Integrand size = 341, antiderivative size = 30 \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=x \left (-2-\log \left (-x+\frac {x}{\frac {1}{x}+\frac {4}{\log (x+\log (x))}}\right )\right )^2 \] Output:
(-2-ln(x/(4/ln(x+ln(x))+1/x)-x))^2*x
\[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=\int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx \] Input:
Integrate[(16*x^2 - 112*x^3 - 128*x^2*Log[x] + (-64*x^2 + 32*x^3 + (-64*x + 32*x^2)*Log[x])*Log[x + Log[x]] + (-8*x + 12*x^2 + (-8 + 12*x)*Log[x])*L og[x + Log[x]]^2 + (8*x^2 - 88*x^3 - 96*x^2*Log[x] + (-48*x^2 + 24*x^3 + ( -48*x + 24*x^2)*Log[x])*Log[x + Log[x]] + (-6*x + 8*x^2 + (-6 + 8*x)*Log[x ])*Log[x + Log[x]]^2)*Log[(-4*x^2 + (-x + x^2)*Log[x + Log[x]])/(4*x + Log [x + Log[x]])] + (-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^ 2)*Log[x])*Log[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^ 2)*Log[(-4*x^2 + (-x + x^2)*Log[x + Log[x]])/(4*x + Log[x + Log[x]])]^2)/( -16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^2)*Log[x])*Log[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2),x]
Output:
Integrate[(16*x^2 - 112*x^3 - 128*x^2*Log[x] + (-64*x^2 + 32*x^3 + (-64*x + 32*x^2)*Log[x])*Log[x + Log[x]] + (-8*x + 12*x^2 + (-8 + 12*x)*Log[x])*L og[x + Log[x]]^2 + (8*x^2 - 88*x^3 - 96*x^2*Log[x] + (-48*x^2 + 24*x^3 + ( -48*x + 24*x^2)*Log[x])*Log[x + Log[x]] + (-6*x + 8*x^2 + (-6 + 8*x)*Log[x ])*Log[x + Log[x]]^2)*Log[(-4*x^2 + (-x + x^2)*Log[x + Log[x]])/(4*x + Log [x + Log[x]])] + (-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^ 2)*Log[x])*Log[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^ 2)*Log[(-4*x^2 + (-x + x^2)*Log[x + Log[x]])/(4*x + Log[x + Log[x]])]^2)/( -16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^2)*Log[x])*Log[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2), 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.
| \(\displaystyle \int \frac {-112 x^3+16 x^2+\left (12 x^2-8 x+(12 x-8) \log (x)\right ) \log ^2(x+\log (x))-128 x^2 \log (x)+\left (-16 x^3+\left (x^2-x+(x-1) \log (x)\right ) \log ^2(x+\log (x))-16 x^2 \log (x)+\left (4 x^3-8 x^2+\left (4 x^2-8 x\right ) \log (x)\right ) \log (x+\log (x))\right ) \log ^2\left (\frac {\left (x^2-x\right ) \log (x+\log (x))-4 x^2}{4 x+\log (x+\log (x))}\right )+\left (-88 x^3+8 x^2+\left (8 x^2-6 x+(8 x-6) \log (x)\right ) \log ^2(x+\log (x))-96 x^2 \log (x)+\left (24 x^3-48 x^2+\left (24 x^2-48 x\right ) \log (x)\right ) \log (x+\log (x))\right ) \log \left (\frac {\left (x^2-x\right ) \log (x+\log (x))-4 x^2}{4 x+\log (x+\log (x))}\right )+\left (32 x^3-64 x^2+\left (32 x^2-64 x\right ) \log (x)\right ) \log (x+\log (x))}{-16 x^3+\left (x^2-x+(x-1) \log (x)\right ) \log ^2(x+\log (x))-16 x^2 \log (x)+\left (4 x^3-8 x^2+\left (4 x^2-8 x\right ) \log (x)\right ) \log (x+\log (x))} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-\left (12 x^2-8 x+(12 x-8) \log (x)\right ) \log ^2(x+\log (x))+128 x^2 \log (x)-\left (-16 x^3+\left (x^2-x+(x-1) \log (x)\right ) \log ^2(x+\log (x))-16 x^2 \log (x)+\left (4 x^3-8 x^2+\left (4 x^2-8 x\right ) \log (x)\right ) \log (x+\log (x))\right ) \log ^2\left (\frac {\left (x^2-x\right ) \log (x+\log (x))-4 x^2}{4 x+\log (x+\log (x))}\right )-\left (-88 x^3+8 x^2+\left (8 x^2-6 x+(8 x-6) \log (x)\right ) \log ^2(x+\log (x))-96 x^2 \log (x)+\left (24 x^3-48 x^2+\left (24 x^2-48 x\right ) \log (x)\right ) \log (x+\log (x))\right ) \log \left (\frac {\left (x^2-x\right ) \log (x+\log (x))-4 x^2}{4 x+\log (x+\log (x))}\right )-\left (32 x^3-64 x^2+\left (32 x^2-64 x\right ) \log (x)\right ) \log (x+\log (x))}{(x+\log (x)) \left (16 x^2-4 x^2 \log (x+\log (x))-x \log ^2(x+\log (x))+\log ^2(x+\log (x))+8 x \log (x+\log (x))\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {112 x^3-16 x^2-2 \left (\log (x) \left (-48 x^2+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )+x \left (4 (1-11 x) x+(4 x-3) \log ^2(x+\log (x))+12 (x-2) x \log (x+\log (x))\right )\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+128 x^2 \log (x)+4 (2-3 x) (x+\log (x)) \log ^2(x+\log (x))+(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x))) \log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )-32 (x-2) x (x+\log (x)) \log (x+\log (x))}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(x-1) \log (x+\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {2 \left (-44 x^3+12 x^3 \log (x+\log (x))+4 x^2+4 x^2 \log ^2(x+\log (x))-48 x^2 \log (x)+12 x^2 \log (x) \log (x+\log (x))-24 x^2 \log (x+\log (x))+4 x \log (x) \log ^2(x+\log (x))-3 x \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))-24 x \log (x) \log (x+\log (x))\right ) \log \left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\log ^2\left (\frac {x ((x-1) \log (x+\log (x))-4 x)}{4 x+\log (x+\log (x))}\right )+\frac {4 (3 x-2) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}+\frac {32 (x-2) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x+x \log (x+\log (x))-\log (x+\log (x)))}\right )dx\) |
Input:
Int[(16*x^2 - 112*x^3 - 128*x^2*Log[x] + (-64*x^2 + 32*x^3 + (-64*x + 32*x ^2)*Log[x])*Log[x + Log[x]] + (-8*x + 12*x^2 + (-8 + 12*x)*Log[x])*Log[x + Log[x]]^2 + (8*x^2 - 88*x^3 - 96*x^2*Log[x] + (-48*x^2 + 24*x^3 + (-48*x + 24*x^2)*Log[x])*Log[x + Log[x]] + (-6*x + 8*x^2 + (-6 + 8*x)*Log[x])*Log [x + Log[x]]^2)*Log[(-4*x^2 + (-x + x^2)*Log[x + Log[x]])/(4*x + Log[x + L og[x]])] + (-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^2)*Log [x])*Log[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2)*Log [(-4*x^2 + (-x + x^2)*Log[x + Log[x]])/(4*x + Log[x + Log[x]])]^2)/(-16*x^ 3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^2)*Log[x])*Log[x + Log[x ]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(75\) vs. \(2(30)=60\).
Time = 60.44 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.53
| method | result | size |
| parallelrisch | \({\ln \left (\frac {\left (x^{2}-x \right ) \ln \left (x +\ln \left (x \right )\right )-4 x^{2}}{\ln \left (x +\ln \left (x \right )\right )+4 x}\right )}^{2} x +4 x \ln \left (\frac {\left (x^{2}-x \right ) \ln \left (x +\ln \left (x \right )\right )-4 x^{2}}{\ln \left (x +\ln \left (x \right )\right )+4 x}\right )+4 x\) | \(76\) |
| risch | \(\text {Expression too large to display}\) | \(5269\) |
Input:
int(((((-1+x)*ln(x)+x^2-x)*ln(x+ln(x))^2+((4*x^2-8*x)*ln(x)+4*x^3-8*x^2)*l n(x+ln(x))-16*x^2*ln(x)-16*x^3)*ln(((x^2-x)*ln(x+ln(x))-4*x^2)/(ln(x+ln(x) )+4*x))^2+(((8*x-6)*ln(x)+8*x^2-6*x)*ln(x+ln(x))^2+((24*x^2-48*x)*ln(x)+24 *x^3-48*x^2)*ln(x+ln(x))-96*x^2*ln(x)-88*x^3+8*x^2)*ln(((x^2-x)*ln(x+ln(x) )-4*x^2)/(ln(x+ln(x))+4*x))+((12*x-8)*ln(x)+12*x^2-8*x)*ln(x+ln(x))^2+((32 *x^2-64*x)*ln(x)+32*x^3-64*x^2)*ln(x+ln(x))-128*x^2*ln(x)-112*x^3+16*x^2)/ (((-1+x)*ln(x)+x^2-x)*ln(x+ln(x))^2+((4*x^2-8*x)*ln(x)+4*x^3-8*x^2)*ln(x+l n(x))-16*x^2*ln(x)-16*x^3),x,method=_RETURNVERBOSE)
Output:
ln(((x^2-x)*ln(x+ln(x))-4*x^2)/(ln(x+ln(x))+4*x))^2*x+4*x*ln(((x^2-x)*ln(x +ln(x))-4*x^2)/(ln(x+ln(x))+4*x))+4*x
Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (28) = 56\).
Time = 0.10 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.63 \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=x \log \left (-\frac {4 \, x^{2} - {\left (x^{2} - x\right )} \log \left (x + \log \left (x\right )\right )}{4 \, x + \log \left (x + \log \left (x\right )\right )}\right )^{2} + 4 \, x \log \left (-\frac {4 \, x^{2} - {\left (x^{2} - x\right )} \log \left (x + \log \left (x\right )\right )}{4 \, x + \log \left (x + \log \left (x\right )\right )}\right ) + 4 \, x \] Input:
integrate(((((-1+x)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^ 3-8*x^2)*log(x+log(x))-16*x^2*log(x)-16*x^3)*log(((x^2-x)*log(x+log(x))-4* x^2)/(log(x+log(x))+4*x))^2+(((8*x-6)*log(x)+8*x^2-6*x)*log(x+log(x))^2+(( 24*x^2-48*x)*log(x)+24*x^3-48*x^2)*log(x+log(x))-96*x^2*log(x)-88*x^3+8*x^ 2)*log(((x^2-x)*log(x+log(x))-4*x^2)/(log(x+log(x))+4*x))+((12*x-8)*log(x) +12*x^2-8*x)*log(x+log(x))^2+((32*x^2-64*x)*log(x)+32*x^3-64*x^2)*log(x+lo g(x))-128*x^2*log(x)-112*x^3+16*x^2)/(((-1+x)*log(x)+x^2-x)*log(x+log(x))^ 2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)*log(x+log(x))-16*x^2*log(x)-16*x^3),x, algorithm="fricas")
Output:
x*log(-(4*x^2 - (x^2 - x)*log(x + log(x)))/(4*x + log(x + log(x))))^2 + 4* x*log(-(4*x^2 - (x^2 - x)*log(x + log(x)))/(4*x + log(x + log(x)))) + 4*x
Exception generated. \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((((-1+x)*ln(x)+x**2-x)*ln(x+ln(x))**2+((4*x**2-8*x)*ln(x)+4*x** 3-8*x**2)*ln(x+ln(x))-16*x**2*ln(x)-16*x**3)*ln(((x**2-x)*ln(x+ln(x))-4*x* *2)/(ln(x+ln(x))+4*x))**2+(((8*x-6)*ln(x)+8*x**2-6*x)*ln(x+ln(x))**2+((24* x**2-48*x)*ln(x)+24*x**3-48*x**2)*ln(x+ln(x))-96*x**2*ln(x)-88*x**3+8*x**2 )*ln(((x**2-x)*ln(x+ln(x))-4*x**2)/(ln(x+ln(x))+4*x))+((12*x-8)*ln(x)+12*x **2-8*x)*ln(x+ln(x))**2+((32*x**2-64*x)*ln(x)+32*x**3-64*x**2)*ln(x+ln(x)) -128*x**2*ln(x)-112*x**3+16*x**2)/(((-1+x)*ln(x)+x**2-x)*ln(x+ln(x))**2+(( 4*x**2-8*x)*ln(x)+4*x**3-8*x**2)*ln(x+ln(x))-16*x**2*ln(x)-16*x**3),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (28) = 56\).
Time = 0.11 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.47 \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=x \log \left ({\left (x - 1\right )} \log \left (x + \log \left (x\right )\right ) - 4 \, x\right )^{2} + x \log \left (4 \, x + \log \left (x + \log \left (x\right )\right )\right )^{2} + x \log \left (x\right )^{2} - 2 \, {\left (x \log \left (4 \, x + \log \left (x + \log \left (x\right )\right )\right ) - x \log \left (x\right ) - 2 \, x\right )} \log \left ({\left (x - 1\right )} \log \left (x + \log \left (x\right )\right ) - 4 \, x\right ) - 2 \, {\left (x \log \left (x\right ) + 2 \, x\right )} \log \left (4 \, x + \log \left (x + \log \left (x\right )\right )\right ) + 4 \, x \log \left (x\right ) + 4 \, x \] Input:
integrate(((((-1+x)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^ 3-8*x^2)*log(x+log(x))-16*x^2*log(x)-16*x^3)*log(((x^2-x)*log(x+log(x))-4* x^2)/(log(x+log(x))+4*x))^2+(((8*x-6)*log(x)+8*x^2-6*x)*log(x+log(x))^2+(( 24*x^2-48*x)*log(x)+24*x^3-48*x^2)*log(x+log(x))-96*x^2*log(x)-88*x^3+8*x^ 2)*log(((x^2-x)*log(x+log(x))-4*x^2)/(log(x+log(x))+4*x))+((12*x-8)*log(x) +12*x^2-8*x)*log(x+log(x))^2+((32*x^2-64*x)*log(x)+32*x^3-64*x^2)*log(x+lo g(x))-128*x^2*log(x)-112*x^3+16*x^2)/(((-1+x)*log(x)+x^2-x)*log(x+log(x))^ 2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)*log(x+log(x))-16*x^2*log(x)-16*x^3),x, algorithm="maxima")
Output:
x*log((x - 1)*log(x + log(x)) - 4*x)^2 + x*log(4*x + log(x + log(x)))^2 + x*log(x)^2 - 2*(x*log(4*x + log(x + log(x))) - x*log(x) - 2*x)*log((x - 1) *log(x + log(x)) - 4*x) - 2*(x*log(x) + 2*x)*log(4*x + log(x + log(x))) + 4*x*log(x) + 4*x
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (28) = 56\).
Time = 16.82 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.80 \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=x \log \left (x \log \left (x + \log \left (x\right )\right ) - 4 \, x - \log \left (x + \log \left (x\right )\right )\right )^{2} + x \log \left (4 \, x + \log \left (x + \log \left (x\right )\right )\right )^{2} + x \log \left (x\right )^{2} - 2 \, {\left (x \log \left (4 \, x + \log \left (x + \log \left (x\right )\right )\right ) - x \log \left (x\right ) - 2 \, x\right )} \log \left (x \log \left (x + \log \left (x\right )\right ) - 4 \, x - \log \left (x + \log \left (x\right )\right )\right ) - 2 \, {\left (x \log \left (x\right ) + 2 \, x\right )} \log \left (4 \, x + \log \left (x + \log \left (x\right )\right )\right ) + 4 \, x \log \left (x\right ) + 4 \, x \] Input:
integrate(((((-1+x)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^ 3-8*x^2)*log(x+log(x))-16*x^2*log(x)-16*x^3)*log(((x^2-x)*log(x+log(x))-4* x^2)/(log(x+log(x))+4*x))^2+(((8*x-6)*log(x)+8*x^2-6*x)*log(x+log(x))^2+(( 24*x^2-48*x)*log(x)+24*x^3-48*x^2)*log(x+log(x))-96*x^2*log(x)-88*x^3+8*x^ 2)*log(((x^2-x)*log(x+log(x))-4*x^2)/(log(x+log(x))+4*x))+((12*x-8)*log(x) +12*x^2-8*x)*log(x+log(x))^2+((32*x^2-64*x)*log(x)+32*x^3-64*x^2)*log(x+lo g(x))-128*x^2*log(x)-112*x^3+16*x^2)/(((-1+x)*log(x)+x^2-x)*log(x+log(x))^ 2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)*log(x+log(x))-16*x^2*log(x)-16*x^3),x, algorithm="giac")
Output:
x*log(x*log(x + log(x)) - 4*x - log(x + log(x)))^2 + x*log(4*x + log(x + l og(x)))^2 + x*log(x)^2 - 2*(x*log(4*x + log(x + log(x))) - x*log(x) - 2*x) *log(x*log(x + log(x)) - 4*x - log(x + log(x))) - 2*(x*log(x) + 2*x)*log(4 *x + log(x + log(x))) + 4*x*log(x) + 4*x
Time = 3.54 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30 \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=x\,{\left (\ln \left (-\frac {\ln \left (x+\ln \left (x\right )\right )\,\left (x-x^2\right )+4\,x^2}{4\,x+\ln \left (x+\ln \left (x\right )\right )}\right )+2\right )}^2 \] Input:
int((log(x + log(x))*(log(x)*(64*x - 32*x^2) + 64*x^2 - 32*x^3) + 128*x^2* log(x) + log(-(log(x + log(x))*(x - x^2) + 4*x^2)/(4*x + log(x + log(x)))) ^2*(log(x + log(x))*(log(x)*(8*x - 4*x^2) + 8*x^2 - 4*x^3) - log(x + log(x ))^2*(log(x)*(x - 1) - x + x^2) + 16*x^2*log(x) + 16*x^3) - log(x + log(x) )^2*(log(x)*(12*x - 8) - 8*x + 12*x^2) + log(-(log(x + log(x))*(x - x^2) + 4*x^2)/(4*x + log(x + log(x))))*(log(x + log(x))*(log(x)*(48*x - 24*x^2) + 48*x^2 - 24*x^3) + 96*x^2*log(x) - log(x + log(x))^2*(log(x)*(8*x - 6) - 6*x + 8*x^2) - 8*x^2 + 88*x^3) - 16*x^2 + 112*x^3)/(log(x + log(x))*(log( x)*(8*x - 4*x^2) + 8*x^2 - 4*x^3) - log(x + log(x))^2*(log(x)*(x - 1) - x + x^2) + 16*x^2*log(x) + 16*x^3),x)
Output:
x*(log(-(log(x + log(x))*(x - x^2) + 4*x^2)/(4*x + log(x + log(x)))) + 2)^ 2
Time = 0.24 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.67 \[ \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx=x \left (\mathrm {log}\left (\frac {\mathrm {log}\left (\mathrm {log}\left (x \right )+x \right ) x^{2}-\mathrm {log}\left (\mathrm {log}\left (x \right )+x \right ) x -4 x^{2}}{\mathrm {log}\left (\mathrm {log}\left (x \right )+x \right )+4 x}\right )^{2}+4 \,\mathrm {log}\left (\frac {\mathrm {log}\left (\mathrm {log}\left (x \right )+x \right ) x^{2}-\mathrm {log}\left (\mathrm {log}\left (x \right )+x \right ) x -4 x^{2}}{\mathrm {log}\left (\mathrm {log}\left (x \right )+x \right )+4 x}\right )+4\right ) \] Input:
int(((((-1+x)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^3-8*x^ 2)*log(x+log(x))-16*x^2*log(x)-16*x^3)*log(((x^2-x)*log(x+log(x))-4*x^2)/( log(x+log(x))+4*x))^2+(((8*x-6)*log(x)+8*x^2-6*x)*log(x+log(x))^2+((24*x^2 -48*x)*log(x)+24*x^3-48*x^2)*log(x+log(x))-96*x^2*log(x)-88*x^3+8*x^2)*log (((x^2-x)*log(x+log(x))-4*x^2)/(log(x+log(x))+4*x))+((12*x-8)*log(x)+12*x^ 2-8*x)*log(x+log(x))^2+((32*x^2-64*x)*log(x)+32*x^3-64*x^2)*log(x+log(x))- 128*x^2*log(x)-112*x^3+16*x^2)/(((-1+x)*log(x)+x^2-x)*log(x+log(x))^2+((4* x^2-8*x)*log(x)+4*x^3-8*x^2)*log(x+log(x))-16*x^2*log(x)-16*x^3),x)
Output:
x*(log((log(log(x) + x)*x**2 - log(log(x) + x)*x - 4*x**2)/(log(log(x) + x ) + 4*x))**2 + 4*log((log(log(x) + x)*x**2 - log(log(x) + x)*x - 4*x**2)/( log(log(x) + x) + 4*x)) + 4)