Integrand size = 177, antiderivative size = 23 \[ \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx=\frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x} \]
[Out]
\[ \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx=\int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{x^2 \left (-4-x+x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx \\ & = \int \frac {-8+2 x-6 x^2-\left (4+x-x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right ) \log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2 \left (4+x-x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx \\ & = \int \left (\frac {2 \left (4-x+3 x^2\right )}{x^2 \left (-4-x+x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}-\frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2}\right ) \, dx \\ & = 2 \int \frac {4-x+3 x^2}{x^2 \left (-4-x+x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx-\int \frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2} \, dx \\ & = 2 \int \left (-\frac {1}{x^2 \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}+\frac {1}{2 x \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}+\frac {9-x}{2 \left (-4-x+x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}\right ) \, dx-\int \frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2} \, dx \\ & = -\left (2 \int \frac {1}{x^2 \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx\right )+\int \frac {1}{x \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx+\int \frac {9-x}{\left (-4-x+x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx-\int \frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2} \, dx \\ & = -\left (2 \int \frac {1}{x^2 \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx\right )+\int \left (\frac {9}{\left (-4-x+x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}-\frac {x}{\left (-4-x+x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}\right ) \, dx+\int \frac {1}{x \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx-\int \frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2} \, dx \\ & = -\left (2 \int \frac {1}{x^2 \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx\right )+9 \int \frac {1}{\left (-4-x+x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx+\int \frac {1}{x \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx-\int \frac {x}{\left (-4-x+x^2\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx-\int \frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2} \, dx \\ & = -\left (2 \int \frac {1}{x^2 \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx\right )+9 \int \left (-\frac {2}{\sqrt {17} \left (1+\sqrt {17}-2 x\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}-\frac {2}{\sqrt {17} \left (-1+\sqrt {17}+2 x\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}\right ) \, dx-\int \left (\frac {1+\frac {1}{\sqrt {17}}}{\left (-1-\sqrt {17}+2 x\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}+\frac {1-\frac {1}{\sqrt {17}}}{\left (-1+\sqrt {17}+2 x\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )}\right ) \, dx+\int \frac {1}{x \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx-\int \frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2} \, dx \\ & = -\left (2 \int \frac {1}{x^2 \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx\right )-\frac {18 \int \frac {1}{\left (1+\sqrt {17}-2 x\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx}{\sqrt {17}}-\frac {18 \int \frac {1}{\left (-1+\sqrt {17}+2 x\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx}{\sqrt {17}}-\frac {1}{17} \left (17-\sqrt {17}\right ) \int \frac {1}{\left (-1+\sqrt {17}+2 x\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx-\frac {1}{17} \left (17+\sqrt {17}\right ) \int \frac {1}{\left (-1-\sqrt {17}+2 x\right ) \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx+\int \frac {1}{x \log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )} \, dx-\int \frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x^2} \, dx \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx=\frac {\log \left (\log \left (\frac {\left (4+x-x^2\right )^4}{128 x^2}\right )\right )}{x} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(49\) vs. \(2(21)=42\).
Time = 0.99 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.17
method | result | size |
parallelrisch | \(\frac {\ln \left (\ln \left (\frac {x^{8}-4 x^{7}-10 x^{6}+44 x^{5}+49 x^{4}-176 x^{3}-160 x^{2}+256 x +256}{128 x^{2}}\right )\right )}{x}\) | \(50\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (21) = 42\).
Time = 0.26 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.13 \[ \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx=\frac {\log \left (\log \left (\frac {x^{8} - 4 \, x^{7} - 10 \, x^{6} + 44 \, x^{5} + 49 \, x^{4} - 176 \, x^{3} - 160 \, x^{2} + 256 \, x + 256}{128 \, x^{2}}\right )\right )}{x} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (17) = 34\).
Time = 0.15 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.43 \[ \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx=\frac {\log {\left (\log {\left (\frac {\frac {x^{8}}{128} - \frac {x^{7}}{32} - \frac {5 x^{6}}{64} + \frac {11 x^{5}}{32} + \frac {49 x^{4}}{128} - \frac {11 x^{3}}{8} - \frac {5 x^{2}}{4} + 2 x + 2}{x^{2}} \right )} \right )}}{x} \]
[In]
[Out]
none
Time = 0.31 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx=\frac {\log \left (-7 \, \log \left (2\right ) + 4 \, \log \left (x^{2} - x - 4\right ) - 2 \, \log \left (x\right )\right )}{x} \]
[In]
[Out]
Exception generated. \[ \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Time = 13.21 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.13 \[ \int \frac {8-2 x+6 x^2+\left (4+x-x^2\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right ) \log \left (\log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )\right )}{\left (-4 x^2-x^3+x^4\right ) \log \left (\frac {256+256 x-160 x^2-176 x^3+49 x^4+44 x^5-10 x^6-4 x^7+x^8}{128 x^2}\right )} \, dx=\frac {\ln \left (\ln \left (\frac {x^8-4\,x^7-10\,x^6+44\,x^5+49\,x^4-176\,x^3-160\,x^2+256\,x+256}{128\,x^2}\right )\right )}{x} \]
[In]
[Out]