Integrand size = 126, antiderivative size = 29 \[ \int \frac {4-10 x+\left (5600-12400 x+7150 x^2-1600 x^3+125 x^4\right ) \log (3)+\left (-750+800 x-150 x^2\right ) \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)}{4 x-5 x^2+\left (6400 x-6400 x^2+2400 x^3-400 x^4+25 x^5\right ) \log (3)+\left (-800 x+400 x^2-50 x^3\right ) \log (3) \log (4 x)+25 x \log (3) \log ^2(4 x)} \, dx=\log \left (x \left (4-5 \left (x-5 \log (3) \left (-(4-x)^2+\log (4 x)\right )^2\right )\right )\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(81\) vs. \(2(29)=58\).
Time = 0.51 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.79, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6874, 6816} \[ \int \frac {4-10 x+\left (5600-12400 x+7150 x^2-1600 x^3+125 x^4\right ) \log (3)+\left (-750+800 x-150 x^2\right ) \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)}{4 x-5 x^2+\left (6400 x-6400 x^2+2400 x^3-400 x^4+25 x^5\right ) \log (3)+\left (-800 x+400 x^2-50 x^3\right ) \log (3) \log (4 x)+25 x \log (3) \log ^2(4 x)} \, dx=\log \left (25 x^4 \log (3)-400 x^3 \log (3)-50 x^2 \log (3) \log (4 x)+2400 x^2 \log (3)+25 \log (3) \log ^2(4 x)+400 x \log (3) \log (4 x)-5 x (1+1280 \log (3))-800 \log (3) \log (4 x)+4 (1+1600 \log (3))\right )+\log (x) \]
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Rule 6816
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{x}+\frac {5 \left (-160 \log (3)+950 x^2 \log (3)-240 x^3 \log (3)+20 x^4 \log (3)-x (1+1200 \log (3))+10 \log (3) \log (4 x)+80 x \log (3) \log (4 x)-20 x^2 \log (3) \log (4 x)\right )}{x \left (2400 x^2 \log (3)-400 x^3 \log (3)+25 x^4 \log (3)-5 x (1+1280 \log (3))+4 (1+1600 \log (3))-800 \log (3) \log (4 x)+400 x \log (3) \log (4 x)-50 x^2 \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)\right )}\right ) \, dx \\ & = \log (x)+5 \int \frac {-160 \log (3)+950 x^2 \log (3)-240 x^3 \log (3)+20 x^4 \log (3)-x (1+1200 \log (3))+10 \log (3) \log (4 x)+80 x \log (3) \log (4 x)-20 x^2 \log (3) \log (4 x)}{x \left (2400 x^2 \log (3)-400 x^3 \log (3)+25 x^4 \log (3)-5 x (1+1280 \log (3))+4 (1+1600 \log (3))-800 \log (3) \log (4 x)+400 x \log (3) \log (4 x)-50 x^2 \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)\right )} \, dx \\ & = \log (x)+\log \left (2400 x^2 \log (3)-400 x^3 \log (3)+25 x^4 \log (3)-5 x (1+1280 \log (3))+4 (1+1600 \log (3))-800 \log (3) \log (4 x)+400 x \log (3) \log (4 x)-50 x^2 \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(29)=58\).
Time = 0.07 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.66 \[ \int \frac {4-10 x+\left (5600-12400 x+7150 x^2-1600 x^3+125 x^4\right ) \log (3)+\left (-750+800 x-150 x^2\right ) \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)}{4 x-5 x^2+\left (6400 x-6400 x^2+2400 x^3-400 x^4+25 x^5\right ) \log (3)+\left (-800 x+400 x^2-50 x^3\right ) \log (3) \log (4 x)+25 x \log (3) \log ^2(4 x)} \, dx=\log (x)+\log \left (4-5 x+6400 \log (3)-6400 x \log (3)+2400 x^2 \log (3)-400 x^3 \log (3)+25 x^4 \log (3)-800 \log (3) \log (4 x)+400 x \log (3) \log (4 x)-50 x^2 \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(28)=56\).
Time = 0.95 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.34
method | result | size |
risch | \(\ln \left (x \right )+\ln \left (\ln \left (4 x \right )^{2}+\left (-2 x^{2}+16 x -32\right ) \ln \left (4 x \right )+\frac {25 x^{4} \ln \left (3\right )-400 x^{3} \ln \left (3\right )+2400 x^{2} \ln \left (3\right )-6400 x \ln \left (3\right )+6400 \ln \left (3\right )-5 x +4}{25 \ln \left (3\right )}\right )\) | \(68\) |
derivativedivides | \(\ln \left (4 x \right )+\ln \left (6400 x^{4} \ln \left (3\right )-12800 \ln \left (3\right ) \ln \left (4 x \right ) x^{2}-102400 x^{3} \ln \left (3\right )+6400 \ln \left (3\right ) \ln \left (4 x \right )^{2}+102400 \ln \left (3\right ) \ln \left (4 x \right ) x +614400 x^{2} \ln \left (3\right )-204800 \ln \left (3\right ) \ln \left (4 x \right )-1638400 x \ln \left (3\right )+1638400 \ln \left (3\right )-1280 x +1024\right )\) | \(80\) |
default | \(\ln \left (4 x \right )+\ln \left (6400 x^{4} \ln \left (3\right )-12800 \ln \left (3\right ) \ln \left (4 x \right ) x^{2}-102400 x^{3} \ln \left (3\right )+6400 \ln \left (3\right ) \ln \left (4 x \right )^{2}+102400 \ln \left (3\right ) \ln \left (4 x \right ) x +614400 x^{2} \ln \left (3\right )-204800 \ln \left (3\right ) \ln \left (4 x \right )-1638400 x \ln \left (3\right )+1638400 \ln \left (3\right )-1280 x +1024\right )\) | \(80\) |
norman | \(\ln \left (4 x \right )+\ln \left (25 x^{4} \ln \left (3\right )-50 \ln \left (3\right ) \ln \left (4 x \right ) x^{2}-400 x^{3} \ln \left (3\right )+25 \ln \left (3\right ) \ln \left (4 x \right )^{2}+400 \ln \left (3\right ) \ln \left (4 x \right ) x +2400 x^{2} \ln \left (3\right )-800 \ln \left (3\right ) \ln \left (4 x \right )-6400 x \ln \left (3\right )+6400 \ln \left (3\right )-5 x +4\right )\) | \(80\) |
parallelrisch | \(\ln \left (\frac {25 x^{4} \ln \left (3\right )-50 \ln \left (3\right ) \ln \left (4 x \right ) x^{2}-400 x^{3} \ln \left (3\right )+25 \ln \left (3\right ) \ln \left (4 x \right )^{2}+400 \ln \left (3\right ) \ln \left (4 x \right ) x +2400 x^{2} \ln \left (3\right )-800 \ln \left (3\right ) \ln \left (4 x \right )-6400 x \ln \left (3\right )+6400 \ln \left (3\right )-5 x +4}{25 \ln \left (3\right )}\right )+\ln \left (4 x \right )\) | \(86\) |
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Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (26) = 52\).
Time = 0.25 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.03 \[ \int \frac {4-10 x+\left (5600-12400 x+7150 x^2-1600 x^3+125 x^4\right ) \log (3)+\left (-750+800 x-150 x^2\right ) \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)}{4 x-5 x^2+\left (6400 x-6400 x^2+2400 x^3-400 x^4+25 x^5\right ) \log (3)+\left (-800 x+400 x^2-50 x^3\right ) \log (3) \log (4 x)+25 x \log (3) \log ^2(4 x)} \, dx=\log \left (-50 \, {\left (x^{2} - 8 \, x + 16\right )} \log \left (3\right ) \log \left (4 \, x\right ) + 25 \, \log \left (3\right ) \log \left (4 \, x\right )^{2} + 25 \, {\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} - 256 \, x + 256\right )} \log \left (3\right ) - 5 \, x + 4\right ) + \log \left (4 \, x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (24) = 48\).
Time = 0.28 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.52 \[ \int \frac {4-10 x+\left (5600-12400 x+7150 x^2-1600 x^3+125 x^4\right ) \log (3)+\left (-750+800 x-150 x^2\right ) \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)}{4 x-5 x^2+\left (6400 x-6400 x^2+2400 x^3-400 x^4+25 x^5\right ) \log (3)+\left (-800 x+400 x^2-50 x^3\right ) \log (3) \log (4 x)+25 x \log (3) \log ^2(4 x)} \, dx=\log {\left (x \right )} + \log {\left (\left (- 2 x^{2} + 16 x - 32\right ) \log {\left (4 x \right )} + \frac {25 x^{4} \log {\left (3 \right )} - 400 x^{3} \log {\left (3 \right )} + 2400 x^{2} \log {\left (3 \right )} - 6400 x \log {\left (3 \right )} - 5 x + 4 + 6400 \log {\left (3 \right )}}{25 \log {\left (3 \right )}} + \log {\left (4 x \right )}^{2} \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (26) = 52\).
Time = 0.30 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.72 \[ \int \frac {4-10 x+\left (5600-12400 x+7150 x^2-1600 x^3+125 x^4\right ) \log (3)+\left (-750+800 x-150 x^2\right ) \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)}{4 x-5 x^2+\left (6400 x-6400 x^2+2400 x^3-400 x^4+25 x^5\right ) \log (3)+\left (-800 x+400 x^2-50 x^3\right ) \log (3) \log (4 x)+25 x \log (3) \log ^2(4 x)} \, dx=\log \left (x\right ) + \log \left (\frac {25 \, x^{4} \log \left (3\right ) - 400 \, x^{3} \log \left (3\right ) - 100 \, {\left (\log \left (3\right ) \log \left (2\right ) - 24 \, \log \left (3\right )\right )} x^{2} + 100 \, \log \left (3\right ) \log \left (2\right )^{2} + 25 \, \log \left (3\right ) \log \left (x\right )^{2} + 5 \, {\left (160 \, \log \left (3\right ) \log \left (2\right ) - 1280 \, \log \left (3\right ) - 1\right )} x - 1600 \, \log \left (3\right ) \log \left (2\right ) - 50 \, {\left (x^{2} \log \left (3\right ) - 8 \, x \log \left (3\right ) - 2 \, \log \left (3\right ) \log \left (2\right ) + 16 \, \log \left (3\right )\right )} \log \left (x\right ) + 6400 \, \log \left (3\right ) + 4}{25 \, \log \left (3\right )}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (26) = 52\).
Time = 0.28 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.66 \[ \int \frac {4-10 x+\left (5600-12400 x+7150 x^2-1600 x^3+125 x^4\right ) \log (3)+\left (-750+800 x-150 x^2\right ) \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)}{4 x-5 x^2+\left (6400 x-6400 x^2+2400 x^3-400 x^4+25 x^5\right ) \log (3)+\left (-800 x+400 x^2-50 x^3\right ) \log (3) \log (4 x)+25 x \log (3) \log ^2(4 x)} \, dx=\log \left (-25 \, x^{4} \log \left (3\right ) + 400 \, x^{3} \log \left (3\right ) + 50 \, x^{2} \log \left (3\right ) \log \left (4 \, x\right ) - 2400 \, x^{2} \log \left (3\right ) - 400 \, x \log \left (3\right ) \log \left (4 \, x\right ) - 25 \, \log \left (3\right ) \log \left (4 \, x\right )^{2} + 6400 \, x \log \left (3\right ) + 800 \, \log \left (3\right ) \log \left (4 \, x\right ) + 5 \, x - 6400 \, \log \left (3\right ) - 4\right ) + \log \left (x\right ) \]
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Timed out. \[ \int \frac {4-10 x+\left (5600-12400 x+7150 x^2-1600 x^3+125 x^4\right ) \log (3)+\left (-750+800 x-150 x^2\right ) \log (3) \log (4 x)+25 \log (3) \log ^2(4 x)}{4 x-5 x^2+\left (6400 x-6400 x^2+2400 x^3-400 x^4+25 x^5\right ) \log (3)+\left (-800 x+400 x^2-50 x^3\right ) \log (3) \log (4 x)+25 x \log (3) \log ^2(4 x)} \, dx=\int \frac {25\,\ln \left (3\right )\,{\ln \left (4\,x\right )}^2-\ln \left (3\right )\,\left (150\,x^2-800\,x+750\right )\,\ln \left (4\,x\right )-10\,x+\ln \left (3\right )\,\left (125\,x^4-1600\,x^3+7150\,x^2-12400\,x+5600\right )+4}{4\,x-5\,x^2+\ln \left (3\right )\,\left (25\,x^5-400\,x^4+2400\,x^3-6400\,x^2+6400\,x\right )-\ln \left (4\,x\right )\,\ln \left (3\right )\,\left (50\,x^3-400\,x^2+800\,x\right )+25\,x\,{\ln \left (4\,x\right )}^2\,\ln \left (3\right )} \,d x \]
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