Integrand size = 172, antiderivative size = 24 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\left (7-x-\frac {4}{3 \left (7+2 x+\frac {\log (x)}{x^2}\right )}\right )^2 \]
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\[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (x^3 \left (572+84 x-24 x^2-19877 x^3-14931 x^4-2646 x^5+252 x^6+72 x^7\right )+x \left (84-12 x-1144 x^2-9093 x^3-3897 x^4+108 x^6\right ) \log (x)+3 x \left (-56-429 x-63 x^2+18 x^3\right ) \log ^2(x)+9 (-7+x) \log ^3(x)\right )}{9 \left (x^2 (7+2 x)+\log (x)\right )^3} \, dx \\ & = \frac {2}{9} \int \frac {x^3 \left (572+84 x-24 x^2-19877 x^3-14931 x^4-2646 x^5+252 x^6+72 x^7\right )+x \left (84-12 x-1144 x^2-9093 x^3-3897 x^4+108 x^6\right ) \log (x)+3 x \left (-56-429 x-63 x^2+18 x^3\right ) \log ^2(x)+9 (-7+x) \log ^3(x)}{\left (x^2 (7+2 x)+\log (x)\right )^3} \, dx \\ & = \frac {2}{9} \int \left (9 (-7+x)+\frac {16 x^3 \left (-1-14 x^2-6 x^3\right )}{\left (7 x^2+2 x^3+\log (x)\right )^3}-\frac {4 x \left (-21+3 x-302 x^2-84 x^3+18 x^4\right )}{\left (7 x^2+2 x^3+\log (x)\right )^2}+\frac {12 x (-14+3 x)}{7 x^2+2 x^3+\log (x)}\right ) \, dx \\ & = (7-x)^2-\frac {8}{9} \int \frac {x \left (-21+3 x-302 x^2-84 x^3+18 x^4\right )}{\left (7 x^2+2 x^3+\log (x)\right )^2} \, dx+\frac {8}{3} \int \frac {x (-14+3 x)}{7 x^2+2 x^3+\log (x)} \, dx+\frac {32}{9} \int \frac {x^3 \left (-1-14 x^2-6 x^3\right )}{\left (7 x^2+2 x^3+\log (x)\right )^3} \, dx \\ & = (7-x)^2-\frac {8}{9} \int \left (-\frac {21 x}{\left (7 x^2+2 x^3+\log (x)\right )^2}+\frac {3 x^2}{\left (7 x^2+2 x^3+\log (x)\right )^2}-\frac {302 x^3}{\left (7 x^2+2 x^3+\log (x)\right )^2}-\frac {84 x^4}{\left (7 x^2+2 x^3+\log (x)\right )^2}+\frac {18 x^5}{\left (7 x^2+2 x^3+\log (x)\right )^2}\right ) \, dx+\frac {8}{3} \int \left (-\frac {14 x}{7 x^2+2 x^3+\log (x)}+\frac {3 x^2}{7 x^2+2 x^3+\log (x)}\right ) \, dx+\frac {32}{9} \int \left (-\frac {x^3}{\left (7 x^2+2 x^3+\log (x)\right )^3}-\frac {14 x^5}{\left (7 x^2+2 x^3+\log (x)\right )^3}-\frac {6 x^6}{\left (7 x^2+2 x^3+\log (x)\right )^3}\right ) \, dx \\ & = (7-x)^2-\frac {8}{3} \int \frac {x^2}{\left (7 x^2+2 x^3+\log (x)\right )^2} \, dx-\frac {32}{9} \int \frac {x^3}{\left (7 x^2+2 x^3+\log (x)\right )^3} \, dx+8 \int \frac {x^2}{7 x^2+2 x^3+\log (x)} \, dx-16 \int \frac {x^5}{\left (7 x^2+2 x^3+\log (x)\right )^2} \, dx+\frac {56}{3} \int \frac {x}{\left (7 x^2+2 x^3+\log (x)\right )^2} \, dx-\frac {64}{3} \int \frac {x^6}{\left (7 x^2+2 x^3+\log (x)\right )^3} \, dx-\frac {112}{3} \int \frac {x}{7 x^2+2 x^3+\log (x)} \, dx-\frac {448}{9} \int \frac {x^5}{\left (7 x^2+2 x^3+\log (x)\right )^3} \, dx+\frac {224}{3} \int \frac {x^4}{\left (7 x^2+2 x^3+\log (x)\right )^2} \, dx+\frac {2416}{9} \int \frac {x^3}{\left (7 x^2+2 x^3+\log (x)\right )^2} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(49\) vs. \(2(24)=48\).
Time = 0.08 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.04 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\frac {1}{9} x \left (-126+9 x+\frac {16 x^3}{\left (x^2 (7+2 x)+\log (x)\right )^2}+\frac {24 (-7+x) x}{x^2 (7+2 x)+\log (x)}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(52\) vs. \(2(23)=46\).
Time = 1.49 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.21
method | result | size |
risch | \(x^{2}-14 x +\frac {8 \left (6 x^{4}-21 x^{3}-145 x^{2}+3 x \ln \left (x \right )-21 \ln \left (x \right )\right ) x^{2}}{9 \left (2 x^{3}+7 x^{2}+\ln \left (x \right )\right )^{2}}\) | \(53\) |
default | \(x^{2}-14 x -\frac {4 \left (126 x^{5}+6 x^{3} \ln \left (x \right )+437 x^{4}+84 x^{2} \ln \left (x \right )+3 \ln \left (x \right )^{2}\right )}{9 \left (2 x^{3}+7 x^{2}+\ln \left (x \right )\right )^{2}}\) | \(56\) |
parallelrisch | \(\frac {36 x^{5} \ln \left (x \right )-126 x \ln \left (x \right )^{2}-378 x^{4} \ln \left (x \right )+9 x^{2} \ln \left (x \right )^{2}-252 x^{7}+36 x^{8}-3039 x^{6}-6342 x^{5}-1160 x^{4}-1740 x^{3} \ln \left (x \right )-168 x^{2} \ln \left (x \right )}{36 x^{6}+252 x^{5}+441 x^{4}+36 x^{3} \ln \left (x \right )+126 x^{2} \ln \left (x \right )+9 \ln \left (x \right )^{2}}\) | \(109\) |
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Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (24) = 48\).
Time = 0.25 (sec) , antiderivative size = 103, normalized size of antiderivative = 4.29 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\frac {36 \, x^{8} - 252 \, x^{7} - 3039 \, x^{6} - 6342 \, x^{5} - 1160 \, x^{4} + 9 \, {\left (x^{2} - 14 \, x\right )} \log \left (x\right )^{2} + 6 \, {\left (6 \, x^{5} - 63 \, x^{4} - 290 \, x^{3} - 28 \, x^{2}\right )} \log \left (x\right )}{9 \, {\left (4 \, x^{6} + 28 \, x^{5} + 49 \, x^{4} + 2 \, {\left (2 \, x^{3} + 7 \, x^{2}\right )} \log \left (x\right ) + \log \left (x\right )^{2}\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (19) = 38\).
Time = 0.13 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.92 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=x^{2} - 14 x + \frac {48 x^{6} - 168 x^{5} - 1160 x^{4} + \left (24 x^{3} - 168 x^{2}\right ) \log {\left (x \right )}}{36 x^{6} + 252 x^{5} + 441 x^{4} + \left (36 x^{3} + 126 x^{2}\right ) \log {\left (x \right )} + 9 \log {\left (x \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (24) = 48\).
Time = 0.24 (sec) , antiderivative size = 103, normalized size of antiderivative = 4.29 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\frac {36 \, x^{8} - 252 \, x^{7} - 3039 \, x^{6} - 6342 \, x^{5} - 1160 \, x^{4} + 9 \, {\left (x^{2} - 14 \, x\right )} \log \left (x\right )^{2} + 6 \, {\left (6 \, x^{5} - 63 \, x^{4} - 290 \, x^{3} - 28 \, x^{2}\right )} \log \left (x\right )}{9 \, {\left (4 \, x^{6} + 28 \, x^{5} + 49 \, x^{4} + 2 \, {\left (2 \, x^{3} + 7 \, x^{2}\right )} \log \left (x\right ) + \log \left (x\right )^{2}\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (24) = 48\).
Time = 0.29 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.12 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=x^{2} - 14 \, x + \frac {8 \, {\left (6 \, x^{6} - 21 \, x^{5} - 145 \, x^{4} + 3 \, x^{3} \log \left (x\right ) - 21 \, x^{2} \log \left (x\right )\right )}}{9 \, {\left (4 \, x^{6} + 28 \, x^{5} + 49 \, x^{4} + 4 \, x^{3} \log \left (x\right ) + 14 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}\right )}} \]
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Timed out. \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\int -\frac {{\ln \left (x\right )}^2\,\left (-108\,x^4+378\,x^3+2574\,x^2+336\,x\right )+\ln \left (x\right )\,\left (-216\,x^7+7794\,x^5+18186\,x^4+2288\,x^3+24\,x^2-168\,x\right )-1144\,x^3-168\,x^4+48\,x^5+39754\,x^6+29862\,x^7+5292\,x^8-504\,x^9-144\,x^{10}-{\ln \left (x\right )}^3\,\left (18\,x-126\right )}{9\,{\ln \left (x\right )}^3+\ln \left (x\right )\,\left (108\,x^6+756\,x^5+1323\,x^4\right )+{\ln \left (x\right )}^2\,\left (54\,x^3+189\,x^2\right )+3087\,x^6+2646\,x^7+756\,x^8+72\,x^9} \,d x \]
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