Integrand size = 202, antiderivative size = 36 \[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx=e^{-\frac {5 x}{4 \left (1+\frac {2+x}{5}\right ) \left (x+\frac {\log (5)}{4 (-2+x)}\right )}} \log (x) \]
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Leaf count is larger than twice the leaf count of optimal. \(222\) vs. \(2(36)=72\).
Time = 0.39 (sec) , antiderivative size = 222, normalized size of antiderivative = 6.17, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {2326} \[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx=\frac {\left (4 x^5-16 x^4+16 x^3+\left (-x^3-14 x^2+14 x\right ) \log (5)\right ) \log (x) \exp \left (-\frac {25 \left (2 x-x^2\right )}{-4 x^3-20 x^2+56 x-(x+7) \log (5)}\right )}{\left (16 x^7+160 x^6-48 x^5-2240 x^4+3136 x^3+\left (x^3+14 x^2+49 x\right ) \log ^2(5)-8 \left (-x^5-12 x^4-21 x^3+98 x^2\right ) \log (5)\right ) \left (\frac {\left (2 x-x^2\right ) \left (-12 x^2-40 x+56-\log (5)\right )}{\left (-4 x^3-20 x^2+56 x-(x+7) \log (5)\right )^2}-\frac {2 (1-x)}{-4 x^3-20 x^2+56 x-(x+7) \log (5)}\right )} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {\exp \left (-\frac {25 \left (2 x-x^2\right )}{56 x-20 x^2-4 x^3-(7+x) \log (5)}\right ) \left (16 x^3-16 x^4+4 x^5+\left (14 x-14 x^2-x^3\right ) \log (5)\right ) \log (x)}{\left (3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7-8 \left (98 x^2-21 x^3-12 x^4-x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)\right ) \left (\frac {\left (2 x-x^2\right ) \left (56-40 x-12 x^2-\log (5)\right )}{\left (56 x-20 x^2-4 x^3-(7+x) \log (5)\right )^2}-\frac {2 (1-x)}{56 x-20 x^2-4 x^3-(7+x) \log (5)}\right )} \\ \end{align*}
Time = 0.11 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.22 \[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx=5^{-\frac {25 (-9+x)}{(252+\log (5)) \left (-8 x+4 x^2+\log (5)\right )}} e^{-\frac {1575}{(7+x) (252+\log (5))}} \log (x) \]
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Time = 35.93 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.81
method | result | size |
risch | \({\mathrm e}^{-\frac {25 \left (-2+x \right ) x}{\left (x +7\right ) \left (4 x^{2}+\ln \left (5\right )-8 x \right )}} \ln \left (x \right )\) | \(29\) |
parallelrisch | \(\frac {\left (-134456 \ln \left (5\right )^{4} x \ln \left (x \right )+9604 \ln \left (5\right )^{4} x^{3} \ln \left (x \right )+2401 \ln \left (5\right )^{5} x \ln \left (x \right )+48020 \ln \left (5\right )^{4} \ln \left (x \right ) x^{2}+16807 \ln \left (5\right )^{5} \ln \left (x \right )\right ) {\mathrm e}^{-\frac {25 x^{2}-50 x}{x \ln \left (5\right )+\ln \left (78125\right )+4 x^{3}+20 x^{2}-56 x}}}{2401 \left (4 x^{3}+x \ln \left (5\right )+20 x^{2}+7 \ln \left (5\right )-56 x \right ) \ln \left (5\right )^{4}}\) | \(117\) |
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Time = 0.25 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.97 \[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx=e^{\left (-\frac {25 \, {\left (x^{2} - 2 \, x\right )}}{4 \, x^{3} + 20 \, x^{2} + {\left (x + 7\right )} \log \left (5\right ) - 56 \, x}\right )} \log \left (x\right ) \]
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Timed out. \[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx=\text {Timed out} \]
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Leaf count of result is larger than twice the leaf count of optimal. 84 vs. \(2 (26) = 52\).
Time = 0.58 (sec) , antiderivative size = 84, normalized size of antiderivative = 2.33 \[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx=e^{\left (-\frac {25 \, x \log \left (5\right )}{4 \, x^{2} {\left (\log \left (5\right ) + 252\right )} - 8 \, x {\left (\log \left (5\right ) + 252\right )} + \log \left (5\right )^{2} + 252 \, \log \left (5\right )} + \frac {225 \, \log \left (5\right )}{4 \, x^{2} {\left (\log \left (5\right ) + 252\right )} - 8 \, x {\left (\log \left (5\right ) + 252\right )} + \log \left (5\right )^{2} + 252 \, \log \left (5\right )} - \frac {1575}{x {\left (\log \left (5\right ) + 252\right )} + 7 \, \log \left (5\right ) + 1764}\right )} \log \left (x\right ) \]
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Time = 0.56 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.03 \[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx=e^{\left (-\frac {25 \, {\left (x^{2} - 2 \, x\right )}}{4 \, x^{3} + 20 \, x^{2} + x \log \left (5\right ) - 56 \, x + 7 \, \log \left (5\right )}\right )} \log \left (x\right ) \]
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Timed out. \[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx=\int \frac {{\mathrm {e}}^{\frac {50\,x-25\,x^2}{\ln \left (5\right )\,\left (x+7\right )-56\,x+20\,x^2+4\,x^3}}\,\left ({\ln \left (5\right )}^2\,\left (x^2+14\,x+49\right )+\ln \left (5\right )\,\left (8\,x^4+96\,x^3+168\,x^2-784\,x\right )-\ln \left (x\right )\,\left (\ln \left (5\right )\,\left (25\,x^3+350\,x^2-350\,x\right )-400\,x^3+400\,x^4-100\,x^5\right )+3136\,x^2-2240\,x^3-48\,x^4+160\,x^5+16\,x^6\right )}{\ln \left (5\right )\,\left (8\,x^5+96\,x^4+168\,x^3-784\,x^2\right )+{\ln \left (5\right )}^2\,\left (x^3+14\,x^2+49\,x\right )+3136\,x^3-2240\,x^4-48\,x^5+160\,x^6+16\,x^7} \,d x \]
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