Integrand size = 113, antiderivative size = 25 \[ \int \frac {-125+x+4000 x^2-32000 e^4 x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx=x-5 \left (5+80 x \left (e^2-x-x^2\right )\right )^2 \log (x) \]
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Leaf count is larger than twice the leaf count of optimal. \(84\) vs. \(2(25)=50\).
Time = 0.12 (sec) , antiderivative size = 84, normalized size of antiderivative = 3.36, number of steps used = 13, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {6, 14, 2403, 2332, 2341} \[ \int \frac {-125+x+4000 x^2-32000 e^4 x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx=-32000 x^6 \log (x)-64000 x^5 \log (x)-32000 \left (1-2 e^2\right ) x^4 \log (x)+4000 \left (1+16 e^2\right ) x^3 \log (x)+4000 \left (1-8 e^4\right ) x^2 \log (x)+\left (1-4000 e^2\right ) x+4000 e^2 x-4000 e^2 x \log (x)-125 \log (x) \]
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Rule 6
Rule 14
Rule 2332
Rule 2341
Rule 2403
Rubi steps \begin{align*} \text {integral}& = \int \frac {-125+x+\left (4000-32000 e^4\right ) x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx \\ & = \int \left (\frac {-125+\left (1-4000 e^2\right ) x+4000 \left (1-8 e^4\right ) x^2+4000 \left (1+16 e^2\right ) x^3-32000 \left (1-2 e^2\right ) x^4-64000 x^5-32000 x^6}{x}-4000 \left (e^2-2 x-3 x^2\right ) \left (1+16 e^2 x-16 x^2-16 x^3\right ) \log (x)\right ) \, dx \\ & = -\left (4000 \int \left (e^2-2 x-3 x^2\right ) \left (1+16 e^2 x-16 x^2-16 x^3\right ) \log (x) \, dx\right )+\int \frac {-125+\left (1-4000 e^2\right ) x+4000 \left (1-8 e^4\right ) x^2+4000 \left (1+16 e^2\right ) x^3-32000 \left (1-2 e^2\right ) x^4-64000 x^5-32000 x^6}{x} \, dx \\ & = -\left (4000 \int \left (e^2 \log (x)+2 \left (-1+8 e^4\right ) x \log (x)-3 \left (1+16 e^2\right ) x^2 \log (x)-32 \left (-1+2 e^2\right ) x^3 \log (x)+80 x^4 \log (x)+48 x^5 \log (x)\right ) \, dx\right )+\int \left (1-4000 e^2-\frac {125}{x}+4000 \left (1-8 e^4\right ) x+4000 \left (1+16 e^2\right ) x^2-32000 \left (1-2 e^2\right ) x^3-64000 x^4-32000 x^5\right ) \, dx \\ & = \left (1-4000 e^2\right ) x+2000 \left (1-8 e^4\right ) x^2+\frac {4000}{3} \left (1+16 e^2\right ) x^3-8000 \left (1-2 e^2\right ) x^4-12800 x^5-\frac {16000 x^6}{3}-125 \log (x)-192000 \int x^5 \log (x) \, dx-320000 \int x^4 \log (x) \, dx-\left (4000 e^2\right ) \int \log (x) \, dx-\left (128000 \left (1-2 e^2\right )\right ) \int x^3 \log (x) \, dx+\left (12000 \left (1+16 e^2\right )\right ) \int x^2 \log (x) \, dx+\left (8000 \left (1-8 e^4\right )\right ) \int x \log (x) \, dx \\ & = 4000 e^2 x+\left (1-4000 e^2\right ) x-125 \log (x)-4000 e^2 x \log (x)+4000 \left (1-8 e^4\right ) x^2 \log (x)+4000 \left (1+16 e^2\right ) x^3 \log (x)-32000 \left (1-2 e^2\right ) x^4 \log (x)-64000 x^5 \log (x)-32000 x^6 \log (x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(79\) vs. \(2(25)=50\).
Time = 0.05 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.16 \[ \int \frac {-125+x+4000 x^2-32000 e^4 x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx=x-125 \log (x)-4000 e^2 x \log (x)+4000 x^2 \log (x)-32000 e^4 x^2 \log (x)+4000 x^3 \log (x)+64000 e^2 x^3 \log (x)-32000 x^4 \log (x)+64000 e^2 x^4 \log (x)-64000 x^5 \log (x)-32000 x^6 \log (x) \]
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Time = 0.10 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04
method | result | size |
risch | \(-125 \left (-16 x^{3}+16 \,{\mathrm e}^{2} x -16 x^{2}+1\right )^{2} \ln \left (x \right )+x\) | \(26\) |
norman | \(x -125 \ln \left (x \right )+\left (-32000 \,{\mathrm e}^{4}+4000\right ) x^{2} \ln \left (x \right )+\left (64000 \,{\mathrm e}^{2}-32000\right ) x^{4} \ln \left (x \right )+\left (64000 \,{\mathrm e}^{2}+4000\right ) x^{3} \ln \left (x \right )-64000 x^{5} \ln \left (x \right )-32000 x^{6} \ln \left (x \right )-4000 x \,{\mathrm e}^{2} \ln \left (x \right )\) | \(66\) |
parallelrisch | \(-32000 x^{6} \ln \left (x \right )+64000 \,{\mathrm e}^{2} \ln \left (x \right ) x^{4}-64000 x^{5} \ln \left (x \right )-32000 x^{2} {\mathrm e}^{4} \ln \left (x \right )+64000 x^{3} {\mathrm e}^{2} \ln \left (x \right )-32000 x^{4} \ln \left (x \right )+4000 x^{3} \ln \left (x \right )-4000 x \,{\mathrm e}^{2} \ln \left (x \right )+4000 x^{2} \ln \left (x \right )-125 \ln \left (x \right )+x\) | \(78\) |
parts | \(x -32000 x^{6} \ln \left (x \right )-4000 \,{\mathrm e}^{2} \left (x \ln \left (x \right )-x \right )-64000 x^{5} \ln \left (x \right )-16000 x^{2} {\mathrm e}^{4}+\frac {64000 x^{3} {\mathrm e}^{2}}{3}-32000 x^{4} \ln \left (x \right )+16000 x^{4} {\mathrm e}^{2}-125 \ln \left (x \right )+4000 x^{3} \ln \left (x \right )+4000 x^{2} \ln \left (x \right )-4000 \,{\mathrm e}^{2} x -64000 \,{\mathrm e}^{4} \left (\frac {x^{2} \ln \left (x \right )}{2}-\frac {x^{2}}{4}\right )+192000 \,{\mathrm e}^{2} \left (\frac {x^{3} \ln \left (x \right )}{3}-\frac {x^{3}}{9}\right )+256000 \,{\mathrm e}^{2} \left (\frac {x^{4} \ln \left (x \right )}{4}-\frac {x^{4}}{16}\right )\) | \(133\) |
default | \(x -32000 x^{6} \ln \left (x \right )-4000 \,{\mathrm e}^{2} \left (x \ln \left (x \right )-x \right )-64000 x^{5} \ln \left (x \right )-16000 x^{2} {\mathrm e}^{4}+\frac {64000 x^{3} {\mathrm e}^{2}}{3}-32000 x^{4} \ln \left (x \right )+16000 x^{4} {\mathrm e}^{2}-125 \ln \left (x \right )+4000 x^{3} \ln \left (x \right )+4000 x^{2} \ln \left (x \right )-4000 \,{\mathrm e}^{2} x -64000 \,{\mathrm e}^{4} \left (\frac {x^{2} \ln \left (x \right )}{2}-\frac {x^{2}}{4}\right )+192000 \,{\mathrm e}^{2} \left (\frac {x^{3} \ln \left (x \right )}{3}-\frac {x^{3}}{9}\right )+256000 \,{\mathrm e}^{2} \left (\frac {x^{4} \ln \left (x \right )}{4}-\frac {x^{4}}{16}\right )\) | \(135\) |
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (22) = 44\).
Time = 0.26 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \[ \int \frac {-125+x+4000 x^2-32000 e^4 x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx=-125 \, {\left (256 \, x^{6} + 512 \, x^{5} + 256 \, x^{4} - 32 \, x^{3} + 256 \, x^{2} e^{4} - 32 \, x^{2} - 32 \, {\left (16 \, x^{4} + 16 \, x^{3} - x\right )} e^{2} + 1\right )} \log \left (x\right ) + x \]
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Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (26) = 52\).
Time = 0.11 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.64 \[ \int \frac {-125+x+4000 x^2-32000 e^4 x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx=x + \left (- 32000 x^{6} - 64000 x^{5} - 32000 x^{4} + 64000 x^{4} e^{2} + 4000 x^{3} + 64000 x^{3} e^{2} - 32000 x^{2} e^{4} + 4000 x^{2} - 4000 x e^{2}\right ) \log {\left (x \right )} - 125 \log {\left (x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 130 vs. \(2 (22) = 44\).
Time = 0.19 (sec) , antiderivative size = 130, normalized size of antiderivative = 5.20 \[ \int \frac {-125+x+4000 x^2-32000 e^4 x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx=-32000 \, x^{6} \log \left (x\right ) - 64000 \, x^{5} \log \left (x\right ) + 16000 \, x^{4} e^{2} - 32000 \, x^{4} \log \left (x\right ) + \frac {64000}{3} \, x^{3} e^{2} + 4000 \, x^{3} \log \left (x\right ) - 16000 \, x^{2} e^{4} + 4000 \, x^{2} \log \left (x\right ) - 16000 \, {\left (2 \, x^{2} \log \left (x\right ) - x^{2}\right )} e^{4} + 16000 \, {\left (4 \, x^{4} \log \left (x\right ) - x^{4}\right )} e^{2} + \frac {64000}{3} \, {\left (3 \, x^{3} \log \left (x\right ) - x^{3}\right )} e^{2} - 4000 \, {\left (x \log \left (x\right ) - x\right )} e^{2} - 4000 \, x e^{2} + x - 125 \, \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (22) = 44\).
Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.00 \[ \int \frac {-125+x+4000 x^2-32000 e^4 x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx=-32000 \, x^{6} \log \left (x\right ) - 64000 \, x^{5} \log \left (x\right ) + 64000 \, x^{4} e^{2} \log \left (x\right ) - 32000 \, x^{4} \log \left (x\right ) + 64000 \, x^{3} e^{2} \log \left (x\right ) + 4000 \, x^{3} \log \left (x\right ) - 32000 \, x^{2} e^{4} \log \left (x\right ) + 4000 \, x^{2} \log \left (x\right ) - 4000 \, x e^{2} \log \left (x\right ) + x - 125 \, \log \left (x\right ) \]
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Time = 8.62 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.68 \[ \int \frac {-125+x+4000 x^2-32000 e^4 x^2+4000 x^3-32000 x^4-64000 x^5-32000 x^6+e^2 \left (-4000 x+64000 x^3+64000 x^4\right )+\left (8000 x^2-64000 e^4 x^2+12000 x^3-128000 x^4-320000 x^5-192000 x^6+e^2 \left (-4000 x+192000 x^3+256000 x^4\right )\right ) \log (x)}{x} \, dx=x^3\,\ln \left (x\right )\,\left (64000\,{\mathrm {e}}^2+4000\right )-64000\,x^5\,\ln \left (x\right )-32000\,x^6\,\ln \left (x\right )-x\,\left (4000\,{\mathrm {e}}^2\,\ln \left (x\right )-1\right )-x^2\,\ln \left (x\right )\,\left (32000\,{\mathrm {e}}^4-4000\right )-125\,\ln \left (x\right )+x^4\,\ln \left (x\right )\,\left (64000\,{\mathrm {e}}^2-32000\right ) \]
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