Integrand size = 91, antiderivative size = 28 \[ \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx=\frac {x \log (x)}{4 (-3+x)^2 \left (1+\frac {1}{8} x (9+5 x)^2\right )} \] Output:
1/4*ln(x)*x/(-3+x)^2/(1/8*x*(5*x+9)^2+1)
Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx=\frac {2 x \log (x)}{(-3+x)^2 \left (8+81 x+90 x^2+25 x^3\right )} \] Input:
Integrate[(-48 - 470*x - 378*x^2 + 30*x^3 + 50*x^4 + (-48 - 16*x + 216*x^2 - 240*x^3 - 200*x^4)*Log[x])/(-1728 - 33264*x - 181611*x^2 - 200033*x^3 + 5697*x^4 + 79731*x^5 + 10255*x^6 - 11475*x^7 - 1125*x^8 + 625*x^9),x]
Output:
(2*x*Log[x])/((-3 + x)^2*(8 + 81*x + 90*x^2 + 25*x^3))
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.
| \(\displaystyle \int \frac {50 x^4+30 x^3-378 x^2+\left (-200 x^4-240 x^3+216 x^2-16 x-48\right ) \log (x)-470 x-48}{625 x^9-1125 x^8-11475 x^7+10255 x^6+79731 x^5+5697 x^4-200033 x^3-181611 x^2-33264 x-1728} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {246573 \left (50 x^4+30 x^3-378 x^2+\left (-200 x^4-240 x^3+216 x^2-16 x-48\right ) \log (x)-470 x-48\right )}{567647723776 (x-3)}+\frac {\left (-6164325 x^2-33653745 x-79239268\right ) \left (50 x^4+30 x^3-378 x^2+\left (-200 x^4-240 x^3+216 x^2-16 x-48\right ) \log (x)-470 x-48\right )}{567647723776 \left (25 x^3+90 x^2+81 x+8\right )}-\frac {81 \left (50 x^4+30 x^3-378 x^2+\left (-200 x^4-240 x^3+216 x^2-16 x-48\right ) \log (x)-470 x-48\right )}{163493008 (x-3)^2}+\frac {\left (-3539925 x^2-16332705 x-23481992\right ) \left (50 x^4+30 x^3-378 x^2+\left (-200 x^4-240 x^3+216 x^2-16 x-48\right ) \log (x)-470 x-48\right )}{653972032 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4+30 x^3-378 x^2+\left (-200 x^4-240 x^3+216 x^2-16 x-48\right ) \log (x)-470 x-48}{3013696 (x-3)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {30 x^3}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {378 x^2}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {470 x}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {48}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}+\frac {50 x^4}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}-\frac {8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)}{(x-3)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 x^4-30 x^3+378 x^2+8 \left (25 x^4+30 x^3-27 x^2+2 x+6\right ) \log (x)+470 x+48}{(3-x)^3 \left (25 x^3+90 x^2+81 x+8\right )^2}dx\) |
Input:
Int[(-48 - 470*x - 378*x^2 + 30*x^3 + 50*x^4 + (-48 - 16*x + 216*x^2 - 240 *x^3 - 200*x^4)*Log[x])/(-1728 - 33264*x - 181611*x^2 - 200033*x^3 + 5697* x^4 + 79731*x^5 + 10255*x^6 - 11475*x^7 - 1125*x^8 + 625*x^9),x]
Output:
$Aborted
Time = 0.78 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00
| method | result | size |
| norman | \(\frac {2 x \ln \left (x \right )}{\left (25 x^{3}+90 x^{2}+81 x +8\right ) \left (-3+x \right )^{2}}\) | \(28\) |
| risch | \(\frac {2 x \ln \left (x \right )}{25 x^{5}-60 x^{4}-234 x^{3}+332 x^{2}+681 x +72}\) | \(33\) |
| parallelrisch | \(\frac {2 x \ln \left (x \right )}{25 x^{5}-60 x^{4}-234 x^{3}+332 x^{2}+681 x +72}\) | \(33\) |
| default | \(\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (25 \textit {\_Z}^{3}+90 \textit {\_Z}^{2}+81 \textit {\_Z} +8\right )}{\sum }\frac {\left (4050 \textit {\_R}^{2}+21305 \textit {\_R} +41232\right ) \ln \left (x -\textit {\_R} \right )}{25 \textit {\_R}^{2}+60 \textit {\_R} +27}\right )}{565068}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (25 \textit {\_Z}^{3}+90 \textit {\_Z}^{2}+81 \textit {\_Z} +8\right )}{\sum }\frac {\left (-4050 \textit {\_R}^{2}-21305 \textit {\_R} -41232\right ) \ln \left (x -\textit {\_R} \right )}{25 \textit {\_R}^{2}+60 \textit {\_R} +27}\right )}{565068}+\frac {\ln \left (x \right ) x \left (4050 x^{2}+21305 x +41232\right )}{4708900 x^{3}+16952040 x^{2}+15256836 x +1506848}-\frac {\ln \left (x \right ) x \left (-6+x \right )}{2604 \left (-3+x \right )^{2}}-\frac {269 \ln \left (x \right ) x}{565068 \left (-3+x \right )}\) | \(157\) |
| parts | \(\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (25 \textit {\_Z}^{3}+90 \textit {\_Z}^{2}+81 \textit {\_Z} +8\right )}{\sum }\frac {\left (4050 \textit {\_R}^{2}+21305 \textit {\_R} +41232\right ) \ln \left (x -\textit {\_R} \right )}{25 \textit {\_R}^{2}+60 \textit {\_R} +27}\right )}{565068}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (25 \textit {\_Z}^{3}+90 \textit {\_Z}^{2}+81 \textit {\_Z} +8\right )}{\sum }\frac {\left (-4050 \textit {\_R}^{2}-21305 \textit {\_R} -41232\right ) \ln \left (x -\textit {\_R} \right )}{25 \textit {\_R}^{2}+60 \textit {\_R} +27}\right )}{565068}+\frac {\ln \left (x \right ) x \left (4050 x^{2}+21305 x +41232\right )}{4708900 x^{3}+16952040 x^{2}+15256836 x +1506848}-\frac {\ln \left (x \right ) x \left (-6+x \right )}{2604 \left (-3+x \right )^{2}}-\frac {269 \ln \left (x \right ) x}{565068 \left (-3+x \right )}\) | \(157\) |
| orering | \(-\frac {3 x \left (-3+x \right ) \left (75 x^{4}+85 x^{3}-135 x^{2}-73 x +8\right ) \left (\left (-200 x^{4}-240 x^{3}+216 x^{2}-16 x -48\right ) \ln \left (x \right )+50 x^{4}+30 x^{3}-378 x^{2}-470 x -48\right )}{4 \left (100 x^{5}-135 x^{4}-234 x^{3}+83 x^{2}+18\right ) \left (625 x^{9}-1125 x^{8}-11475 x^{7}+10255 x^{6}+79731 x^{5}+5697 x^{4}-200033 x^{3}-181611 x^{2}-33264 x -1728\right )}-\frac {x^{2} \left (25 x^{3}+90 x^{2}+81 x +8\right ) \left (-3+x \right )^{2} \left (\frac {\left (-800 x^{3}-720 x^{2}+432 x -16\right ) \ln \left (x \right )+\frac {-200 x^{4}-240 x^{3}+216 x^{2}-16 x -48}{x}+200 x^{3}+90 x^{2}-756 x -470}{625 x^{9}-1125 x^{8}-11475 x^{7}+10255 x^{6}+79731 x^{5}+5697 x^{4}-200033 x^{3}-181611 x^{2}-33264 x -1728}-\frac {\left (\left (-200 x^{4}-240 x^{3}+216 x^{2}-16 x -48\right ) \ln \left (x \right )+50 x^{4}+30 x^{3}-378 x^{2}-470 x -48\right ) \left (5625 x^{8}-9000 x^{7}-80325 x^{6}+61530 x^{5}+398655 x^{4}+22788 x^{3}-600099 x^{2}-363222 x -33264\right )}{\left (625 x^{9}-1125 x^{8}-11475 x^{7}+10255 x^{6}+79731 x^{5}+5697 x^{4}-200033 x^{3}-181611 x^{2}-33264 x -1728\right )^{2}}\right )}{4 \left (100 x^{5}-135 x^{4}-234 x^{3}+83 x^{2}+18\right )}\) | \(429\) |
Input:
int(((-200*x^4-240*x^3+216*x^2-16*x-48)*ln(x)+50*x^4+30*x^3-378*x^2-470*x- 48)/(625*x^9-1125*x^8-11475*x^7+10255*x^6+79731*x^5+5697*x^4-200033*x^3-18 1611*x^2-33264*x-1728),x,method=_RETURNVERBOSE)
Output:
2*x*ln(x)/(25*x^3+90*x^2+81*x+8)/(-3+x)^2
Time = 0.10 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.14 \[ \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx=\frac {2 \, x \log \left (x\right )}{25 \, x^{5} - 60 \, x^{4} - 234 \, x^{3} + 332 \, x^{2} + 681 \, x + 72} \] Input:
integrate(((-200*x^4-240*x^3+216*x^2-16*x-48)*log(x)+50*x^4+30*x^3-378*x^2 -470*x-48)/(625*x^9-1125*x^8-11475*x^7+10255*x^6+79731*x^5+5697*x^4-200033 *x^3-181611*x^2-33264*x-1728),x, algorithm="fricas")
Output:
2*x*log(x)/(25*x^5 - 60*x^4 - 234*x^3 + 332*x^2 + 681*x + 72)
Time = 0.12 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx=\frac {2 x \log {\left (x \right )}}{25 x^{5} - 60 x^{4} - 234 x^{3} + 332 x^{2} + 681 x + 72} \] Input:
integrate(((-200*x**4-240*x**3+216*x**2-16*x-48)*ln(x)+50*x**4+30*x**3-378 *x**2-470*x-48)/(625*x**9-1125*x**8-11475*x**7+10255*x**6+79731*x**5+5697* x**4-200033*x**3-181611*x**2-33264*x-1728),x)
Output:
2*x*log(x)/(25*x**5 - 60*x**4 - 234*x**3 + 332*x**2 + 681*x + 72)
Time = 0.03 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.14 \[ \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx=\frac {2 \, x \log \left (x\right )}{25 \, x^{5} - 60 \, x^{4} - 234 \, x^{3} + 332 \, x^{2} + 681 \, x + 72} \] Input:
integrate(((-200*x^4-240*x^3+216*x^2-16*x-48)*log(x)+50*x^4+30*x^3-378*x^2 -470*x-48)/(625*x^9-1125*x^8-11475*x^7+10255*x^6+79731*x^5+5697*x^4-200033 *x^3-181611*x^2-33264*x-1728),x, algorithm="maxima")
Output:
2*x*log(x)/(25*x^5 - 60*x^4 - 234*x^3 + 332*x^2 + 681*x + 72)
Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (23) = 46\).
Time = 0.12 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.79 \[ \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx=\frac {1}{188356} \, {\left (\frac {6725 \, x^{2} + 28110 \, x - 1296}{25 \, x^{3} + 90 \, x^{2} + 81 \, x + 8} - \frac {269 \, x - 1458}{x^{2} - 6 \, x + 9}\right )} \log \left (x\right ) \] Input:
integrate(((-200*x^4-240*x^3+216*x^2-16*x-48)*log(x)+50*x^4+30*x^3-378*x^2 -470*x-48)/(625*x^9-1125*x^8-11475*x^7+10255*x^6+79731*x^5+5697*x^4-200033 *x^3-181611*x^2-33264*x-1728),x, algorithm="giac")
Output:
1/188356*((6725*x^2 + 28110*x - 1296)/(25*x^3 + 90*x^2 + 81*x + 8) - (269* x - 1458)/(x^2 - 6*x + 9))*log(x)
Time = 4.09 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.14 \[ \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx=\frac {2\,x\,\ln \left (x\right )}{25\,\left (x^5-\frac {12\,x^4}{5}-\frac {234\,x^3}{25}+\frac {332\,x^2}{25}+\frac {681\,x}{25}+\frac {72}{25}\right )} \] Input:
int((470*x + log(x)*(16*x - 216*x^2 + 240*x^3 + 200*x^4 + 48) + 378*x^2 - 30*x^3 - 50*x^4 + 48)/(33264*x + 181611*x^2 + 200033*x^3 - 5697*x^4 - 7973 1*x^5 - 10255*x^6 + 11475*x^7 + 1125*x^8 - 625*x^9 + 1728),x)
Output:
(2*x*log(x))/(25*((681*x)/25 + (332*x^2)/25 - (234*x^3)/25 - (12*x^4)/5 + x^5 + 72/25))
Time = 0.21 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.14 \[ \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx=\frac {2 \,\mathrm {log}\left (x \right ) x}{25 x^{5}-60 x^{4}-234 x^{3}+332 x^{2}+681 x +72} \] Input:
int(((-200*x^4-240*x^3+216*x^2-16*x-48)*log(x)+50*x^4+30*x^3-378*x^2-470*x -48)/(625*x^9-1125*x^8-11475*x^7+10255*x^6+79731*x^5+5697*x^4-200033*x^3-1 81611*x^2-33264*x-1728),x)
Output:
(2*log(x)*x)/(25*x**5 - 60*x**4 - 234*x**3 + 332*x**2 + 681*x + 72)