Integrand size = 202, antiderivative size = 28 \begin {dmath*} \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\frac {\log (x)}{16-8 x+\frac {5}{x^2+\frac {4}{4-\log (x)}}} \end {dmath*}
Time = 0.07 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75 \begin {dmath*} \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\frac {\log (x) \left (4+4 x^2-x^2 \log (x)\right )}{84-32 x+64 x^2-32 x^3+\left (-5-16 x^2+8 x^3\right ) \log (x)} \end {dmath*}
Integrate[(336 - 128*x + 592*x^2 - 256*x^3 + 256*x^4 - 128*x^5 + (128*x - 8*x^2 + 320*x^3 - 128*x^4 + 192*x^5)*Log[x] + (-75*x^2 - 64*x^3 + 16*x^4 - 72*x^5)*Log[x]^2 + (10*x^2 + 8*x^5)*Log[x]^3)/(7056*x - 5376*x^2 + 11776* x^3 - 9472*x^4 + 6144*x^5 - 4096*x^6 + 1024*x^7 + (-840*x + 320*x^2 - 3328 *x^3 + 2688*x^4 - 2560*x^5 + 2048*x^6 - 512*x^7)*Log[x] + (25*x + 160*x^3 - 80*x^4 + 256*x^5 - 256*x^6 + 64*x^7)*Log[x]^2),x]
(Log[x]*(4 + 4*x^2 - x^2*Log[x]))/(84 - 32*x + 64*x^2 - 32*x^3 + (-5 - 16* x^2 + 8*x^3)*Log[x])
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.
| \(\displaystyle \int \frac {-128 x^5+256 x^4-256 x^3+592 x^2+\left (8 x^5+10 x^2\right ) \log ^3(x)+\left (-72 x^5+16 x^4-64 x^3-75 x^2\right ) \log ^2(x)+\left (192 x^5-128 x^4+320 x^3-8 x^2+128 x\right ) \log (x)-128 x+336}{1024 x^7-4096 x^6+6144 x^5-9472 x^4+11776 x^3-5376 x^2+\left (64 x^7-256 x^6+256 x^5-80 x^4+160 x^3+25 x\right ) \log ^2(x)+\left (-512 x^7+2048 x^6-2560 x^5+2688 x^4-3328 x^3+320 x^2-840 x\right ) \log (x)+7056 x} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-128 x^5+256 x^4-256 x^3+592 x^2+\left (8 x^5+10 x^2\right ) \log ^3(x)+\left (-72 x^5+16 x^4-64 x^3-75 x^2\right ) \log ^2(x)+\left (192 x^5-128 x^4+320 x^3-8 x^2+128 x\right ) \log (x)-128 x+336}{x \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \left (4 x^3+5\right ) \log ^3(x)-x^2 \left (72 x^3-16 x^2+64 x+75\right ) \log ^2(x)+8 x \left (24 x^4-16 x^3+40 x^2-x+16\right ) \log (x)-16 \left (8 x^5-16 x^4+16 x^3-37 x^2+8 x-21\right )}{x \left (-32 x^3+64 x^2+\left (8 x^3-16 x^2-5\right ) \log (x)-32 x+84\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4 x^3+5\right ) \log (x)}{\left (8 x^3-16 x^2-5\right )^2}+\frac {640 \left (48 x^5-160 x^4+192 x^3-254 x^2+232 x+5\right )}{\left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )}-\frac {x \left (64 x^6-256 x^5+256 x^4-80 x^3+160 x^2-960 x+1305\right )}{\left (8 x^3-16 x^2-5\right )^3}+\frac {80 \left (512 x^9-3072 x^8+10752 x^7-32704 x^6+63232 x^5-67200 x^4+59992 x^3-45488 x^2-3160 x-525\right )}{x \left (8 x^3-16 x^2-5\right )^3 \left (-32 x^3+8 x^3 \log (x)+64 x^2-16 x^2 \log (x)-32 x-5 \log (x)+84\right )^2}\right )dx\) |
Int[(336 - 128*x + 592*x^2 - 256*x^3 + 256*x^4 - 128*x^5 + (128*x - 8*x^2 + 320*x^3 - 128*x^4 + 192*x^5)*Log[x] + (-75*x^2 - 64*x^3 + 16*x^4 - 72*x^ 5)*Log[x]^2 + (10*x^2 + 8*x^5)*Log[x]^3)/(7056*x - 5376*x^2 + 11776*x^3 - 9472*x^4 + 6144*x^5 - 4096*x^6 + 1024*x^7 + (-840*x + 320*x^2 - 3328*x^3 + 2688*x^4 - 2560*x^5 + 2048*x^6 - 512*x^7)*Log[x] + (25*x + 160*x^3 - 80*x ^4 + 256*x^5 - 256*x^6 + 64*x^7)*Log[x]^2),x]
3.6.86.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs. \(2(28)=56\).
Time = 1.43 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07
| method | result | size |
| default | \(\frac {4 \ln \left (x \right )+4 x^{2} \ln \left (x \right )-x^{2} \ln \left (x \right )^{2}}{8 x^{3} \ln \left (x \right )-16 x^{2} \ln \left (x \right )-32 x^{3}+64 x^{2}-5 \ln \left (x \right )-32 x +84}\) | \(58\) |
| parallelrisch | \(\frac {-8 x^{2} \ln \left (x \right )^{2}+32 \ln \left (x \right )+32 x^{2} \ln \left (x \right )}{64 x^{3} \ln \left (x \right )-128 x^{2} \ln \left (x \right )-256 x^{3}+512 x^{2}-40 \ln \left (x \right )-256 x +672}\) | \(59\) |
| risch | \(-\frac {x^{2} \ln \left (x \right )}{8 x^{3}-16 x^{2}-5}-\frac {20}{64 x^{6}-256 x^{5}+256 x^{4}-80 x^{3}+160 x^{2}+25}-\frac {80 \left (8 x^{3}-16 x^{2}+8 x -21\right )}{\left (64 x^{6}-256 x^{5}+256 x^{4}-80 x^{3}+160 x^{2}+25\right ) \left (8 x^{3} \ln \left (x \right )-16 x^{2} \ln \left (x \right )-32 x^{3}+64 x^{2}-5 \ln \left (x \right )-32 x +84\right )}\) | \(135\) |
int(((8*x^5+10*x^2)*ln(x)^3+(-72*x^5+16*x^4-64*x^3-75*x^2)*ln(x)^2+(192*x^ 5-128*x^4+320*x^3-8*x^2+128*x)*ln(x)-128*x^5+256*x^4-256*x^3+592*x^2-128*x +336)/((64*x^7-256*x^6+256*x^5-80*x^4+160*x^3+25*x)*ln(x)^2+(-512*x^7+2048 *x^6-2560*x^5+2688*x^4-3328*x^3+320*x^2-840*x)*ln(x)+1024*x^7-4096*x^6+614 4*x^5-9472*x^4+11776*x^3-5376*x^2+7056*x),x,method=_RETURNVERBOSE)
Time = 0.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86 \begin {dmath*} \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\frac {x^{2} \log \left (x\right )^{2} - 4 \, {\left (x^{2} + 1\right )} \log \left (x\right )}{32 \, x^{3} - 64 \, x^{2} - {\left (8 \, x^{3} - 16 \, x^{2} - 5\right )} \log \left (x\right ) + 32 \, x - 84} \end {dmath*}
integrate(((8*x^5+10*x^2)*log(x)^3+(-72*x^5+16*x^4-64*x^3-75*x^2)*log(x)^2 +(192*x^5-128*x^4+320*x^3-8*x^2+128*x)*log(x)-128*x^5+256*x^4-256*x^3+592* x^2-128*x+336)/((64*x^7-256*x^6+256*x^5-80*x^4+160*x^3+25*x)*log(x)^2+(-51 2*x^7+2048*x^6-2560*x^5+2688*x^4-3328*x^3+320*x^2-840*x)*log(x)+1024*x^7-4 096*x^6+6144*x^5-9472*x^4+11776*x^3-5376*x^2+7056*x),x, algorithm=\
(x^2*log(x)^2 - 4*(x^2 + 1)*log(x))/(32*x^3 - 64*x^2 - (8*x^3 - 16*x^2 - 5 )*log(x) + 32*x - 84)
Leaf count of result is larger than twice the leaf count of optimal. 153 vs. \(2 (19) = 38\).
Time = 0.43 (sec) , antiderivative size = 153, normalized size of antiderivative = 5.46 \begin {dmath*} \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=- \frac {x^{2} \log {\left (x \right )}}{8 x^{3} - 16 x^{2} - 5} + \frac {- 640 x^{3} + 1280 x^{2} - 640 x + 1680}{- 2048 x^{9} + 12288 x^{8} - 26624 x^{7} + 32512 x^{6} - 39936 x^{5} + 34304 x^{4} - 12640 x^{3} + 15040 x^{2} - 800 x + \left (512 x^{9} - 3072 x^{8} + 6144 x^{7} - 5056 x^{6} + 3840 x^{5} - 3840 x^{4} + 600 x^{3} - 1200 x^{2} - 125\right ) \log {\left (x \right )} + 2100} - \frac {20}{64 x^{6} - 256 x^{5} + 256 x^{4} - 80 x^{3} + 160 x^{2} + 25} \end {dmath*}
integrate(((8*x**5+10*x**2)*ln(x)**3+(-72*x**5+16*x**4-64*x**3-75*x**2)*ln (x)**2+(192*x**5-128*x**4+320*x**3-8*x**2+128*x)*ln(x)-128*x**5+256*x**4-2 56*x**3+592*x**2-128*x+336)/((64*x**7-256*x**6+256*x**5-80*x**4+160*x**3+2 5*x)*ln(x)**2+(-512*x**7+2048*x**6-2560*x**5+2688*x**4-3328*x**3+320*x**2- 840*x)*ln(x)+1024*x**7-4096*x**6+6144*x**5-9472*x**4+11776*x**3-5376*x**2+ 7056*x),x)
-x**2*log(x)/(8*x**3 - 16*x**2 - 5) + (-640*x**3 + 1280*x**2 - 640*x + 168 0)/(-2048*x**9 + 12288*x**8 - 26624*x**7 + 32512*x**6 - 39936*x**5 + 34304 *x**4 - 12640*x**3 + 15040*x**2 - 800*x + (512*x**9 - 3072*x**8 + 6144*x** 7 - 5056*x**6 + 3840*x**5 - 3840*x**4 + 600*x**3 - 1200*x**2 - 125)*log(x) + 2100) - 20/(64*x**6 - 256*x**5 + 256*x**4 - 80*x**3 + 160*x**2 + 25)
Time = 0.24 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86 \begin {dmath*} \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\frac {x^{2} \log \left (x\right )^{2} - 4 \, {\left (x^{2} + 1\right )} \log \left (x\right )}{32 \, x^{3} - 64 \, x^{2} - {\left (8 \, x^{3} - 16 \, x^{2} - 5\right )} \log \left (x\right ) + 32 \, x - 84} \end {dmath*}
integrate(((8*x^5+10*x^2)*log(x)^3+(-72*x^5+16*x^4-64*x^3-75*x^2)*log(x)^2 +(192*x^5-128*x^4+320*x^3-8*x^2+128*x)*log(x)-128*x^5+256*x^4-256*x^3+592* x^2-128*x+336)/((64*x^7-256*x^6+256*x^5-80*x^4+160*x^3+25*x)*log(x)^2+(-51 2*x^7+2048*x^6-2560*x^5+2688*x^4-3328*x^3+320*x^2-840*x)*log(x)+1024*x^7-4 096*x^6+6144*x^5-9472*x^4+11776*x^3-5376*x^2+7056*x),x, algorithm=\
(x^2*log(x)^2 - 4*(x^2 + 1)*log(x))/(32*x^3 - 64*x^2 - (8*x^3 - 16*x^2 - 5 )*log(x) + 32*x - 84)
Leaf count of result is larger than twice the leaf count of optimal. 177 vs. \(2 (27) = 54\).
Time = 0.30 (sec) , antiderivative size = 177, normalized size of antiderivative = 6.32 \begin {dmath*} \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=-\frac {x^{2} \log \left (x\right )}{8 \, x^{3} - 16 \, x^{2} - 5} - \frac {80 \, {\left (8 \, x^{3} - 16 \, x^{2} + 8 \, x - 21\right )}}{512 \, x^{9} \log \left (x\right ) - 2048 \, x^{9} - 3072 \, x^{8} \log \left (x\right ) + 12288 \, x^{8} + 6144 \, x^{7} \log \left (x\right ) - 26624 \, x^{7} - 5056 \, x^{6} \log \left (x\right ) + 32512 \, x^{6} + 3840 \, x^{5} \log \left (x\right ) - 39936 \, x^{5} - 3840 \, x^{4} \log \left (x\right ) + 34304 \, x^{4} + 600 \, x^{3} \log \left (x\right ) - 12640 \, x^{3} - 1200 \, x^{2} \log \left (x\right ) + 15040 \, x^{2} - 800 \, x - 125 \, \log \left (x\right ) + 2100} - \frac {20}{64 \, x^{6} - 256 \, x^{5} + 256 \, x^{4} - 80 \, x^{3} + 160 \, x^{2} + 25} \end {dmath*}
integrate(((8*x^5+10*x^2)*log(x)^3+(-72*x^5+16*x^4-64*x^3-75*x^2)*log(x)^2 +(192*x^5-128*x^4+320*x^3-8*x^2+128*x)*log(x)-128*x^5+256*x^4-256*x^3+592* x^2-128*x+336)/((64*x^7-256*x^6+256*x^5-80*x^4+160*x^3+25*x)*log(x)^2+(-51 2*x^7+2048*x^6-2560*x^5+2688*x^4-3328*x^3+320*x^2-840*x)*log(x)+1024*x^7-4 096*x^6+6144*x^5-9472*x^4+11776*x^3-5376*x^2+7056*x),x, algorithm=\
-x^2*log(x)/(8*x^3 - 16*x^2 - 5) - 80*(8*x^3 - 16*x^2 + 8*x - 21)/(512*x^9 *log(x) - 2048*x^9 - 3072*x^8*log(x) + 12288*x^8 + 6144*x^7*log(x) - 26624 *x^7 - 5056*x^6*log(x) + 32512*x^6 + 3840*x^5*log(x) - 39936*x^5 - 3840*x^ 4*log(x) + 34304*x^4 + 600*x^3*log(x) - 12640*x^3 - 1200*x^2*log(x) + 1504 0*x^2 - 800*x - 125*log(x) + 2100) - 20/(64*x^6 - 256*x^5 + 256*x^4 - 80*x ^3 + 160*x^2 + 25)
Timed out. \begin {dmath*} \int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx=\int \frac {\ln \left (x\right )\,\left (192\,x^5-128\,x^4+320\,x^3-8\,x^2+128\,x\right )-128\,x+{\ln \left (x\right )}^3\,\left (8\,x^5+10\,x^2\right )+592\,x^2-256\,x^3+256\,x^4-128\,x^5-{\ln \left (x\right )}^2\,\left (72\,x^5-16\,x^4+64\,x^3+75\,x^2\right )+336}{7056\,x-\ln \left (x\right )\,\left (512\,x^7-2048\,x^6+2560\,x^5-2688\,x^4+3328\,x^3-320\,x^2+840\,x\right )-5376\,x^2+11776\,x^3-9472\,x^4+6144\,x^5-4096\,x^6+1024\,x^7+{\ln \left (x\right )}^2\,\left (64\,x^7-256\,x^6+256\,x^5-80\,x^4+160\,x^3+25\,x\right )} \,d x \end {dmath*}
int((log(x)*(128*x - 8*x^2 + 320*x^3 - 128*x^4 + 192*x^5) - 128*x + log(x) ^3*(10*x^2 + 8*x^5) + 592*x^2 - 256*x^3 + 256*x^4 - 128*x^5 - log(x)^2*(75 *x^2 + 64*x^3 - 16*x^4 + 72*x^5) + 336)/(7056*x - log(x)*(840*x - 320*x^2 + 3328*x^3 - 2688*x^4 + 2560*x^5 - 2048*x^6 + 512*x^7) - 5376*x^2 + 11776* x^3 - 9472*x^4 + 6144*x^5 - 4096*x^6 + 1024*x^7 + log(x)^2*(25*x + 160*x^3 - 80*x^4 + 256*x^5 - 256*x^6 + 64*x^7)),x)
int((log(x)*(128*x - 8*x^2 + 320*x^3 - 128*x^4 + 192*x^5) - 128*x + log(x) ^3*(10*x^2 + 8*x^5) + 592*x^2 - 256*x^3 + 256*x^4 - 128*x^5 - log(x)^2*(75 *x^2 + 64*x^3 - 16*x^4 + 72*x^5) + 336)/(7056*x - log(x)*(840*x - 320*x^2 + 3328*x^3 - 2688*x^4 + 2560*x^5 - 2048*x^6 + 512*x^7) - 5376*x^2 + 11776* x^3 - 9472*x^4 + 6144*x^5 - 4096*x^6 + 1024*x^7 + log(x)^2*(25*x + 160*x^3 - 80*x^4 + 256*x^5 - 256*x^6 + 64*x^7)), x)