Integrand size = 313, antiderivative size = 33 \[ \int \frac {\left (-12+30 x-24 x^2+(24-12 x) \log (2-x)\right ) \log (x)+\left (72 x-96 x^2+14 x^3+24 x^4-8 x^5+\left (-96 x+64 x^2+24 x^3-16 x^4\right ) \log (2-x)+\left (32 x-8 x^3\right ) \log ^2(2-x)\right ) \log (3 \log (x))+\left (72 x-114 x^2+47 x^3+4 x^4-4 x^5+\left (-96 x+88 x^2-4 x^3-8 x^4\right ) \log (2-x)+\left (32 x-8 x^2-4 x^3\right ) \log ^2(2-x)\right ) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+\left (-72 x^2+84 x^3-24 x^4+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (-18 x^4+33 x^5-20 x^6+4 x^7+\left (24 x^4-28 x^5+8 x^6\right ) \log (2-x)+\left (-8 x^4+4 x^5\right ) \log ^2(2-x)\right ) \log (x) \log ^4(3 \log (x))} \, dx=\frac {2+x}{-\frac {3}{-\frac {3}{2}+x+\log (2-x)}+x^2 \log ^2(3 \log (x))} \] Output:
(2+x)/(ln(3*ln(x))^2*x^2-3/(x-3/2+ln(2-x)))
Time = 0.19 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.36 \[ \int \frac {\left (-12+30 x-24 x^2+(24-12 x) \log (2-x)\right ) \log (x)+\left (72 x-96 x^2+14 x^3+24 x^4-8 x^5+\left (-96 x+64 x^2+24 x^3-16 x^4\right ) \log (2-x)+\left (32 x-8 x^3\right ) \log ^2(2-x)\right ) \log (3 \log (x))+\left (72 x-114 x^2+47 x^3+4 x^4-4 x^5+\left (-96 x+88 x^2-4 x^3-8 x^4\right ) \log (2-x)+\left (32 x-8 x^2-4 x^3\right ) \log ^2(2-x)\right ) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+\left (-72 x^2+84 x^3-24 x^4+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (-18 x^4+33 x^5-20 x^6+4 x^7+\left (24 x^4-28 x^5+8 x^6\right ) \log (2-x)+\left (-8 x^4+4 x^5\right ) \log ^2(2-x)\right ) \log (x) \log ^4(3 \log (x))} \, dx=\frac {(2+x) (-3+2 x+2 \log (2-x))}{-6+x^2 (-3+2 x+2 \log (2-x)) \log ^2(3 \log (x))} \] Input:
Integrate[((-12 + 30*x - 24*x^2 + (24 - 12*x)*Log[2 - x])*Log[x] + (72*x - 96*x^2 + 14*x^3 + 24*x^4 - 8*x^5 + (-96*x + 64*x^2 + 24*x^3 - 16*x^4)*Log [2 - x] + (32*x - 8*x^3)*Log[2 - x]^2)*Log[3*Log[x]] + (72*x - 114*x^2 + 4 7*x^3 + 4*x^4 - 4*x^5 + (-96*x + 88*x^2 - 4*x^3 - 8*x^4)*Log[2 - x] + (32* x - 8*x^2 - 4*x^3)*Log[2 - x]^2)*Log[x]*Log[3*Log[x]]^2)/((-72 + 36*x)*Log [x] + (-72*x^2 + 84*x^3 - 24*x^4 + (48*x^2 - 24*x^3)*Log[2 - x])*Log[x]*Lo g[3*Log[x]]^2 + (-18*x^4 + 33*x^5 - 20*x^6 + 4*x^7 + (24*x^4 - 28*x^5 + 8* x^6)*Log[2 - x] + (-8*x^4 + 4*x^5)*Log[2 - x]^2)*Log[x]*Log[3*Log[x]]^4),x ]
Output:
((2 + x)*(-3 + 2*x + 2*Log[2 - x]))/(-6 + x^2*(-3 + 2*x + 2*Log[2 - x])*Lo g[3*Log[x]]^2)
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.
| \(\displaystyle \int \frac {\left (-24 x^2+30 x+(24-12 x) \log (2-x)-12\right ) \log (x)+\left (-4 x^5+4 x^4+47 x^3-114 x^2+\left (-4 x^3-8 x^2+32 x\right ) \log ^2(2-x)+\left (-8 x^4-4 x^3+88 x^2-96 x\right ) \log (2-x)+72 x\right ) \log (x) \log ^2(3 \log (x))+\left (-8 x^5+24 x^4+14 x^3+\left (32 x-8 x^3\right ) \log ^2(2-x)-96 x^2+\left (-16 x^4+24 x^3+64 x^2-96 x\right ) \log (2-x)+72 x\right ) \log (3 \log (x))}{\left (-24 x^4+84 x^3-72 x^2+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (4 x^7-20 x^6+33 x^5-18 x^4+\left (4 x^5-8 x^4\right ) \log ^2(2-x)+\left (8 x^6-28 x^5+24 x^4\right ) \log (2-x)\right ) \log (x) \log ^4(3 \log (x))+(36 x-72) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log (x) \left (6 \left (4 x^2-5 x+2\right )+4 x \left (x^2+2 x-8\right ) \log ^2(2-x) \log ^2(3 \log (x))+(3-2 x)^2 x \left (x^2+2 x-8\right ) \log ^2(3 \log (x))+4 (x-2) \log (2-x) \left (x \left (2 x^2+5 x-12\right ) \log ^2(3 \log (x))+3\right )\right )+2 x \left (x^2-4\right ) \log (3 \log (x)) (2 x+2 \log (2-x)-3)^2}{(2-x) \log (x) \left (6-x^2 (2 x+2 \log (2-x)-3) \log ^2(3 \log (x))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {(x+4) (2 x+2 \log (2-x)-3)}{x \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )}-\frac {2 (x+2) \left (4 x^5 \log (3 \log (x))+8 x^4 \log (2-x) \log (3 \log (x))-20 x^4 \log (3 \log (x))+4 x^3 \log ^2(2-x) \log (3 \log (x))-28 x^3 \log (2-x) \log (3 \log (x))+33 x^3 \log (3 \log (x))-8 x^2 \log ^2(2-x) \log (3 \log (x))+18 x^2 \log (x)+24 x^2 \log (2-x) \log (3 \log (x))-18 x^2 \log (3 \log (x))+12 x \log (2-x) \log (x)-48 x \log (x)-24 \log (2-x) \log (x)+36 \log (x)\right )}{(x-2) x \log (x) \left (2 x^3 \log ^2(3 \log (x))+2 x^2 \log (2-x) \log ^2(3 \log (x))-3 x^2 \log ^2(3 \log (x))-6\right )^2}\right )dx\) |
Input:
Int[((-12 + 30*x - 24*x^2 + (24 - 12*x)*Log[2 - x])*Log[x] + (72*x - 96*x^ 2 + 14*x^3 + 24*x^4 - 8*x^5 + (-96*x + 64*x^2 + 24*x^3 - 16*x^4)*Log[2 - x ] + (32*x - 8*x^3)*Log[2 - x]^2)*Log[3*Log[x]] + (72*x - 114*x^2 + 47*x^3 + 4*x^4 - 4*x^5 + (-96*x + 88*x^2 - 4*x^3 - 8*x^4)*Log[2 - x] + (32*x - 8* x^2 - 4*x^3)*Log[2 - x]^2)*Log[x]*Log[3*Log[x]]^2)/((-72 + 36*x)*Log[x] + (-72*x^2 + 84*x^3 - 24*x^4 + (48*x^2 - 24*x^3)*Log[2 - x])*Log[x]*Log[3*Lo g[x]]^2 + (-18*x^4 + 33*x^5 - 20*x^6 + 4*x^7 + (24*x^4 - 28*x^5 + 8*x^6)*L og[2 - x] + (-8*x^4 + 4*x^5)*Log[2 - x]^2)*Log[x]*Log[3*Log[x]]^4),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(72\) vs. \(2(31)=62\).
Time = 0.07 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.21
\[\frac {2 x^{2}+2 x \ln \left (2-x \right )+x +4 \ln \left (2-x \right )-6}{2 \ln \left (2-x \right ) \ln \left (3 \ln \left (x \right )\right )^{2} x^{2}+2 \ln \left (3 \ln \left (x \right )\right )^{2} x^{3}-3 \ln \left (3 \ln \left (x \right )\right )^{2} x^{2}-6}\]
Input:
int((((-4*x^3-8*x^2+32*x)*ln(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*ln(2-x)-4*x ^5+4*x^4+47*x^3-114*x^2+72*x)*ln(x)*ln(3*ln(x))^2+((-8*x^3+32*x)*ln(2-x)^2 +(-16*x^4+24*x^3+64*x^2-96*x)*ln(2-x)-8*x^5+24*x^4+14*x^3-96*x^2+72*x)*ln( 3*ln(x))+((-12*x+24)*ln(2-x)-24*x^2+30*x-12)*ln(x))/(((4*x^5-8*x^4)*ln(2-x )^2+(8*x^6-28*x^5+24*x^4)*ln(2-x)+4*x^7-20*x^6+33*x^5-18*x^4)*ln(x)*ln(3*l n(x))^4+((-24*x^3+48*x^2)*ln(2-x)-24*x^4+84*x^3-72*x^2)*ln(x)*ln(3*ln(x))^ 2+(36*x-72)*ln(x)),x)
Output:
(2*x^2+2*x*ln(2-x)+x+4*ln(2-x)-6)/(2*ln(2-x)*ln(3*ln(x))^2*x^2+2*ln(3*ln(x ))^2*x^3-3*ln(3*ln(x))^2*x^2-6)
Time = 0.10 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.64 \[ \int \frac {\left (-12+30 x-24 x^2+(24-12 x) \log (2-x)\right ) \log (x)+\left (72 x-96 x^2+14 x^3+24 x^4-8 x^5+\left (-96 x+64 x^2+24 x^3-16 x^4\right ) \log (2-x)+\left (32 x-8 x^3\right ) \log ^2(2-x)\right ) \log (3 \log (x))+\left (72 x-114 x^2+47 x^3+4 x^4-4 x^5+\left (-96 x+88 x^2-4 x^3-8 x^4\right ) \log (2-x)+\left (32 x-8 x^2-4 x^3\right ) \log ^2(2-x)\right ) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+\left (-72 x^2+84 x^3-24 x^4+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (-18 x^4+33 x^5-20 x^6+4 x^7+\left (24 x^4-28 x^5+8 x^6\right ) \log (2-x)+\left (-8 x^4+4 x^5\right ) \log ^2(2-x)\right ) \log (x) \log ^4(3 \log (x))} \, dx=\frac {2 \, x^{2} + 2 \, {\left (x + 2\right )} \log \left (-x + 2\right ) + x - 6}{{\left (2 \, x^{3} + 2 \, x^{2} \log \left (-x + 2\right ) - 3 \, x^{2}\right )} \log \left (3 \, \log \left (x\right )\right )^{2} - 6} \] Input:
integrate((((-4*x^3-8*x^2+32*x)*log(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*log( 2-x)-4*x^5+4*x^4+47*x^3-114*x^2+72*x)*log(x)*log(3*log(x))^2+((-8*x^3+32*x )*log(2-x)^2+(-16*x^4+24*x^3+64*x^2-96*x)*log(2-x)-8*x^5+24*x^4+14*x^3-96* x^2+72*x)*log(3*log(x))+((-12*x+24)*log(2-x)-24*x^2+30*x-12)*log(x))/(((4* x^5-8*x^4)*log(2-x)^2+(8*x^6-28*x^5+24*x^4)*log(2-x)+4*x^7-20*x^6+33*x^5-1 8*x^4)*log(x)*log(3*log(x))^4+((-24*x^3+48*x^2)*log(2-x)-24*x^4+84*x^3-72* x^2)*log(x)*log(3*log(x))^2+(36*x-72)*log(x)),x, algorithm="fricas")
Output:
(2*x^2 + 2*(x + 2)*log(-x + 2) + x - 6)/((2*x^3 + 2*x^2*log(-x + 2) - 3*x^ 2)*log(3*log(x))^2 - 6)
Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (26) = 52\).
Time = 0.90 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.61 \[ \int \frac {\left (-12+30 x-24 x^2+(24-12 x) \log (2-x)\right ) \log (x)+\left (72 x-96 x^2+14 x^3+24 x^4-8 x^5+\left (-96 x+64 x^2+24 x^3-16 x^4\right ) \log (2-x)+\left (32 x-8 x^3\right ) \log ^2(2-x)\right ) \log (3 \log (x))+\left (72 x-114 x^2+47 x^3+4 x^4-4 x^5+\left (-96 x+88 x^2-4 x^3-8 x^4\right ) \log (2-x)+\left (32 x-8 x^2-4 x^3\right ) \log ^2(2-x)\right ) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+\left (-72 x^2+84 x^3-24 x^4+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (-18 x^4+33 x^5-20 x^6+4 x^7+\left (24 x^4-28 x^5+8 x^6\right ) \log (2-x)+\left (-8 x^4+4 x^5\right ) \log ^2(2-x)\right ) \log (x) \log ^4(3 \log (x))} \, dx=\frac {2 x^{2} + 2 x \log {\left (2 - x \right )} + x + 4 \log {\left (2 - x \right )} - 6}{\left (2 x^{3} + 2 x^{2} \log {\left (2 - x \right )} - 3 x^{2}\right ) \log {\left (3 \log {\left (x \right )} \right )}^{2} - 6} \] Input:
integrate((((-4*x**3-8*x**2+32*x)*ln(2-x)**2+(-8*x**4-4*x**3+88*x**2-96*x) *ln(2-x)-4*x**5+4*x**4+47*x**3-114*x**2+72*x)*ln(x)*ln(3*ln(x))**2+((-8*x* *3+32*x)*ln(2-x)**2+(-16*x**4+24*x**3+64*x**2-96*x)*ln(2-x)-8*x**5+24*x**4 +14*x**3-96*x**2+72*x)*ln(3*ln(x))+((-12*x+24)*ln(2-x)-24*x**2+30*x-12)*ln (x))/(((4*x**5-8*x**4)*ln(2-x)**2+(8*x**6-28*x**5+24*x**4)*ln(2-x)+4*x**7- 20*x**6+33*x**5-18*x**4)*ln(x)*ln(3*ln(x))**4+((-24*x**3+48*x**2)*ln(2-x)- 24*x**4+84*x**3-72*x**2)*ln(x)*ln(3*ln(x))**2+(36*x-72)*ln(x)),x)
Output:
(2*x**2 + 2*x*log(2 - x) + x + 4*log(2 - x) - 6)/((2*x**3 + 2*x**2*log(2 - x) - 3*x**2)*log(3*log(x))**2 - 6)
\[ \int \frac {\left (-12+30 x-24 x^2+(24-12 x) \log (2-x)\right ) \log (x)+\left (72 x-96 x^2+14 x^3+24 x^4-8 x^5+\left (-96 x+64 x^2+24 x^3-16 x^4\right ) \log (2-x)+\left (32 x-8 x^3\right ) \log ^2(2-x)\right ) \log (3 \log (x))+\left (72 x-114 x^2+47 x^3+4 x^4-4 x^5+\left (-96 x+88 x^2-4 x^3-8 x^4\right ) \log (2-x)+\left (32 x-8 x^2-4 x^3\right ) \log ^2(2-x)\right ) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+\left (-72 x^2+84 x^3-24 x^4+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (-18 x^4+33 x^5-20 x^6+4 x^7+\left (24 x^4-28 x^5+8 x^6\right ) \log (2-x)+\left (-8 x^4+4 x^5\right ) \log ^2(2-x)\right ) \log (x) \log ^4(3 \log (x))} \, dx=\int { -\frac {{\left (4 \, x^{5} - 4 \, x^{4} - 47 \, x^{3} + 4 \, {\left (x^{3} + 2 \, x^{2} - 8 \, x\right )} \log \left (-x + 2\right )^{2} + 114 \, x^{2} + 4 \, {\left (2 \, x^{4} + x^{3} - 22 \, x^{2} + 24 \, x\right )} \log \left (-x + 2\right ) - 72 \, x\right )} \log \left (x\right ) \log \left (3 \, \log \left (x\right )\right )^{2} + 6 \, {\left (4 \, x^{2} + 2 \, {\left (x - 2\right )} \log \left (-x + 2\right ) - 5 \, x + 2\right )} \log \left (x\right ) + 2 \, {\left (4 \, x^{5} - 12 \, x^{4} - 7 \, x^{3} + 4 \, {\left (x^{3} - 4 \, x\right )} \log \left (-x + 2\right )^{2} + 48 \, x^{2} + 4 \, {\left (2 \, x^{4} - 3 \, x^{3} - 8 \, x^{2} + 12 \, x\right )} \log \left (-x + 2\right ) - 36 \, x\right )} \log \left (3 \, \log \left (x\right )\right )}{{\left (4 \, x^{7} - 20 \, x^{6} + 33 \, x^{5} - 18 \, x^{4} + 4 \, {\left (x^{5} - 2 \, x^{4}\right )} \log \left (-x + 2\right )^{2} + 4 \, {\left (2 \, x^{6} - 7 \, x^{5} + 6 \, x^{4}\right )} \log \left (-x + 2\right )\right )} \log \left (x\right ) \log \left (3 \, \log \left (x\right )\right )^{4} - 12 \, {\left (2 \, x^{4} - 7 \, x^{3} + 6 \, x^{2} + 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \left (-x + 2\right )\right )} \log \left (x\right ) \log \left (3 \, \log \left (x\right )\right )^{2} + 36 \, {\left (x - 2\right )} \log \left (x\right )} \,d x } \] Input:
integrate((((-4*x^3-8*x^2+32*x)*log(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*log( 2-x)-4*x^5+4*x^4+47*x^3-114*x^2+72*x)*log(x)*log(3*log(x))^2+((-8*x^3+32*x )*log(2-x)^2+(-16*x^4+24*x^3+64*x^2-96*x)*log(2-x)-8*x^5+24*x^4+14*x^3-96* x^2+72*x)*log(3*log(x))+((-12*x+24)*log(2-x)-24*x^2+30*x-12)*log(x))/(((4* x^5-8*x^4)*log(2-x)^2+(8*x^6-28*x^5+24*x^4)*log(2-x)+4*x^7-20*x^6+33*x^5-1 8*x^4)*log(x)*log(3*log(x))^4+((-24*x^3+48*x^2)*log(2-x)-24*x^4+84*x^3-72* x^2)*log(x)*log(3*log(x))^2+(36*x-72)*log(x)),x, algorithm="maxima")
Output:
(x + 2)/(x^2*log(3)^2 + 2*x^2*log(3)*log(log(x)) + x^2*log(log(x))^2) - in tegrate(12*((x^6 - x^5 - 4*x^4 + 4*x^3)*log(x)*log(log(x))^3 + 3*(x^6*log( 3) - x^5*log(3) - 4*x^4*log(3) + 4*x^3*log(3))*log(x)*log(log(x))^2 + 6*x^ 3 + 3*(x^6*log(3)^2 - x^5*log(3)^2 - 4*x^4*log(3)^2 + 2*(2*log(3)^2 + 1)*x ^3 - 4*x^2 - 8*x + 16)*log(x)*log(log(x)) - 12*x^2 + (x^6*log(3)^3 - x^5*l og(3)^3 - 4*x^4*log(3)^3 + 2*(2*log(3)^3 + 3*log(3))*x^3 - 12*x^2*log(3) - 24*x*log(3) + 48*log(3))*log(x) - 24*x + 48)/((2*x^7 - 7*x^6 + 6*x^5)*log (x)*log(log(x))^5 + 5*(2*x^7*log(3) - 7*x^6*log(3) + 6*x^5*log(3))*log(x)* log(log(x))^4 + 2*(10*x^7*log(3)^2 - 35*x^6*log(3)^2 + 30*x^5*log(3)^2 - 3 *x^4 + 6*x^3)*log(x)*log(log(x))^3 + 2*(10*x^7*log(3)^3 - 35*x^6*log(3)^3 + 30*x^5*log(3)^3 - 9*x^4*log(3) + 18*x^3*log(3))*log(x)*log(log(x))^2 + ( 10*x^7*log(3)^4 - 35*x^6*log(3)^4 + 30*x^5*log(3)^4 - 18*x^4*log(3)^2 + 36 *x^3*log(3)^2)*log(x)*log(log(x)) + (2*x^7*log(3)^5 - 7*x^6*log(3)^5 + 6*x ^5*log(3)^5 - 6*x^4*log(3)^3 + 12*x^3*log(3)^3)*log(x) + 2*((x^6 - 2*x^5)* log(x)*log(log(x))^5 + 5*(x^6*log(3) - 2*x^5*log(3))*log(x)*log(log(x))^4 + 10*(x^6*log(3)^2 - 2*x^5*log(3)^2)*log(x)*log(log(x))^3 + 10*(x^6*log(3) ^3 - 2*x^5*log(3)^3)*log(x)*log(log(x))^2 + 5*(x^6*log(3)^4 - 2*x^5*log(3) ^4)*log(x)*log(log(x)) + (x^6*log(3)^5 - 2*x^5*log(3)^5)*log(x))*log(-x + 2)), x)
Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (35) = 70\).
Time = 0.80 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.33 \[ \int \frac {\left (-12+30 x-24 x^2+(24-12 x) \log (2-x)\right ) \log (x)+\left (72 x-96 x^2+14 x^3+24 x^4-8 x^5+\left (-96 x+64 x^2+24 x^3-16 x^4\right ) \log (2-x)+\left (32 x-8 x^3\right ) \log ^2(2-x)\right ) \log (3 \log (x))+\left (72 x-114 x^2+47 x^3+4 x^4-4 x^5+\left (-96 x+88 x^2-4 x^3-8 x^4\right ) \log (2-x)+\left (32 x-8 x^2-4 x^3\right ) \log ^2(2-x)\right ) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+\left (-72 x^2+84 x^3-24 x^4+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (-18 x^4+33 x^5-20 x^6+4 x^7+\left (24 x^4-28 x^5+8 x^6\right ) \log (2-x)+\left (-8 x^4+4 x^5\right ) \log ^2(2-x)\right ) \log (x) \log ^4(3 \log (x))} \, dx=\frac {6 \, {\left (x + 2\right )}}{2 \, x^{5} \log \left (3 \, \log \left (x\right )\right )^{4} + 2 \, x^{4} \log \left (-x + 2\right ) \log \left (3 \, \log \left (x\right )\right )^{4} - 3 \, x^{4} \log \left (3 \, \log \left (x\right )\right )^{4} - 6 \, x^{2} \log \left (3 \, \log \left (x\right )\right )^{2}} + \frac {x + 2}{x^{2} \log \left (3 \, \log \left (x\right )\right )^{2}} \] Input:
integrate((((-4*x^3-8*x^2+32*x)*log(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*log( 2-x)-4*x^5+4*x^4+47*x^3-114*x^2+72*x)*log(x)*log(3*log(x))^2+((-8*x^3+32*x )*log(2-x)^2+(-16*x^4+24*x^3+64*x^2-96*x)*log(2-x)-8*x^5+24*x^4+14*x^3-96* x^2+72*x)*log(3*log(x))+((-12*x+24)*log(2-x)-24*x^2+30*x-12)*log(x))/(((4* x^5-8*x^4)*log(2-x)^2+(8*x^6-28*x^5+24*x^4)*log(2-x)+4*x^7-20*x^6+33*x^5-1 8*x^4)*log(x)*log(3*log(x))^4+((-24*x^3+48*x^2)*log(2-x)-24*x^4+84*x^3-72* x^2)*log(x)*log(3*log(x))^2+(36*x-72)*log(x)),x, algorithm="giac")
Output:
6*(x + 2)/(2*x^5*log(3*log(x))^4 + 2*x^4*log(-x + 2)*log(3*log(x))^4 - 3*x ^4*log(3*log(x))^4 - 6*x^2*log(3*log(x))^2) + (x + 2)/(x^2*log(3*log(x))^2 )
Timed out. \[ \int \frac {\left (-12+30 x-24 x^2+(24-12 x) \log (2-x)\right ) \log (x)+\left (72 x-96 x^2+14 x^3+24 x^4-8 x^5+\left (-96 x+64 x^2+24 x^3-16 x^4\right ) \log (2-x)+\left (32 x-8 x^3\right ) \log ^2(2-x)\right ) \log (3 \log (x))+\left (72 x-114 x^2+47 x^3+4 x^4-4 x^5+\left (-96 x+88 x^2-4 x^3-8 x^4\right ) \log (2-x)+\left (32 x-8 x^2-4 x^3\right ) \log ^2(2-x)\right ) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+\left (-72 x^2+84 x^3-24 x^4+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (-18 x^4+33 x^5-20 x^6+4 x^7+\left (24 x^4-28 x^5+8 x^6\right ) \log (2-x)+\left (-8 x^4+4 x^5\right ) \log ^2(2-x)\right ) \log (x) \log ^4(3 \log (x))} \, dx=\int -\frac {\ln \left (x\right )\,\left ({\ln \left (2-x\right )}^2\,\left (4\,x^3+8\,x^2-32\,x\right )-72\,x+114\,x^2-47\,x^3-4\,x^4+4\,x^5+\ln \left (2-x\right )\,\left (8\,x^4+4\,x^3-88\,x^2+96\,x\right )\right )\,{\ln \left (3\,\ln \left (x\right )\right )}^2+\left (96\,x^2-{\ln \left (2-x\right )}^2\,\left (32\,x-8\,x^3\right )-72\,x-14\,x^3-24\,x^4+8\,x^5+\ln \left (2-x\right )\,\left (16\,x^4-24\,x^3-64\,x^2+96\,x\right )\right )\,\ln \left (3\,\ln \left (x\right )\right )+\ln \left (x\right )\,\left (\ln \left (2-x\right )\,\left (12\,x-24\right )-30\,x+24\,x^2+12\right )}{\ln \left (x\right )\,\left (\ln \left (2-x\right )\,\left (8\,x^6-28\,x^5+24\,x^4\right )-{\ln \left (2-x\right )}^2\,\left (8\,x^4-4\,x^5\right )-18\,x^4+33\,x^5-20\,x^6+4\,x^7\right )\,{\ln \left (3\,\ln \left (x\right )\right )}^4+\ln \left (x\right )\,\left (\ln \left (2-x\right )\,\left (48\,x^2-24\,x^3\right )-72\,x^2+84\,x^3-24\,x^4\right )\,{\ln \left (3\,\ln \left (x\right )\right )}^2+\ln \left (x\right )\,\left (36\,x-72\right )} \,d x \] Input:
int(-(log(x)*(log(2 - x)*(12*x - 24) - 30*x + 24*x^2 + 12) - log(3*log(x)) *(72*x + log(2 - x)^2*(32*x - 8*x^3) - 96*x^2 + 14*x^3 + 24*x^4 - 8*x^5 - log(2 - x)*(96*x - 64*x^2 - 24*x^3 + 16*x^4)) + log(3*log(x))^2*log(x)*(lo g(2 - x)^2*(8*x^2 - 32*x + 4*x^3) - 72*x + 114*x^2 - 47*x^3 - 4*x^4 + 4*x^ 5 + log(2 - x)*(96*x - 88*x^2 + 4*x^3 + 8*x^4)))/(log(x)*(36*x - 72) + log (3*log(x))^2*log(x)*(log(2 - x)*(48*x^2 - 24*x^3) - 72*x^2 + 84*x^3 - 24*x ^4) + log(3*log(x))^4*log(x)*(log(2 - x)*(24*x^4 - 28*x^5 + 8*x^6) - log(2 - x)^2*(8*x^4 - 4*x^5) - 18*x^4 + 33*x^5 - 20*x^6 + 4*x^7)),x)
Output:
int(-(log(x)*(log(2 - x)*(12*x - 24) - 30*x + 24*x^2 + 12) - log(3*log(x)) *(72*x + log(2 - x)^2*(32*x - 8*x^3) - 96*x^2 + 14*x^3 + 24*x^4 - 8*x^5 - log(2 - x)*(96*x - 64*x^2 - 24*x^3 + 16*x^4)) + log(3*log(x))^2*log(x)*(lo g(2 - x)^2*(8*x^2 - 32*x + 4*x^3) - 72*x + 114*x^2 - 47*x^3 - 4*x^4 + 4*x^ 5 + log(2 - x)*(96*x - 88*x^2 + 4*x^3 + 8*x^4)))/(log(x)*(36*x - 72) + log (3*log(x))^2*log(x)*(log(2 - x)*(48*x^2 - 24*x^3) - 72*x^2 + 84*x^3 - 24*x ^4) + log(3*log(x))^4*log(x)*(log(2 - x)*(24*x^4 - 28*x^5 + 8*x^6) - log(2 - x)^2*(8*x^4 - 4*x^5) - 18*x^4 + 33*x^5 - 20*x^6 + 4*x^7)), x)
Time = 0.23 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.18 \[ \int \frac {\left (-12+30 x-24 x^2+(24-12 x) \log (2-x)\right ) \log (x)+\left (72 x-96 x^2+14 x^3+24 x^4-8 x^5+\left (-96 x+64 x^2+24 x^3-16 x^4\right ) \log (2-x)+\left (32 x-8 x^3\right ) \log ^2(2-x)\right ) \log (3 \log (x))+\left (72 x-114 x^2+47 x^3+4 x^4-4 x^5+\left (-96 x+88 x^2-4 x^3-8 x^4\right ) \log (2-x)+\left (32 x-8 x^2-4 x^3\right ) \log ^2(2-x)\right ) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+\left (-72 x^2+84 x^3-24 x^4+\left (48 x^2-24 x^3\right ) \log (2-x)\right ) \log (x) \log ^2(3 \log (x))+\left (-18 x^4+33 x^5-20 x^6+4 x^7+\left (24 x^4-28 x^5+8 x^6\right ) \log (2-x)+\left (-8 x^4+4 x^5\right ) \log ^2(2-x)\right ) \log (x) \log ^4(3 \log (x))} \, dx=\frac {2 \,\mathrm {log}\left (-x +2\right ) x +4 \,\mathrm {log}\left (-x +2\right )+2 x^{2}+x -6}{2 \,\mathrm {log}\left (-x +2\right ) \mathrm {log}\left (3 \,\mathrm {log}\left (x \right )\right )^{2} x^{2}+2 \mathrm {log}\left (3 \,\mathrm {log}\left (x \right )\right )^{2} x^{3}-3 \mathrm {log}\left (3 \,\mathrm {log}\left (x \right )\right )^{2} x^{2}-6} \] Input:
int((((-4*x^3-8*x^2+32*x)*log(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*log(2-x)-4 *x^5+4*x^4+47*x^3-114*x^2+72*x)*log(x)*log(3*log(x))^2+((-8*x^3+32*x)*log( 2-x)^2+(-16*x^4+24*x^3+64*x^2-96*x)*log(2-x)-8*x^5+24*x^4+14*x^3-96*x^2+72 *x)*log(3*log(x))+((-12*x+24)*log(2-x)-24*x^2+30*x-12)*log(x))/(((4*x^5-8* x^4)*log(2-x)^2+(8*x^6-28*x^5+24*x^4)*log(2-x)+4*x^7-20*x^6+33*x^5-18*x^4) *log(x)*log(3*log(x))^4+((-24*x^3+48*x^2)*log(2-x)-24*x^4+84*x^3-72*x^2)*l og(x)*log(3*log(x))^2+(36*x-72)*log(x)),x)
Output:
(2*log( - x + 2)*x + 4*log( - x + 2) + 2*x**2 + x - 6)/(2*log( - x + 2)*lo g(3*log(x))**2*x**2 + 2*log(3*log(x))**2*x**3 - 3*log(3*log(x))**2*x**2 - 6)