Integrand size = 137, antiderivative size = 34 \[ \int \frac {720+720 x+364 x^2-588 x^3-48 x^4-52 x^5+24 x^6+16 x^7-4 x^8+\left (1200 x+1512 x^2-732 x^3+368 x^4+60 x^5-40 x^6-40 x^7+8 x^8\right ) \log (x)}{3600 x-2400 x^2+40 x^3-480 x^4+89 x^5+190 x^6-9 x^7+4 x^8-9 x^9-2 x^{10}+x^{11}} \, dx=\frac {\left (1+x \left (\frac {5}{3-x}+x\right )\right ) \log (x)}{5-\frac {1}{4} x^2 (1+x)^2} \] Output:
((x+5/(3-x))*x+1)*ln(x)/(5-1/4*x^2*(1+x)^2)
Time = 0.03 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.24 \[ \int \frac {720+720 x+364 x^2-588 x^3-48 x^4-52 x^5+24 x^6+16 x^7-4 x^8+\left (1200 x+1512 x^2-732 x^3+368 x^4+60 x^5-40 x^6-40 x^7+8 x^8\right ) \log (x)}{3600 x-2400 x^2+40 x^3-480 x^4+89 x^5+190 x^6-9 x^7+4 x^8-9 x^9-2 x^{10}+x^{11}} \, dx=-\frac {4 \left (-3-4 x-3 x^2+x^3\right ) \log (x)}{60-20 x-3 x^2-5 x^3-x^4+x^5} \] Input:
Integrate[(720 + 720*x + 364*x^2 - 588*x^3 - 48*x^4 - 52*x^5 + 24*x^6 + 16 *x^7 - 4*x^8 + (1200*x + 1512*x^2 - 732*x^3 + 368*x^4 + 60*x^5 - 40*x^6 - 40*x^7 + 8*x^8)*Log[x])/(3600*x - 2400*x^2 + 40*x^3 - 480*x^4 + 89*x^5 + 1 90*x^6 - 9*x^7 + 4*x^8 - 9*x^9 - 2*x^10 + x^11),x]
Output:
(-4*(-3 - 4*x - 3*x^2 + x^3)*Log[x])/(60 - 20*x - 3*x^2 - 5*x^3 - x^4 + x^ 5)
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-4 x^8+16 x^7+24 x^6-52 x^5-48 x^4-588 x^3+364 x^2+\left (8 x^8-40 x^7-40 x^6+60 x^5+368 x^4-732 x^3+1512 x^2+1200 x\right ) \log (x)+720 x+720}{x^{11}-2 x^{10}-9 x^9+4 x^8-9 x^7+190 x^6+89 x^5-480 x^4+40 x^3-2400 x^2+3600 x} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-4 x^8+16 x^7+24 x^6-52 x^5-48 x^4-588 x^3+364 x^2+\left (8 x^8-40 x^7-40 x^6+60 x^5+368 x^4-732 x^3+1512 x^2+1200 x\right ) \log (x)+720 x+720}{x \left (x^{10}-2 x^9-9 x^8+4 x^7-9 x^6+190 x^5+89 x^4-480 x^3+40 x^2-2400 x+3600\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (-\frac {21 \left (-4 x^8+16 x^7+24 x^6-52 x^5-48 x^4-588 x^3+364 x^2+\left (8 x^8-40 x^7-40 x^6+60 x^5+368 x^4-732 x^3+1512 x^2+1200 x\right ) \log (x)+720 x+720\right )}{119164 (x-3) x}+\frac {-4 x^8+16 x^7+24 x^6-52 x^5-48 x^4-588 x^3+364 x^2+\left (8 x^8-40 x^7-40 x^6+60 x^5+368 x^4-732 x^3+1512 x^2+1200 x\right ) \log (x)+720 x+720}{15376 (x-3)^2 x}+\frac {\left (84 x^3+389 x^2+1096 x+2792\right ) \left (-4 x^8+16 x^7+24 x^6-52 x^5-48 x^4-588 x^3+364 x^2+\left (8 x^8-40 x^7-40 x^6+60 x^5+368 x^4-732 x^3+1512 x^2+1200 x\right ) \log (x)+720 x+720\right )}{476656 x \left (x^4+2 x^3+x^2-20\right )}+\frac {\left (42 x^3+179 x^2+424 x+776\right ) \left (-4 x^8+16 x^7+24 x^6-52 x^5-48 x^4-588 x^3+364 x^2+\left (8 x^8-40 x^7-40 x^6+60 x^5+368 x^4-732 x^3+1512 x^2+1200 x\right ) \log (x)+720 x+720\right )}{3844 x \left (x^4+2 x^3+x^2-20\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (-x^8+4 x^7+6 x^6-13 x^5-12 x^4-147 x^3+91 x^2+\left (2 x^7-10 x^6-10 x^5+15 x^4+92 x^3-183 x^2+378 x+300\right ) x \log (x)+180 x+180\right )}{(3-x)^2 x \left (-x^4-2 x^3-x^2+20\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int \frac {-x^8+4 x^7+6 x^6-13 x^5-12 x^4-147 x^3+91 x^2+\left (2 x^7-10 x^6-10 x^5+15 x^4+92 x^3-183 x^2+378 x+300\right ) \log (x) x+180 x+180}{(3-x)^2 x \left (-x^4-2 x^3-x^2+20\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^7}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}+\frac {4 x^6}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}+\frac {6 x^5}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}-\frac {13 x^4}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}-\frac {12 x^3}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}-\frac {147 x^2}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}+\frac {91 x}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}+\frac {\left (2 x^7-10 x^6-10 x^5+15 x^4+92 x^3-183 x^2+378 x+300\right ) \log (x)}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}+\frac {180}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2}+\frac {180}{(x-3)^2 \left (x^4+2 x^3+x^2-20\right )^2 x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 \left (-\frac {(2 x+1) \left (1076651-638651 (2 x+1)^2\right )}{392395520 \left (-x^4-2 x^3-x^2+20\right )}-\frac {3 (2 x+1) \left (971889-248449 (2 x+1)^2\right )}{196197760 \left (-x^4-2 x^3-x^2+20\right )}+\frac {66249-2569 (2 x+1)^2}{307520 \left (-x^4-2 x^3-x^2+20\right )}+\frac {63 \left (41 (2 x+1)^2+439\right )}{61504 \left (-x^4-2 x^3-x^2+20\right )}-\frac {441 \left (117 (2 x+1)^2+5003\right )}{1230080 \left (-x^4-2 x^3-x^2+20\right )}+\frac {9 \left (137 (2 x+1)^2+2967\right )}{61504 \left (-x^4-2 x^3-x^2+20\right )}+\frac {91 \left (489 (2 x+1)^2+7111\right )}{1230080 \left (-x^4-2 x^3-x^2+20\right )}-\frac {3 \left (1549 (2 x+1)^2+22211\right )}{307520 \left (-x^4-2 x^3-x^2+20\right )}-\frac {13 \left (2291 (2 x+1)^2+2029\right )}{1230080 \left (-x^4-2 x^3-x^2+20\right )}+\frac {45 (2 x+1) \left (3459 (2 x+1)^2+73789\right )}{19619776 \left (-x^4-2 x^3-x^2+20\right )}+\frac {3 \left (3649 (2 x+1)^2+115951\right )}{615040 \left (-x^4-2 x^3-x^2+20\right )}+\frac {9 (2 x+1) \left (9113 (2 x+1)^2+208583\right )}{19619776 \left (-x^4-2 x^3-x^2+20\right )}-\frac {3 \left (10823 (2 x+1)^2+65257\right )}{1230080 \left (-x^4-2 x^3-x^2+20\right )}-\frac {3 (2 x+1) \left (26269 (2 x+1)^2+1903251\right )}{98098880 \left (-x^4-2 x^3-x^2+20\right )}+\frac {91 (2 x+1) \left (37129 (2 x+1)^2+305671\right )}{392395520 \left (-x^4-2 x^3-x^2+20\right )}-\frac {147 (2 x+1) \left (59431 (2 x+1)^2+981369\right )}{392395520 \left (-x^4-2 x^3-x^2+20\right )}-\frac {13 (2 x+1) \left (233931 (2 x+1)^2+2591029\right )}{392395520 \left (-x^4-2 x^3-x^2+20\right )}+\frac {(2 x+1) \left (457791 (2 x+1)^2+18980129\right )}{98098880 \left (-x^4-2 x^3-x^2+20\right )}-\frac {9 \sqrt {\frac {5}{319} \left (-374872511+217966480 \sqrt {5}\right )} \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{476656}-\frac {\left (18349+2554604 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{196197760 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}-\frac {3 \left (836711+993796 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{98098880 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}+\frac {81 \left (2189-618 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{476656 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}-\frac {243 \left (1359-986 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{953312 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}+\frac {351 \left (3963-1420 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{1906624 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}+\frac {441 \left (9171-2288 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{1906624 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}+\frac {9 \left (335657-36452 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{9809888 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}+\frac {\left (530671-86022 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{1906624 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}-\frac {3 \left (2920549-105076 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{49049440 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}-\frac {\left (650777-134136 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{476656 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}+\frac {91 \left (551329-148516 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{196197760 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}-\frac {147 \left (1620631-237724 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{196197760 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}-\frac {39 \left (1490457-311908 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{196197760 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}+\frac {3 \left (9871557-610388 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{49049440 \sqrt {5 \left (-1+8 \sqrt {5}\right )}}+\frac {91 \left (2722-2355 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{1906624 \sqrt {-1+8 \sqrt {5}}}+\frac {9 \left (3352-9435 \sqrt {5}\right ) \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{2383280 \sqrt {-1+8 \sqrt {5}}}+\frac {27 \left (39777-4612 \sqrt {5}\right ) \sqrt {\frac {5}{-1+8 \sqrt {5}}} \arctan \left (\frac {2 x+1}{\sqrt {-1+8 \sqrt {5}}}\right )}{9809888}+\frac {3 \left (9871557+610388 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{49049440 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {39 \left (1490457+311908 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{196197760 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {147 \left (1620631+237724 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{196197760 \sqrt {5 \left (1+8 \sqrt {5}\right )}}+\frac {91 \left (551329+148516 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{196197760 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {\left (650777+134136 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{476656 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {3 \left (2920549+105076 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{49049440 \sqrt {5 \left (1+8 \sqrt {5}\right )}}+\frac {\left (530671+86022 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{1906624 \sqrt {5 \left (1+8 \sqrt {5}\right )}}+\frac {9 \left (335657+36452 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{9809888 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {9 \left (3352+9435 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{2383280 \sqrt {1+8 \sqrt {5}}}+\frac {27 \sqrt {\frac {5}{1+8 \sqrt {5}}} \left (39777+4612 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{9809888}-\frac {91 \left (2722+2355 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{1906624 \sqrt {1+8 \sqrt {5}}}+\frac {441 \left (9171+2288 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{1906624 \sqrt {5 \left (1+8 \sqrt {5}\right )}}+\frac {351 \left (3963+1420 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{1906624 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {9 \sqrt {\frac {5}{1+8 \sqrt {5}}} \left (4793+1052 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{476656}-\frac {243 \left (1359+986 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{953312 \sqrt {5 \left (1+8 \sqrt {5}\right )}}+\frac {81 \left (2189+618 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{476656 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {3 \left (836711-993796 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{98098880 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {\left (18349-2554604 \sqrt {5}\right ) \text {arctanh}\left (\frac {2 x+1}{\sqrt {1+8 \sqrt {5}}}\right )}{196197760 \sqrt {5 \left (1+8 \sqrt {5}\right )}}-\frac {5 x \log (x)}{124 (3-x)}+\frac {\log (x)}{20}-\frac {9 \left (5048+1525 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{4766560}+\frac {729 \left (220-47 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{4766560}+\frac {63 \left (120-113 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{953312}-\frac {351 \left (256-177 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{3813248}-\frac {81 \left (530-419 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{4766560}+\frac {243 \left (970-513 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{9533120}-\frac {441 \left (1900-1629 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{19066240}+\frac {91 \left (2210-2001 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{19066240}-\frac {\left (255150-308257 \sqrt {5}\right ) \log \left (x^2+x+2 \sqrt {5}\right )}{19066240}-\frac {\left (255150+308257 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{19066240}+\frac {91 \left (2210+2001 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{19066240}-\frac {441 \left (1900+1629 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{19066240}+\frac {243 \left (970+513 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{9533120}-\frac {81 \left (530+419 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{4766560}-\frac {351 \left (256+177 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{3813248}+\frac {63 \left (120+113 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{953312}+\frac {729 \left (220+47 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{4766560}-\frac {9 \left (5048-1525 \sqrt {5}\right ) \log \left (-\sqrt {5} x^2-\sqrt {5} x+10\right )}{4766560}+\frac {2960}{31} \int \frac {\log (x)}{\left (x^4+2 x^3+x^2-20\right )^2}dx+\frac {3942}{31} \int \frac {x \log (x)}{\left (x^4+2 x^3+x^2-20\right )^2}dx+\frac {608}{31} \int \frac {x^2 \log (x)}{\left (x^4+2 x^3+x^2-20\right )^2}dx+\frac {196}{31} \int \frac {x^3 \log (x)}{\left (x^4+2 x^3+x^2-20\right )^2}dx+\frac {88}{31} \int \frac {\log (x)}{x^4+2 x^3+x^2-20}dx+\frac {92}{31} \int \frac {x \log (x)}{x^4+2 x^3+x^2-20}dx+\frac {15}{124} \int \frac {x^2 \log (x)}{x^4+2 x^3+x^2-20}dx\right )\) |
Input:
Int[(720 + 720*x + 364*x^2 - 588*x^3 - 48*x^4 - 52*x^5 + 24*x^6 + 16*x^7 - 4*x^8 + (1200*x + 1512*x^2 - 732*x^3 + 368*x^4 + 60*x^5 - 40*x^6 - 40*x^7 + 8*x^8)*Log[x])/(3600*x - 2400*x^2 + 40*x^3 - 480*x^4 + 89*x^5 + 190*x^6 - 9*x^7 + 4*x^8 - 9*x^9 - 2*x^10 + x^11),x]
Output:
$Aborted
Time = 3.75 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.26
| method | result | size |
| risch | \(-\frac {4 \left (x^{3}-3 x^{2}-4 x -3\right ) \ln \left (x \right )}{x^{5}-x^{4}-5 x^{3}-3 x^{2}-20 x +60}\) | \(43\) |
| norman | \(\frac {12 \ln \left (x \right )-4 x^{3} \ln \left (x \right )+12 x^{2} \ln \left (x \right )+16 x \ln \left (x \right )}{x^{5}-x^{4}-5 x^{3}-3 x^{2}-20 x +60}\) | \(51\) |
| parallelrisch | \(\frac {12 \ln \left (x \right )-4 x^{3} \ln \left (x \right )+12 x^{2} \ln \left (x \right )+16 x \ln \left (x \right )}{x^{5}-x^{4}-5 x^{3}-3 x^{2}-20 x +60}\) | \(51\) |
| orering | \(-\frac {\left (5 x^{11}-39 x^{10}+26 x^{9}+202 x^{8}+243 x^{7}-901 x^{6}+409 x^{5}-1287 x^{4}-3443 x^{3}-3135 x^{2}-540 x +540\right ) \left (\left (8 x^{8}-40 x^{7}-40 x^{6}+60 x^{5}+368 x^{4}-732 x^{3}+1512 x^{2}+1200 x \right ) \ln \left (x \right )-4 x^{8}+16 x^{7}+24 x^{6}-52 x^{5}-48 x^{4}-588 x^{3}+364 x^{2}+720 x +720\right )}{\left (4 x^{10}-34 x^{9}+42 x^{8}+197 x^{7}+141 x^{6}+549 x^{5}-3022 x^{4}+396 x^{3}+4347 x^{2}-1068 x -900\right ) \left (x^{11}-2 x^{10}-9 x^{9}+4 x^{8}-9 x^{7}+190 x^{6}+89 x^{5}-480 x^{4}+40 x^{3}-2400 x^{2}+3600 x \right )}-\frac {\left (x^{6}-6 x^{5}+x^{4}+18 x^{3}+34 x^{2}+24 x +9\right ) x \left (x^{4}+2 x^{3}+x^{2}-20\right ) \left (-3+x \right ) \left (\frac {\left (64 x^{7}-280 x^{6}-240 x^{5}+300 x^{4}+1472 x^{3}-2196 x^{2}+3024 x +1200\right ) \ln \left (x \right )+\frac {8 x^{8}-40 x^{7}-40 x^{6}+60 x^{5}+368 x^{4}-732 x^{3}+1512 x^{2}+1200 x}{x}-32 x^{7}+112 x^{6}+144 x^{5}-260 x^{4}-192 x^{3}-1764 x^{2}+728 x +720}{x^{11}-2 x^{10}-9 x^{9}+4 x^{8}-9 x^{7}+190 x^{6}+89 x^{5}-480 x^{4}+40 x^{3}-2400 x^{2}+3600 x}-\frac {\left (\left (8 x^{8}-40 x^{7}-40 x^{6}+60 x^{5}+368 x^{4}-732 x^{3}+1512 x^{2}+1200 x \right ) \ln \left (x \right )-4 x^{8}+16 x^{7}+24 x^{6}-52 x^{5}-48 x^{4}-588 x^{3}+364 x^{2}+720 x +720\right ) \left (11 x^{10}-20 x^{9}-81 x^{8}+32 x^{7}-63 x^{6}+1140 x^{5}+445 x^{4}-1920 x^{3}+120 x^{2}-4800 x +3600\right )}{\left (x^{11}-2 x^{10}-9 x^{9}+4 x^{8}-9 x^{7}+190 x^{6}+89 x^{5}-480 x^{4}+40 x^{3}-2400 x^{2}+3600 x \right )^{2}}\right )}{4 x^{10}-34 x^{9}+42 x^{8}+197 x^{7}+141 x^{6}+549 x^{5}-3022 x^{4}+396 x^{3}+4347 x^{2}-1068 x -900}\) | \(704\) |
| default | \(\text {Expression too large to display}\) | \(1272\) |
| parts | \(\text {Expression too large to display}\) | \(1272\) |
Input:
int(((8*x^8-40*x^7-40*x^6+60*x^5+368*x^4-732*x^3+1512*x^2+1200*x)*ln(x)-4* x^8+16*x^7+24*x^6-52*x^5-48*x^4-588*x^3+364*x^2+720*x+720)/(x^11-2*x^10-9* x^9+4*x^8-9*x^7+190*x^6+89*x^5-480*x^4+40*x^3-2400*x^2+3600*x),x,method=_R ETURNVERBOSE)
Output:
-4*(x^3-3*x^2-4*x-3)/(x^5-x^4-5*x^3-3*x^2-20*x+60)*ln(x)
Time = 0.09 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.24 \[ \int \frac {720+720 x+364 x^2-588 x^3-48 x^4-52 x^5+24 x^6+16 x^7-4 x^8+\left (1200 x+1512 x^2-732 x^3+368 x^4+60 x^5-40 x^6-40 x^7+8 x^8\right ) \log (x)}{3600 x-2400 x^2+40 x^3-480 x^4+89 x^5+190 x^6-9 x^7+4 x^8-9 x^9-2 x^{10}+x^{11}} \, dx=-\frac {4 \, {\left (x^{3} - 3 \, x^{2} - 4 \, x - 3\right )} \log \left (x\right )}{x^{5} - x^{4} - 5 \, x^{3} - 3 \, x^{2} - 20 \, x + 60} \] Input:
integrate(((8*x^8-40*x^7-40*x^6+60*x^5+368*x^4-732*x^3+1512*x^2+1200*x)*lo g(x)-4*x^8+16*x^7+24*x^6-52*x^5-48*x^4-588*x^3+364*x^2+720*x+720)/(x^11-2* x^10-9*x^9+4*x^8-9*x^7+190*x^6+89*x^5-480*x^4+40*x^3-2400*x^2+3600*x),x, a lgorithm="fricas")
Output:
-4*(x^3 - 3*x^2 - 4*x - 3)*log(x)/(x^5 - x^4 - 5*x^3 - 3*x^2 - 20*x + 60)
Time = 0.15 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.15 \[ \int \frac {720+720 x+364 x^2-588 x^3-48 x^4-52 x^5+24 x^6+16 x^7-4 x^8+\left (1200 x+1512 x^2-732 x^3+368 x^4+60 x^5-40 x^6-40 x^7+8 x^8\right ) \log (x)}{3600 x-2400 x^2+40 x^3-480 x^4+89 x^5+190 x^6-9 x^7+4 x^8-9 x^9-2 x^{10}+x^{11}} \, dx=\frac {\left (- 4 x^{3} + 12 x^{2} + 16 x + 12\right ) \log {\left (x \right )}}{x^{5} - x^{4} - 5 x^{3} - 3 x^{2} - 20 x + 60} \] Input:
integrate(((8*x**8-40*x**7-40*x**6+60*x**5+368*x**4-732*x**3+1512*x**2+120 0*x)*ln(x)-4*x**8+16*x**7+24*x**6-52*x**5-48*x**4-588*x**3+364*x**2+720*x+ 720)/(x**11-2*x**10-9*x**9+4*x**8-9*x**7+190*x**6+89*x**5-480*x**4+40*x**3 -2400*x**2+3600*x),x)
Output:
(-4*x**3 + 12*x**2 + 16*x + 12)*log(x)/(x**5 - x**4 - 5*x**3 - 3*x**2 - 20 *x + 60)
Time = 0.04 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.24 \[ \int \frac {720+720 x+364 x^2-588 x^3-48 x^4-52 x^5+24 x^6+16 x^7-4 x^8+\left (1200 x+1512 x^2-732 x^3+368 x^4+60 x^5-40 x^6-40 x^7+8 x^8\right ) \log (x)}{3600 x-2400 x^2+40 x^3-480 x^4+89 x^5+190 x^6-9 x^7+4 x^8-9 x^9-2 x^{10}+x^{11}} \, dx=-\frac {4 \, {\left (x^{3} - 3 \, x^{2} - 4 \, x - 3\right )} \log \left (x\right )}{x^{5} - x^{4} - 5 \, x^{3} - 3 \, x^{2} - 20 \, x + 60} \] Input:
integrate(((8*x^8-40*x^7-40*x^6+60*x^5+368*x^4-732*x^3+1512*x^2+1200*x)*lo g(x)-4*x^8+16*x^7+24*x^6-52*x^5-48*x^4-588*x^3+364*x^2+720*x+720)/(x^11-2* x^10-9*x^9+4*x^8-9*x^7+190*x^6+89*x^5-480*x^4+40*x^3-2400*x^2+3600*x),x, a lgorithm="maxima")
Output:
-4*(x^3 - 3*x^2 - 4*x - 3)*log(x)/(x^5 - x^4 - 5*x^3 - 3*x^2 - 20*x + 60)
Time = 0.12 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.24 \[ \int \frac {720+720 x+364 x^2-588 x^3-48 x^4-52 x^5+24 x^6+16 x^7-4 x^8+\left (1200 x+1512 x^2-732 x^3+368 x^4+60 x^5-40 x^6-40 x^7+8 x^8\right ) \log (x)}{3600 x-2400 x^2+40 x^3-480 x^4+89 x^5+190 x^6-9 x^7+4 x^8-9 x^9-2 x^{10}+x^{11}} \, dx=-\frac {4 \, {\left (x^{3} - 3 \, x^{2} - 4 \, x - 3\right )} \log \left (x\right )}{x^{5} - x^{4} - 5 \, x^{3} - 3 \, x^{2} - 20 \, x + 60} \] Input:
integrate(((8*x^8-40*x^7-40*x^6+60*x^5+368*x^4-732*x^3+1512*x^2+1200*x)*lo g(x)-4*x^8+16*x^7+24*x^6-52*x^5-48*x^4-588*x^3+364*x^2+720*x+720)/(x^11-2* x^10-9*x^9+4*x^8-9*x^7+190*x^6+89*x^5-480*x^4+40*x^3-2400*x^2+3600*x),x, a lgorithm="giac")
Output:
-4*(x^3 - 3*x^2 - 4*x - 3)*log(x)/(x^5 - x^4 - 5*x^3 - 3*x^2 - 20*x + 60)
Time = 3.36 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.47 \[ \int \frac {720+720 x+364 x^2-588 x^3-48 x^4-52 x^5+24 x^6+16 x^7-4 x^8+\left (1200 x+1512 x^2-732 x^3+368 x^4+60 x^5-40 x^6-40 x^7+8 x^8\right ) \log (x)}{3600 x-2400 x^2+40 x^3-480 x^4+89 x^5+190 x^6-9 x^7+4 x^8-9 x^9-2 x^{10}+x^{11}} \, dx=\frac {15\,\ln \left (x\right )}{31\,\left (x-3\right )}-\frac {\ln \left (x\right )\,\left (15\,x^3+199\,x^2+240\,x+224\right )}{31\,\left (x^4+2\,x^3+x^2-20\right )} \] Input:
int((720*x + 364*x^2 - 588*x^3 - 48*x^4 - 52*x^5 + 24*x^6 + 16*x^7 - 4*x^8 + log(x)*(1200*x + 1512*x^2 - 732*x^3 + 368*x^4 + 60*x^5 - 40*x^6 - 40*x^ 7 + 8*x^8) + 720)/(3600*x - 2400*x^2 + 40*x^3 - 480*x^4 + 89*x^5 + 190*x^6 - 9*x^7 + 4*x^8 - 9*x^9 - 2*x^10 + x^11),x)
Output:
(15*log(x))/(31*(x - 3)) - (log(x)*(240*x + 199*x^2 + 15*x^3 + 224))/(31*( x^2 + 2*x^3 + x^4 - 20))
Time = 0.23 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.29 \[ \int \frac {720+720 x+364 x^2-588 x^3-48 x^4-52 x^5+24 x^6+16 x^7-4 x^8+\left (1200 x+1512 x^2-732 x^3+368 x^4+60 x^5-40 x^6-40 x^7+8 x^8\right ) \log (x)}{3600 x-2400 x^2+40 x^3-480 x^4+89 x^5+190 x^6-9 x^7+4 x^8-9 x^9-2 x^{10}+x^{11}} \, dx=\frac {4 \,\mathrm {log}\left (x \right ) \left (-x^{3}+3 x^{2}+4 x +3\right )}{x^{5}-x^{4}-5 x^{3}-3 x^{2}-20 x +60} \] Input:
int(((8*x^8-40*x^7-40*x^6+60*x^5+368*x^4-732*x^3+1512*x^2+1200*x)*log(x)-4 *x^8+16*x^7+24*x^6-52*x^5-48*x^4-588*x^3+364*x^2+720*x+720)/(x^11-2*x^10-9 *x^9+4*x^8-9*x^7+190*x^6+89*x^5-480*x^4+40*x^3-2400*x^2+3600*x),x)
Output:
(4*log(x)*( - x**3 + 3*x**2 + 4*x + 3))/(x**5 - x**4 - 5*x**3 - 3*x**2 - 2 0*x + 60)