Integrand size = 95, antiderivative size = 30 \[ \int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx=\frac {5 x^2}{\frac {3}{5 x^2}-(-4+x) \left (1+x-x^2\right ) \log (2)} \]
[Out]
\[ \int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx=\int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {25 \left (204+57 x-1315 x^4 \log (2)+5 x^2 (3+272 \log (2))+5 x^3 (3+280 \log (2))\right )}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2}-\frac {25 \left (68+19 x+5 x^2+x^3\right )}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)}\right ) \, dx \\ & = 25 \int \frac {204+57 x-1315 x^4 \log (2)+5 x^2 (3+272 \log (2))+5 x^3 (3+280 \log (2))}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2} \, dx-25 \int \frac {68+19 x+5 x^2+x^3}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx \\ & = \frac {6575 \log (2)}{\log (32) \left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )}-25 \int \left (\frac {68}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)}+\frac {19 x}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)}+\frac {5 x^2}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)}+\frac {x^3}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)}\right ) \, dx+\frac {5 \int \frac {1020 \log (32)+5 x \left (10520 \log ^2(2)+57 \log (32)\right )-25 x^3 \left (5260 \log ^2(2)-3 \log (32)-280 \log (2) \log (32)\right )+25 x^2 \left (2367 \log ^2(2)+3 \log (32)+272 \log (2) \log (32)\right )}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2} \, dx}{\log (32)} \\ & = \frac {6575 \log (2)}{\log (32) \left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )}-25 \int \frac {x^3}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx-125 \int \frac {x^2}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx-475 \int \frac {x}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx-1700 \int \frac {1}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx+\frac {5 \int \left (\frac {1020 \log (32)}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2}+\frac {5 x \left (10520 \log ^2(2)+57 \log (32)\right )}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2}-\frac {25 x^3 \left (5260 \log ^2(2)-3 \log (32)-280 \log (2) \log (32)\right )}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2}+\frac {25 x^2 \left (2367 \log ^2(2)+3 \log (32)+272 \log (2) \log (32)\right )}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2}\right ) \, dx}{\log (32)} \\ & = \frac {6575 \log (2)}{\log (32) \left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )}-25 \int \frac {x^3}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx-125 \int \frac {x^2}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx-475 \int \frac {x}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx-1700 \int \frac {1}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \, dx+5100 \int \frac {1}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2} \, dx+\left (125 \left (3+280 \log (2)-\frac {5260 \log ^2(2)}{\log (32)}\right )\right ) \int \frac {x^3}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2} \, dx+\left (125 \left (3+272 \log (2)+\frac {2367 \log ^2(2)}{\log (32)}\right )\right ) \int \frac {x^2}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2} \, dx+\left (25 \left (57+\frac {10520 \log ^2(2)}{\log (32)}\right )\right ) \int \frac {x}{\left (3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)\right )^2} \, dx \\ \end{align*}
Time = 0.19 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20 \[ \int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx=\frac {25 x^4}{3+20 x^2 \log (2)+15 x^3 \log (2)-25 x^4 \log (2)+x^5 \log (32)} \]
[In]
[Out]
Time = 0.14 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23
method | result | size |
default | \(\frac {5 x^{4}}{x^{5} \ln \left (2\right )-5 x^{4} \ln \left (2\right )+3 x^{3} \ln \left (2\right )+4 x^{2} \ln \left (2\right )+\frac {3}{5}}\) | \(37\) |
risch | \(\frac {5 x^{4}}{x^{5} \ln \left (2\right )-5 x^{4} \ln \left (2\right )+3 x^{3} \ln \left (2\right )+4 x^{2} \ln \left (2\right )+\frac {3}{5}}\) | \(37\) |
gosper | \(\frac {25 x^{4}}{5 x^{5} \ln \left (2\right )-25 x^{4} \ln \left (2\right )+15 x^{3} \ln \left (2\right )+20 x^{2} \ln \left (2\right )+3}\) | \(38\) |
norman | \(\frac {25 x^{4}}{5 x^{5} \ln \left (2\right )-25 x^{4} \ln \left (2\right )+15 x^{3} \ln \left (2\right )+20 x^{2} \ln \left (2\right )+3}\) | \(38\) |
parallelrisch | \(\frac {25 x^{4}}{5 x^{5} \ln \left (2\right )-25 x^{4} \ln \left (2\right )+15 x^{3} \ln \left (2\right )+20 x^{2} \ln \left (2\right )+3}\) | \(38\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx=\frac {25 \, x^{4}}{5 \, {\left (x^{5} - 5 \, x^{4} + 3 \, x^{3} + 4 \, x^{2}\right )} \log \left (2\right ) + 3} \]
[In]
[Out]
Time = 2.25 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30 \[ \int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx=\frac {25 x^{4}}{5 x^{5} \log {\left (2 \right )} - 25 x^{4} \log {\left (2 \right )} + 15 x^{3} \log {\left (2 \right )} + 20 x^{2} \log {\left (2 \right )} + 3} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23 \[ \int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx=\frac {25 \, x^{4}}{5 \, x^{5} \log \left (2\right ) - 25 \, x^{4} \log \left (2\right ) + 15 \, x^{3} \log \left (2\right ) + 20 \, x^{2} \log \left (2\right ) + 3} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23 \[ \int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx=\frac {25 \, x^{4}}{5 \, x^{5} \log \left (2\right ) - 25 \, x^{4} \log \left (2\right ) + 15 \, x^{3} \log \left (2\right ) + 20 \, x^{2} \log \left (2\right ) + 3} \]
[In]
[Out]
Time = 0.34 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23 \[ \int \frac {300 x^3+\left (1000 x^5+375 x^6-125 x^8\right ) \log (2)}{9+\left (120 x^2+90 x^3-150 x^4+30 x^5\right ) \log (2)+\left (400 x^4+600 x^5-775 x^6-550 x^7+775 x^8-250 x^9+25 x^{10}\right ) \log ^2(2)} \, dx=\frac {25\,x^4}{5\,\ln \left (2\right )\,x^5-25\,\ln \left (2\right )\,x^4+15\,\ln \left (2\right )\,x^3+20\,\ln \left (2\right )\,x^2+3} \]
[In]
[Out]