3+e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)} \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{-2 x^2+x^3} \, dx=\frac {e^{5 \left (e^{\left (3-x+\log ^2(-2+x)\right )^2}+x^2\right )}}{x}+\log (4) \]
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Leaf count is larger than twice the leaf count of optimal. \(223\) vs. \(2(30)=60\).
Time = 10.32 (sec) , antiderivative size = 223, normalized size of antiderivative = 7.43, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {1607, 2326} \[ \int \frac {e^{5 e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)}+5 x^2} \left (2-x-20 x^2+10 x^3+e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)} \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{-2 x^2+x^3} \, dx=\frac {\exp \left (5 \exp \left (x^2-6 x+\log ^4(x-2)+2 (3-x) \log ^2(x-2)+9\right )+5 x^2\right ) \left (-\left (x^3-5 x^2+\left (2 x-x^2\right ) \log ^2(x-2)+2 \left (3 x-x^2\right ) \log (x-2)+6 x+2 x \log ^3(x-2)\right ) \exp \left (x^2-6 x+\log ^4(x-2)+2 (3-x) \log ^2(x-2)+9\right )-x^3+2 x^2\right )}{(2-x) x^2 \left (x-\left (-x+\frac {2 \log ^3(x-2)}{2-x}+\log ^2(x-2)+\frac {2 (3-x) \log (x-2)}{2-x}+3\right ) \exp \left (x^2-6 x+\log ^4(x-2)+2 (3-x) \log ^2(x-2)+9\right )\right )} \]
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Rule 1607
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (5 \exp \left (9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)\right )+5 x^2\right ) \left (2-x-20 x^2+10 x^3+\exp \left (9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)\right ) \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{(-2+x) x^2} \, dx \\ & = \frac {\exp \left (5 \exp \left (9-6 x+x^2+2 (3-x) \log ^2(-2+x)+\log ^4(-2+x)\right )+5 x^2\right ) \left (2 x^2-x^3-\exp \left (9-6 x+x^2+2 (3-x) \log ^2(-2+x)+\log ^4(-2+x)\right ) \left (6 x-5 x^2+x^3+2 \left (3 x-x^2\right ) \log (-2+x)+\left (2 x-x^2\right ) \log ^2(-2+x)+2 x \log ^3(-2+x)\right )\right )}{(2-x) x^2 \left (x-\exp \left (9-6 x+x^2+2 (3-x) \log ^2(-2+x)+\log ^4(-2+x)\right ) \left (3-x+\frac {2 (3-x) \log (-2+x)}{2-x}+\log ^2(-2+x)+\frac {2 \log ^3(-2+x)}{2-x}\right )\right )} \\ \end{align*}
Time = 0.31 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \frac {e^{5 e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)}+5 x^2} \left (2-x-20 x^2+10 x^3+e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)} \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{-2 x^2+x^3} \, dx=\frac {e^{5 \left (e^{\left (3-x+\log ^2(-2+x)\right )^2}+x^2\right )}}{x} \]
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Time = 0.49 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93
method | result | size |
risch | \(\frac {{\mathrm e}^{5 \,{\mathrm e}^{\left (-3-\ln \left (-2+x \right )^{2}+x \right )^{2}}+5 x^{2}}}{x}\) | \(28\) |
parallelrisch | \(\frac {{\mathrm e}^{5 \,{\mathrm e}^{\ln \left (-2+x \right )^{4}+\left (6-2 x \right ) \ln \left (-2+x \right )^{2}+x^{2}-6 x +9}+5 x^{2}}}{x}\) | \(41\) |
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Time = 0.24 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30 \[ \int \frac {e^{5 e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)}+5 x^2} \left (2-x-20 x^2+10 x^3+e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)} \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{-2 x^2+x^3} \, dx=\frac {e^{\left (5 \, x^{2} + 5 \, e^{\left (\log \left (x - 2\right )^{4} - 2 \, {\left (x - 3\right )} \log \left (x - 2\right )^{2} + x^{2} - 6 \, x + 9\right )}\right )}}{x} \]
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Time = 2.30 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23 \[ \int \frac {e^{5 e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)}+5 x^2} \left (2-x-20 x^2+10 x^3+e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)} \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{-2 x^2+x^3} \, dx=\frac {e^{5 x^{2} + 5 e^{x^{2} - 6 x + \left (6 - 2 x\right ) \log {\left (x - 2 \right )}^{2} + \log {\left (x - 2 \right )}^{4} + 9}}}{x} \]
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\[ \int \frac {e^{5 e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)}+5 x^2} \left (2-x-20 x^2+10 x^3+e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)} \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{-2 x^2+x^3} \, dx=\int { \frac {{\left (10 \, x^{3} - 20 \, x^{2} + 10 \, {\left (2 \, x \log \left (x - 2\right )^{3} + x^{3} - {\left (x^{2} - 2 \, x\right )} \log \left (x - 2\right )^{2} - 5 \, x^{2} - 2 \, {\left (x^{2} - 3 \, x\right )} \log \left (x - 2\right ) + 6 \, x\right )} e^{\left (\log \left (x - 2\right )^{4} - 2 \, {\left (x - 3\right )} \log \left (x - 2\right )^{2} + x^{2} - 6 \, x + 9\right )} - x + 2\right )} e^{\left (5 \, x^{2} + 5 \, e^{\left (\log \left (x - 2\right )^{4} - 2 \, {\left (x - 3\right )} \log \left (x - 2\right )^{2} + x^{2} - 6 \, x + 9\right )}\right )}}{x^{3} - 2 \, x^{2}} \,d x } \]
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\[ \int \frac {e^{5 e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)}+5 x^2} \left (2-x-20 x^2+10 x^3+e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)} \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{-2 x^2+x^3} \, dx=\int { \frac {{\left (10 \, x^{3} - 20 \, x^{2} + 10 \, {\left (2 \, x \log \left (x - 2\right )^{3} + x^{3} - {\left (x^{2} - 2 \, x\right )} \log \left (x - 2\right )^{2} - 5 \, x^{2} - 2 \, {\left (x^{2} - 3 \, x\right )} \log \left (x - 2\right ) + 6 \, x\right )} e^{\left (\log \left (x - 2\right )^{4} - 2 \, {\left (x - 3\right )} \log \left (x - 2\right )^{2} + x^{2} - 6 \, x + 9\right )} - x + 2\right )} e^{\left (5 \, x^{2} + 5 \, e^{\left (\log \left (x - 2\right )^{4} - 2 \, {\left (x - 3\right )} \log \left (x - 2\right )^{2} + x^{2} - 6 \, x + 9\right )}\right )}}{x^{3} - 2 \, x^{2}} \,d x } \]
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Time = 7.98 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {e^{5 e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)}+5 x^2} \left (2-x-20 x^2+10 x^3+e^{9-6 x+x^2+(6-2 x) \log ^2(-2+x)+\log ^4(-2+x)} \left (60 x-50 x^2+10 x^3+\left (60 x-20 x^2\right ) \log (-2+x)+\left (20 x-10 x^2\right ) \log ^2(-2+x)+20 x \log ^3(-2+x)\right )\right )}{-2 x^2+x^3} \, dx=\frac {{\mathrm {e}}^{5\,x^2}\,{\mathrm {e}}^{5\,{\mathrm {e}}^{{\ln \left (x-2\right )}^4}\,{\mathrm {e}}^{-6\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^9\,{\mathrm {e}}^{6\,{\ln \left (x-2\right )}^2}\,{\mathrm {e}}^{-2\,x\,{\ln \left (x-2\right )}^2}}}{x} \]
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