Integrand size = 83, antiderivative size = 33 \[ \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{-25 x^3+x^4} \, dx=\frac {e^{6+2 x^2+2 x \left (-e^x-x+\log (25-x)\right )} \log (2)}{x^2} \]
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Leaf count is larger than twice the leaf count of optimal. \(102\) vs. \(2(33)=66\).
Time = 7.80 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.09, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1607, 6873, 12, 2326} \[ \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{-25 x^3+x^4} \, dx=\frac {e^{2 \left (3-e^x x\right )} (25-x)^{2 x-1} \log (2) \left (-e^x x^3+24 e^x x^2+x^2+x^2 \log (25-x)+25 e^x x-25 x \log (25-x)\right )}{x^3 \left (e^x x+\frac {x}{25-x}+e^x-\log (25-x)\right )} \]
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Rule 12
Rule 1607
Rule 2326
Rule 6873
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{(-25+x) x^3} \, dx \\ & = \int \frac {2 e^{-2 \left (-3+e^x x-x \log (25-x)\right )} \log (2) \left (-25+x-25 e^x x-x^2-24 e^x x^2+e^x x^3+25 x \log (25-x)-x^2 \log (25-x)\right )}{(25-x) x^3} \, dx \\ & = (2 \log (2)) \int \frac {e^{-2 \left (-3+e^x x-x \log (25-x)\right )} \left (-25+x-25 e^x x-x^2-24 e^x x^2+e^x x^3+25 x \log (25-x)-x^2 \log (25-x)\right )}{(25-x) x^3} \, dx \\ & = \frac {e^{2 \left (3-e^x x\right )} (25-x)^{-1+2 x} \log (2) \left (25 e^x x+x^2+24 e^x x^2-e^x x^3-25 x \log (25-x)+x^2 \log (25-x)\right )}{x^3 \left (e^x+e^x x+\frac {x}{25-x}-\log (25-x)\right )} \\ \end{align*}
Time = 4.35 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.76 \[ \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{-25 x^3+x^4} \, dx=\frac {e^{6-2 e^x x} (25-x)^{2 x} \log (2)}{x^2} \]
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Time = 3.45 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.73
method | result | size |
risch | \(\frac {\ln \left (2\right ) \left (-x +25\right )^{2 x} {\mathrm e}^{-2 \,{\mathrm e}^{x} x +6}}{x^{2}}\) | \(24\) |
parallelrisch | \(\frac {\ln \left (2\right ) {\mathrm e}^{2 x \ln \left (-x +25\right )-2 \,{\mathrm e}^{x} x +6}}{x^{2}}\) | \(25\) |
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Time = 0.24 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.70 \[ \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{-25 x^3+x^4} \, dx=\frac {e^{\left (-2 \, x e^{x} + 2 \, x \log \left (-x + 25\right ) + 6\right )} \log \left (2\right )}{x^{2}} \]
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Time = 0.19 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.73 \[ \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{-25 x^3+x^4} \, dx=\frac {e^{- 2 x e^{x} + 2 x \log {\left (25 - x \right )} + 6} \log {\left (2 \right )}}{x^{2}} \]
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Time = 0.34 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.70 \[ \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{-25 x^3+x^4} \, dx=\frac {e^{\left (-2 \, x e^{x} + 2 \, x \log \left (-x + 25\right ) + 6\right )} \log \left (2\right )}{x^{2}} \]
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\[ \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{-25 x^3+x^4} \, dx=\int { -\frac {2 \, {\left ({\left (x^{3} - 24 \, x^{2} - 25 \, x\right )} e^{x} \log \left (2\right ) - {\left (x^{2} - 25 \, x\right )} \log \left (2\right ) \log \left (-x + 25\right ) - {\left (x^{2} - x + 25\right )} \log \left (2\right )\right )} e^{\left (-2 \, x e^{x} + 2 \, x \log \left (-x + 25\right ) + 6\right )}}{x^{4} - 25 \, x^{3}} \,d x } \]
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Time = 8.86 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.70 \[ \int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{-25 x^3+x^4} \, dx=\frac {{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^6\,\ln \left (2\right )\,{\left (25-x\right )}^{2\,x}}{x^2} \]
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