Integrand size = 110, antiderivative size = 23 \[ \int \frac {1953125 x^3-1953125 x^4+781250 x^5-156250 x^6+15625 x^7-625 x^8+e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8} \, dx=-4+e^{\frac {\log ^4(3)}{625 (-5+x)^4 x^2}}-x \]
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Leaf count is larger than twice the leaf count of optimal. \(76\) vs. \(2(23)=46\).
Time = 1.05 (sec) , antiderivative size = 76, normalized size of antiderivative = 3.30, number of steps used = 14, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {6873, 12, 6874, 45, 37, 6838} \[ \int \frac {1953125 x^3-1953125 x^4+781250 x^5-156250 x^6+15625 x^7-625 x^8+e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8} \, dx=\frac {25 x^4}{2 (5-x)^4}+e^{\frac {\log ^4(3)}{625 (5-x)^4 x^2}}-x+\frac {250}{5-x}-\frac {1875}{(5-x)^2}+\frac {6250}{(5-x)^3}-\frac {15625}{2 (5-x)^4} \]
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Rule 12
Rule 37
Rule 45
Rule 6838
Rule 6873
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8-e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{625 (5-x)^5 x^3} \, dx \\ & = \frac {1}{625} \int \frac {-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8-e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{(5-x)^5 x^3} \, dx \\ & = \frac {1}{625} \int \left (\frac {1953125}{(-5+x)^5}-\frac {1953125 x}{(-5+x)^5}+\frac {781250 x^2}{(-5+x)^5}-\frac {156250 x^3}{(-5+x)^5}+\frac {15625 x^4}{(-5+x)^5}-\frac {625 x^5}{(-5+x)^5}-\frac {2 e^{\frac {\log ^4(3)}{625 (-5+x)^4 x^2}} (-5+3 x) \log ^4(3)}{(-5+x)^5 x^3}\right ) \, dx \\ & = -\frac {3125}{4 (5-x)^4}+25 \int \frac {x^4}{(-5+x)^5} \, dx-250 \int \frac {x^3}{(-5+x)^5} \, dx+1250 \int \frac {x^2}{(-5+x)^5} \, dx-3125 \int \frac {x}{(-5+x)^5} \, dx-\frac {1}{625} \left (2 \log ^4(3)\right ) \int \frac {e^{\frac {\log ^4(3)}{625 (-5+x)^4 x^2}} (-5+3 x)}{(-5+x)^5 x^3} \, dx-\int \frac {x^5}{(-5+x)^5} \, dx \\ & = e^{\frac {\log ^4(3)}{625 (5-x)^4 x^2}}-\frac {3125}{4 (5-x)^4}+\frac {25 x^4}{2 (5-x)^4}+25 \int \left (\frac {625}{(-5+x)^5}+\frac {500}{(-5+x)^4}+\frac {150}{(-5+x)^3}+\frac {20}{(-5+x)^2}+\frac {1}{-5+x}\right ) \, dx+1250 \int \left (\frac {25}{(-5+x)^5}+\frac {10}{(-5+x)^4}+\frac {1}{(-5+x)^3}\right ) \, dx-3125 \int \left (\frac {5}{(-5+x)^5}+\frac {1}{(-5+x)^4}\right ) \, dx-\int \left (1+\frac {3125}{(-5+x)^5}+\frac {3125}{(-5+x)^4}+\frac {1250}{(-5+x)^3}+\frac {250}{(-5+x)^2}+\frac {25}{-5+x}\right ) \, dx \\ & = e^{\frac {\log ^4(3)}{625 (5-x)^4 x^2}}-\frac {15625}{2 (5-x)^4}+\frac {6250}{(5-x)^3}-\frac {1875}{(5-x)^2}+\frac {250}{5-x}-x+\frac {25 x^4}{2 (5-x)^4} \\ \end{align*}
Time = 0.17 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {1953125 x^3-1953125 x^4+781250 x^5-156250 x^6+15625 x^7-625 x^8+e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8} \, dx=e^{\frac {\log ^4(3)}{625 (-5+x)^4 x^2}}-x \]
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Time = 1.13 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87
method | result | size |
risch | \(-x +{\mathrm e}^{\frac {\ln \left (3\right )^{4}}{625 x^{2} \left (-5+x \right )^{4}}}\) | \(20\) |
parallelrisch | \(-x +{\mathrm e}^{\frac {\ln \left (3\right )^{4}}{625 x^{2} \left (x^{4}-20 x^{3}+150 x^{2}-500 x +625\right )}}-50\) | \(36\) |
parts | \(-x +\frac {x^{6} {\mathrm e}^{\frac {\ln \left (3\right )^{4}}{625 x^{6}-12500 x^{5}+93750 x^{4}-312500 x^{3}+390625 x^{2}}}+625 x^{2} {\mathrm e}^{\frac {\ln \left (3\right )^{4}}{625 x^{6}-12500 x^{5}+93750 x^{4}-312500 x^{3}+390625 x^{2}}}-500 x^{3} {\mathrm e}^{\frac {\ln \left (3\right )^{4}}{625 x^{6}-12500 x^{5}+93750 x^{4}-312500 x^{3}+390625 x^{2}}}+150 x^{4} {\mathrm e}^{\frac {\ln \left (3\right )^{4}}{625 x^{6}-12500 x^{5}+93750 x^{4}-312500 x^{3}+390625 x^{2}}}-20 x^{5} {\mathrm e}^{\frac {\ln \left (3\right )^{4}}{625 x^{6}-12500 x^{5}+93750 x^{4}-312500 x^{3}+390625 x^{2}}}}{x^{2} \left (-5+x \right )^{4}}\) | \(209\) |
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Time = 0.26 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.61 \[ \int \frac {1953125 x^3-1953125 x^4+781250 x^5-156250 x^6+15625 x^7-625 x^8+e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8} \, dx=-x + e^{\left (\frac {\log \left (3\right )^{4}}{625 \, {\left (x^{6} - 20 \, x^{5} + 150 \, x^{4} - 500 \, x^{3} + 625 \, x^{2}\right )}}\right )} \]
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Time = 0.27 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39 \[ \int \frac {1953125 x^3-1953125 x^4+781250 x^5-156250 x^6+15625 x^7-625 x^8+e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8} \, dx=- x + e^{\frac {\log {\left (3 \right )}^{4}}{625 x^{6} - 12500 x^{5} + 93750 x^{4} - 312500 x^{3} + 390625 x^{2}}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 290 vs. \(2 (20) = 40\).
Time = 0.44 (sec) , antiderivative size = 290, normalized size of antiderivative = 12.61 \[ \int \frac {1953125 x^3-1953125 x^4+781250 x^5-156250 x^6+15625 x^7-625 x^8+e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8} \, dx=-x - \frac {125 \, {\left (48 \, x^{3} - 540 \, x^{2} + 2200 \, x - 3125\right )}}{12 \, {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )}} + \frac {125 \, {\left (24 \, x^{3} - 300 \, x^{2} + 1300 \, x - 1925\right )}}{12 \, {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )}} + \frac {125 \, {\left (4 \, x^{3} - 30 \, x^{2} + 100 \, x - 125\right )}}{2 \, {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )}} - \frac {625 \, {\left (6 \, x^{2} - 20 \, x + 25\right )}}{6 \, {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )}} + \frac {3125 \, {\left (4 \, x - 5\right )}}{12 \, {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )}} - \frac {3125}{4 \, {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )}} + e^{\left (\frac {\log \left (3\right )^{4}}{15625 \, {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )}} - \frac {2 \, \log \left (3\right )^{4}}{78125 \, {\left (x^{3} - 15 \, x^{2} + 75 \, x - 125\right )}} + \frac {3 \, \log \left (3\right )^{4}}{390625 \, {\left (x^{2} - 10 \, x + 25\right )}} - \frac {4 \, \log \left (3\right )^{4}}{1953125 \, {\left (x - 5\right )}} + \frac {4 \, \log \left (3\right )^{4}}{1953125 \, x} + \frac {\log \left (3\right )^{4}}{390625 \, x^{2}}\right )} \]
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Time = 0.31 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.61 \[ \int \frac {1953125 x^3-1953125 x^4+781250 x^5-156250 x^6+15625 x^7-625 x^8+e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8} \, dx=-x + e^{\left (\frac {\log \left (3\right )^{4}}{625 \, {\left (x^{6} - 20 \, x^{5} + 150 \, x^{4} - 500 \, x^{3} + 625 \, x^{2}\right )}}\right )} \]
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Time = 14.78 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.65 \[ \int \frac {1953125 x^3-1953125 x^4+781250 x^5-156250 x^6+15625 x^7-625 x^8+e^{\frac {\log ^4(3)}{390625 x^2-312500 x^3+93750 x^4-12500 x^5+625 x^6}} (10-6 x) \log ^4(3)}{-1953125 x^3+1953125 x^4-781250 x^5+156250 x^6-15625 x^7+625 x^8} \, dx={\mathrm {e}}^{\frac {{\ln \left (3\right )}^4}{625\,x^6-12500\,x^5+93750\,x^4-312500\,x^3+390625\,x^2}}-x \]
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