Integrand size = 125, antiderivative size = 28 \[ \int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx=\frac {x}{-4-x+\frac {\left (2 x+\frac {x}{6+x}\right )^2}{x}+\log (x)} \]
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\[ \int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx=\int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(6+x) \left (-1080-540 x-64 x^2-x^3+(6+x)^3 \log (x)\right )}{\left (144-85 x-36 x^2-3 x^3-(6+x)^2 \log (x)\right )^2} \, dx \\ & = \int \left (\frac {-1296-5652 x-3096 x^2-695 x^3-73 x^4-3 x^5}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2}+\frac {(6+x)^2}{-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)}\right ) \, dx \\ & = \int \frac {-1296-5652 x-3096 x^2-695 x^3-73 x^4-3 x^5}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2} \, dx+\int \frac {(6+x)^2}{-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)} \, dx \\ & = \int \left (-\frac {1296}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2}-\frac {5652 x}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2}-\frac {3096 x^2}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2}-\frac {695 x^3}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2}-\frac {73 x^4}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2}-\frac {3 x^5}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2}\right ) \, dx+\int \left (\frac {36}{-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)}+\frac {12 x}{-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)}+\frac {x^2}{-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)}\right ) \, dx \\ & = -\left (3 \int \frac {x^5}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2} \, dx\right )+12 \int \frac {x}{-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)} \, dx+36 \int \frac {1}{-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)} \, dx-73 \int \frac {x^4}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2} \, dx-695 \int \frac {x^3}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2} \, dx-1296 \int \frac {1}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2} \, dx-3096 \int \frac {x^2}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2} \, dx-5652 \int \frac {x}{\left (-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)\right )^2} \, dx+\int \frac {x^2}{-144+85 x+36 x^2+3 x^3+36 \log (x)+12 x \log (x)+x^2 \log (x)} \, dx \\ \end{align*}
Time = 0.53 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.14 \[ \int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx=\frac {x (6+x)^2}{-144+85 x+36 x^2+3 x^3+(6+x)^2 \log (x)} \]
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Time = 1.16 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.43
method | result | size |
risch | \(\frac {\left (6+x \right )^{2} x}{x^{2} \ln \left (x \right )+3 x^{3}+12 x \ln \left (x \right )+36 x^{2}+36 \ln \left (x \right )+85 x -144}\) | \(40\) |
default | \(\frac {x^{3}+12 x^{2}+36 x}{x^{2} \ln \left (x \right )+3 x^{3}+12 x \ln \left (x \right )+36 x^{2}+36 \ln \left (x \right )+85 x -144}\) | \(46\) |
parallelrisch | \(\frac {x^{3}+12 x^{2}+36 x}{x^{2} \ln \left (x \right )+3 x^{3}+12 x \ln \left (x \right )+36 x^{2}+36 \ln \left (x \right )+85 x -144}\) | \(46\) |
norman | \(\frac {-12 \ln \left (x \right )+\frac {23 x}{3}-4 x \ln \left (x \right )-\frac {x^{2} \ln \left (x \right )}{3}+48}{x^{2} \ln \left (x \right )+3 x^{3}+12 x \ln \left (x \right )+36 x^{2}+36 \ln \left (x \right )+85 x -144}\) | \(55\) |
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Time = 0.25 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.46 \[ \int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx=\frac {x^{3} + 12 \, x^{2} + 36 \, x}{3 \, x^{3} + 36 \, x^{2} + {\left (x^{2} + 12 \, x + 36\right )} \log \left (x\right ) + 85 \, x - 144} \]
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Time = 0.21 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32 \[ \int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx=\frac {x^{3} + 12 x^{2} + 36 x}{3 x^{3} + 36 x^{2} + 85 x + \left (x^{2} + 12 x + 36\right ) \log {\left (x \right )} - 144} \]
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Time = 0.22 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.46 \[ \int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx=\frac {x^{3} + 12 \, x^{2} + 36 \, x}{3 \, x^{3} + 36 \, x^{2} + {\left (x^{2} + 12 \, x + 36\right )} \log \left (x\right ) + 85 \, x - 144} \]
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Time = 0.28 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.61 \[ \int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx=\frac {x^{3} + 12 \, x^{2} + 36 \, x}{3 \, x^{3} + x^{2} \log \left (x\right ) + 36 \, x^{2} + 12 \, x \log \left (x\right ) + 85 \, x + 36 \, \log \left (x\right ) - 144} \]
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Timed out. \[ \int \frac {-6480-4320 x-924 x^2-70 x^3-x^4+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log (x)}{20736-24480 x-3143 x^2+5256 x^3+1806 x^4+216 x^5+9 x^6+\left (-10368+2664 x+4344 x^2+1250 x^3+144 x^4+6 x^5\right ) \log (x)+\left (1296+864 x+216 x^2+24 x^3+x^4\right ) \log ^2(x)} \, dx=\int -\frac {4320\,x-\ln \left (x\right )\,\left (x^4+24\,x^3+216\,x^2+864\,x+1296\right )+924\,x^2+70\,x^3+x^4+6480}{{\ln \left (x\right )}^2\,\left (x^4+24\,x^3+216\,x^2+864\,x+1296\right )-24480\,x+\ln \left (x\right )\,\left (6\,x^5+144\,x^4+1250\,x^3+4344\,x^2+2664\,x-10368\right )-3143\,x^2+5256\,x^3+1806\,x^4+216\,x^5+9\,x^6+20736} \,d x \]
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