Integrand size = 170, antiderivative size = 24 \[ \int \frac {-8+16 x-8 x^2+\left (-12-14 x+34 x^2-6 x^3-2 x^4\right ) \log (6+x)+\left (-24+20 x+4 x^2\right ) \log (6+x) \log \left (\log ^2(6+x)\right )}{\left (6 x^3+19 x^4+21 x^5+9 x^6+x^7\right ) \log (6+x)+\left (36 x^2+78 x^3+48 x^4+6 x^5\right ) \log (6+x) \log \left (\log ^2(6+x)\right )+\left (72 x+84 x^2+12 x^3\right ) \log (6+x) \log ^2\left (\log ^2(6+x)\right )+(48+8 x) \log (6+x) \log ^3\left (\log ^2(6+x)\right )} \, dx=\frac {1}{\left (-x+\frac {2 \left (x+\log \left (\log ^2(6+x)\right )\right )}{1-x}\right )^2} \] Output:
1/(2*(x+ln(ln(6+x)^2))/(1-x)-x)^2
Time = 0.74 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {-8+16 x-8 x^2+\left (-12-14 x+34 x^2-6 x^3-2 x^4\right ) \log (6+x)+\left (-24+20 x+4 x^2\right ) \log (6+x) \log \left (\log ^2(6+x)\right )}{\left (6 x^3+19 x^4+21 x^5+9 x^6+x^7\right ) \log (6+x)+\left (36 x^2+78 x^3+48 x^4+6 x^5\right ) \log (6+x) \log \left (\log ^2(6+x)\right )+\left (72 x+84 x^2+12 x^3\right ) \log (6+x) \log ^2\left (\log ^2(6+x)\right )+(48+8 x) \log (6+x) \log ^3\left (\log ^2(6+x)\right )} \, dx=\frac {(-1+x)^2}{\left (x+x^2+2 \log \left (\log ^2(6+x)\right )\right )^2} \] Input:
Integrate[(-8 + 16*x - 8*x^2 + (-12 - 14*x + 34*x^2 - 6*x^3 - 2*x^4)*Log[6 + x] + (-24 + 20*x + 4*x^2)*Log[6 + x]*Log[Log[6 + x]^2])/((6*x^3 + 19*x^ 4 + 21*x^5 + 9*x^6 + x^7)*Log[6 + x] + (36*x^2 + 78*x^3 + 48*x^4 + 6*x^5)* Log[6 + x]*Log[Log[6 + x]^2] + (72*x + 84*x^2 + 12*x^3)*Log[6 + x]*Log[Log [6 + x]^2]^2 + (48 + 8*x)*Log[6 + x]*Log[Log[6 + x]^2]^3),x]
Output:
(-1 + x)^2/(x + x^2 + 2*Log[Log[6 + x]^2])^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.
| \(\displaystyle \int \frac {-8 x^2+\left (4 x^2+20 x-24\right ) \log (x+6) \log \left (\log ^2(x+6)\right )+\left (-2 x^4-6 x^3+34 x^2-14 x-12\right ) \log (x+6)+16 x-8}{\left (12 x^3+84 x^2+72 x\right ) \log (x+6) \log ^2\left (\log ^2(x+6)\right )+\left (6 x^5+48 x^4+78 x^3+36 x^2\right ) \log (x+6) \log \left (\log ^2(x+6)\right )+\left (x^7+9 x^6+21 x^5+19 x^4+6 x^3\right ) \log (x+6)+(8 x+48) \log (x+6) \log ^3\left (\log ^2(x+6)\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 (1-x) \left ((x+6) \log (x+6) \left (x^2-2 x-2 \log \left (\log ^2(x+6)\right )-1\right )+4 (x-1)\right )}{(x+6) \log (x+6) \left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {(1-x) \left (4 (1-x)+(x+6) \log (x+6) \left (-x^2+2 x+2 \log \left (\log ^2(x+6)\right )+1\right )\right )}{(x+6) \log (x+6) \left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {(1-x) \left (4 (1-x)+(x+6) \log (x+6) \left (-x^2+2 x+2 \log \left (\log ^2(x+6)\right )+1\right )\right )}{(x+6) \log (x+6) \left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log (x+6) x^2+13 \log (x+6) x+6 \log (x+6)+4\right ) (x-1)^2}{(x+6) \log (x+6) \left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}+\frac {1-x}{\left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (-48 \int \frac {1}{\left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx-98 \int \frac {x}{\left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx-3 \int \frac {x^2}{\left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx-32 \int \frac {1}{\log (x+6) \left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx+4 \int \frac {x}{\log (x+6) \left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx+\int \frac {1}{\left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^2}dx-\int \frac {x}{\left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^2}dx+2 \int \frac {x^3}{\left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^3}dx-\frac {49}{2 \left (x^2+x+2 \log \left (\log ^2(x+6)\right )\right )^2}\right )\) |
Input:
Int[(-8 + 16*x - 8*x^2 + (-12 - 14*x + 34*x^2 - 6*x^3 - 2*x^4)*Log[6 + x] + (-24 + 20*x + 4*x^2)*Log[6 + x]*Log[Log[6 + x]^2])/((6*x^3 + 19*x^4 + 21 *x^5 + 9*x^6 + x^7)*Log[6 + x] + (36*x^2 + 78*x^3 + 48*x^4 + 6*x^5)*Log[6 + x]*Log[Log[6 + x]^2] + (72*x + 84*x^2 + 12*x^3)*Log[6 + x]*Log[Log[6 + x ]^2]^2 + (48 + 8*x)*Log[6 + x]*Log[Log[6 + x]^2]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs. \(2(24)=48\).
Time = 3.29 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.50
| method | result | size |
| parallelrisch | \(\frac {52 x^{2}-104 x +52}{52 x^{4}+104 x^{3}+208 x^{2} \ln \left (\ln \left (6+x \right )^{2}\right )+52 x^{2}+208 x \ln \left (\ln \left (6+x \right )^{2}\right )+208 \ln \left (\ln \left (6+x \right )^{2}\right )^{2}}\) | \(60\) |
| risch | \(\frac {x^{2}-2 x +1}{\left (4 \ln \left (\ln \left (6+x \right )\right )-i \pi \operatorname {csgn}\left (i \ln \left (6+x \right )\right )^{2} \operatorname {csgn}\left (i \ln \left (6+x \right )^{2}\right )+2 i \pi \,\operatorname {csgn}\left (i \ln \left (6+x \right )\right ) \operatorname {csgn}\left (i \ln \left (6+x \right )^{2}\right )^{2}+x^{2}+x -i \pi \operatorname {csgn}\left (i \ln \left (6+x \right )^{2}\right )^{3}\right )^{2}}\) | \(88\) |
| default | \(\text {Expression too large to display}\) | \(1934\) |
Input:
int(((4*x^2+20*x-24)*ln(6+x)*ln(ln(6+x)^2)+(-2*x^4-6*x^3+34*x^2-14*x-12)*l n(6+x)-8*x^2+16*x-8)/((8*x+48)*ln(6+x)*ln(ln(6+x)^2)^3+(12*x^3+84*x^2+72*x )*ln(6+x)*ln(ln(6+x)^2)^2+(6*x^5+48*x^4+78*x^3+36*x^2)*ln(6+x)*ln(ln(6+x)^ 2)+(x^7+9*x^6+21*x^5+19*x^4+6*x^3)*ln(6+x)),x,method=_RETURNVERBOSE)
Output:
1/52*(52*x^2-104*x+52)/(x^4+2*x^3+4*x^2*ln(ln(6+x)^2)+x^2+4*x*ln(ln(6+x)^2 )+4*ln(ln(6+x)^2)^2)
Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (20) = 40\).
Time = 0.09 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.00 \[ \int \frac {-8+16 x-8 x^2+\left (-12-14 x+34 x^2-6 x^3-2 x^4\right ) \log (6+x)+\left (-24+20 x+4 x^2\right ) \log (6+x) \log \left (\log ^2(6+x)\right )}{\left (6 x^3+19 x^4+21 x^5+9 x^6+x^7\right ) \log (6+x)+\left (36 x^2+78 x^3+48 x^4+6 x^5\right ) \log (6+x) \log \left (\log ^2(6+x)\right )+\left (72 x+84 x^2+12 x^3\right ) \log (6+x) \log ^2\left (\log ^2(6+x)\right )+(48+8 x) \log (6+x) \log ^3\left (\log ^2(6+x)\right )} \, dx=\frac {x^{2} - 2 \, x + 1}{x^{4} + 2 \, x^{3} + x^{2} + 4 \, {\left (x^{2} + x\right )} \log \left (\log \left (x + 6\right )^{2}\right ) + 4 \, \log \left (\log \left (x + 6\right )^{2}\right )^{2}} \] Input:
integrate(((4*x^2+20*x-24)*log(6+x)*log(log(6+x)^2)+(-2*x^4-6*x^3+34*x^2-1 4*x-12)*log(6+x)-8*x^2+16*x-8)/((8*x+48)*log(6+x)*log(log(6+x)^2)^3+(12*x^ 3+84*x^2+72*x)*log(6+x)*log(log(6+x)^2)^2+(6*x^5+48*x^4+78*x^3+36*x^2)*log (6+x)*log(log(6+x)^2)+(x^7+9*x^6+21*x^5+19*x^4+6*x^3)*log(6+x)),x, algorit hm="fricas")
Output:
(x^2 - 2*x + 1)/(x^4 + 2*x^3 + x^2 + 4*(x^2 + x)*log(log(x + 6)^2) + 4*log (log(x + 6)^2)^2)
Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (20) = 40\).
Time = 0.14 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.00 \[ \int \frac {-8+16 x-8 x^2+\left (-12-14 x+34 x^2-6 x^3-2 x^4\right ) \log (6+x)+\left (-24+20 x+4 x^2\right ) \log (6+x) \log \left (\log ^2(6+x)\right )}{\left (6 x^3+19 x^4+21 x^5+9 x^6+x^7\right ) \log (6+x)+\left (36 x^2+78 x^3+48 x^4+6 x^5\right ) \log (6+x) \log \left (\log ^2(6+x)\right )+\left (72 x+84 x^2+12 x^3\right ) \log (6+x) \log ^2\left (\log ^2(6+x)\right )+(48+8 x) \log (6+x) \log ^3\left (\log ^2(6+x)\right )} \, dx=\frac {x^{2} - 2 x + 1}{x^{4} + 2 x^{3} + x^{2} + \left (4 x^{2} + 4 x\right ) \log {\left (\log {\left (x + 6 \right )}^{2} \right )} + 4 \log {\left (\log {\left (x + 6 \right )}^{2} \right )}^{2}} \] Input:
integrate(((4*x**2+20*x-24)*ln(6+x)*ln(ln(6+x)**2)+(-2*x**4-6*x**3+34*x**2 -14*x-12)*ln(6+x)-8*x**2+16*x-8)/((8*x+48)*ln(6+x)*ln(ln(6+x)**2)**3+(12*x **3+84*x**2+72*x)*ln(6+x)*ln(ln(6+x)**2)**2+(6*x**5+48*x**4+78*x**3+36*x** 2)*ln(6+x)*ln(ln(6+x)**2)+(x**7+9*x**6+21*x**5+19*x**4+6*x**3)*ln(6+x)),x)
Output:
(x**2 - 2*x + 1)/(x**4 + 2*x**3 + x**2 + (4*x**2 + 4*x)*log(log(x + 6)**2) + 4*log(log(x + 6)**2)**2)
Leaf count of result is larger than twice the leaf count of optimal. 44 vs. \(2 (20) = 40\).
Time = 0.10 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.83 \[ \int \frac {-8+16 x-8 x^2+\left (-12-14 x+34 x^2-6 x^3-2 x^4\right ) \log (6+x)+\left (-24+20 x+4 x^2\right ) \log (6+x) \log \left (\log ^2(6+x)\right )}{\left (6 x^3+19 x^4+21 x^5+9 x^6+x^7\right ) \log (6+x)+\left (36 x^2+78 x^3+48 x^4+6 x^5\right ) \log (6+x) \log \left (\log ^2(6+x)\right )+\left (72 x+84 x^2+12 x^3\right ) \log (6+x) \log ^2\left (\log ^2(6+x)\right )+(48+8 x) \log (6+x) \log ^3\left (\log ^2(6+x)\right )} \, dx=\frac {x^{2} - 2 \, x + 1}{x^{4} + 2 \, x^{3} + x^{2} + 8 \, {\left (x^{2} + x\right )} \log \left (\log \left (x + 6\right )\right ) + 16 \, \log \left (\log \left (x + 6\right )\right )^{2}} \] Input:
integrate(((4*x^2+20*x-24)*log(6+x)*log(log(6+x)^2)+(-2*x^4-6*x^3+34*x^2-1 4*x-12)*log(6+x)-8*x^2+16*x-8)/((8*x+48)*log(6+x)*log(log(6+x)^2)^3+(12*x^ 3+84*x^2+72*x)*log(6+x)*log(log(6+x)^2)^2+(6*x^5+48*x^4+78*x^3+36*x^2)*log (6+x)*log(log(6+x)^2)+(x^7+9*x^6+21*x^5+19*x^4+6*x^3)*log(6+x)),x, algorit hm="maxima")
Output:
(x^2 - 2*x + 1)/(x^4 + 2*x^3 + x^2 + 8*(x^2 + x)*log(log(x + 6)) + 16*log( log(x + 6))^2)
Leaf count of result is larger than twice the leaf count of optimal. 257 vs. \(2 (20) = 40\).
Time = 0.86 (sec) , antiderivative size = 257, normalized size of antiderivative = 10.71 \[ \int \frac {-8+16 x-8 x^2+\left (-12-14 x+34 x^2-6 x^3-2 x^4\right ) \log (6+x)+\left (-24+20 x+4 x^2\right ) \log (6+x) \log \left (\log ^2(6+x)\right )}{\left (6 x^3+19 x^4+21 x^5+9 x^6+x^7\right ) \log (6+x)+\left (36 x^2+78 x^3+48 x^4+6 x^5\right ) \log (6+x) \log \left (\log ^2(6+x)\right )+\left (72 x+84 x^2+12 x^3\right ) \log (6+x) \log ^2\left (\log ^2(6+x)\right )+(48+8 x) \log (6+x) \log ^3\left (\log ^2(6+x)\right )} \, dx=\frac {2 \, x^{4} \log \left (x + 6\right ) + 9 \, x^{3} \log \left (x + 6\right ) - 18 \, x^{2} \log \left (x + 6\right ) + 4 \, x^{2} + x \log \left (x + 6\right ) - 8 \, x + 6 \, \log \left (x + 6\right ) + 4}{2 \, x^{6} \log \left (x + 6\right ) + 17 \, x^{5} \log \left (x + 6\right ) + 8 \, x^{4} \log \left (\log \left (x + 6\right )^{2}\right ) \log \left (x + 6\right ) + 34 \, x^{4} \log \left (x + 6\right ) + 60 \, x^{3} \log \left (\log \left (x + 6\right )^{2}\right ) \log \left (x + 6\right ) + 8 \, x^{2} \log \left (\log \left (x + 6\right )^{2}\right )^{2} \log \left (x + 6\right ) + 4 \, x^{4} + 25 \, x^{3} \log \left (x + 6\right ) + 76 \, x^{2} \log \left (\log \left (x + 6\right )^{2}\right ) \log \left (x + 6\right ) + 52 \, x \log \left (\log \left (x + 6\right )^{2}\right )^{2} \log \left (x + 6\right ) + 8 \, x^{3} + 16 \, x^{2} \log \left (\log \left (x + 6\right )^{2}\right ) + 6 \, x^{2} \log \left (x + 6\right ) + 24 \, x \log \left (\log \left (x + 6\right )^{2}\right ) \log \left (x + 6\right ) + 24 \, \log \left (\log \left (x + 6\right )^{2}\right )^{2} \log \left (x + 6\right ) + 4 \, x^{2} + 16 \, x \log \left (\log \left (x + 6\right )^{2}\right ) + 16 \, \log \left (\log \left (x + 6\right )^{2}\right )^{2}} \] Input:
integrate(((4*x^2+20*x-24)*log(6+x)*log(log(6+x)^2)+(-2*x^4-6*x^3+34*x^2-1 4*x-12)*log(6+x)-8*x^2+16*x-8)/((8*x+48)*log(6+x)*log(log(6+x)^2)^3+(12*x^ 3+84*x^2+72*x)*log(6+x)*log(log(6+x)^2)^2+(6*x^5+48*x^4+78*x^3+36*x^2)*log (6+x)*log(log(6+x)^2)+(x^7+9*x^6+21*x^5+19*x^4+6*x^3)*log(6+x)),x, algorit hm="giac")
Output:
(2*x^4*log(x + 6) + 9*x^3*log(x + 6) - 18*x^2*log(x + 6) + 4*x^2 + x*log(x + 6) - 8*x + 6*log(x + 6) + 4)/(2*x^6*log(x + 6) + 17*x^5*log(x + 6) + 8* x^4*log(log(x + 6)^2)*log(x + 6) + 34*x^4*log(x + 6) + 60*x^3*log(log(x + 6)^2)*log(x + 6) + 8*x^2*log(log(x + 6)^2)^2*log(x + 6) + 4*x^4 + 25*x^3*l og(x + 6) + 76*x^2*log(log(x + 6)^2)*log(x + 6) + 52*x*log(log(x + 6)^2)^2 *log(x + 6) + 8*x^3 + 16*x^2*log(log(x + 6)^2) + 6*x^2*log(x + 6) + 24*x*l og(log(x + 6)^2)*log(x + 6) + 24*log(log(x + 6)^2)^2*log(x + 6) + 4*x^2 + 16*x*log(log(x + 6)^2) + 16*log(log(x + 6)^2)^2)
Timed out. \[ \int \frac {-8+16 x-8 x^2+\left (-12-14 x+34 x^2-6 x^3-2 x^4\right ) \log (6+x)+\left (-24+20 x+4 x^2\right ) \log (6+x) \log \left (\log ^2(6+x)\right )}{\left (6 x^3+19 x^4+21 x^5+9 x^6+x^7\right ) \log (6+x)+\left (36 x^2+78 x^3+48 x^4+6 x^5\right ) \log (6+x) \log \left (\log ^2(6+x)\right )+\left (72 x+84 x^2+12 x^3\right ) \log (6+x) \log ^2\left (\log ^2(6+x)\right )+(48+8 x) \log (6+x) \log ^3\left (\log ^2(6+x)\right )} \, dx=\int -\frac {\ln \left (x+6\right )\,\left (2\,x^4+6\,x^3-34\,x^2+14\,x+12\right )-16\,x+8\,x^2-\ln \left ({\ln \left (x+6\right )}^2\right )\,\ln \left (x+6\right )\,\left (4\,x^2+20\,x-24\right )+8}{\ln \left (x+6\right )\,\left (8\,x+48\right )\,{\ln \left ({\ln \left (x+6\right )}^2\right )}^3+\ln \left (x+6\right )\,\left (12\,x^3+84\,x^2+72\,x\right )\,{\ln \left ({\ln \left (x+6\right )}^2\right )}^2+\ln \left (x+6\right )\,\left (6\,x^5+48\,x^4+78\,x^3+36\,x^2\right )\,\ln \left ({\ln \left (x+6\right )}^2\right )+\ln \left (x+6\right )\,\left (x^7+9\,x^6+21\,x^5+19\,x^4+6\,x^3\right )} \,d x \] Input:
int(-(log(x + 6)*(14*x - 34*x^2 + 6*x^3 + 2*x^4 + 12) - 16*x + 8*x^2 - log (log(x + 6)^2)*log(x + 6)*(20*x + 4*x^2 - 24) + 8)/(log(x + 6)*(6*x^3 + 19 *x^4 + 21*x^5 + 9*x^6 + x^7) + log(log(x + 6)^2)^3*log(x + 6)*(8*x + 48) + log(log(x + 6)^2)^2*log(x + 6)*(72*x + 84*x^2 + 12*x^3) + log(log(x + 6)^ 2)*log(x + 6)*(36*x^2 + 78*x^3 + 48*x^4 + 6*x^5)),x)
Output:
int(-(log(x + 6)*(14*x - 34*x^2 + 6*x^3 + 2*x^4 + 12) - 16*x + 8*x^2 - log (log(x + 6)^2)*log(x + 6)*(20*x + 4*x^2 - 24) + 8)/(log(x + 6)*(6*x^3 + 19 *x^4 + 21*x^5 + 9*x^6 + x^7) + log(log(x + 6)^2)^3*log(x + 6)*(8*x + 48) + log(log(x + 6)^2)^2*log(x + 6)*(72*x + 84*x^2 + 12*x^3) + log(log(x + 6)^ 2)*log(x + 6)*(36*x^2 + 78*x^3 + 48*x^4 + 6*x^5)), x)
Time = 0.15 (sec) , antiderivative size = 223, normalized size of antiderivative = 9.29 \[ \int \frac {-8+16 x-8 x^2+\left (-12-14 x+34 x^2-6 x^3-2 x^4\right ) \log (6+x)+\left (-24+20 x+4 x^2\right ) \log (6+x) \log \left (\log ^2(6+x)\right )}{\left (6 x^3+19 x^4+21 x^5+9 x^6+x^7\right ) \log (6+x)+\left (36 x^2+78 x^3+48 x^4+6 x^5\right ) \log (6+x) \log \left (\log ^2(6+x)\right )+\left (72 x+84 x^2+12 x^3\right ) \log (6+x) \log ^2\left (\log ^2(6+x)\right )+(48+8 x) \log (6+x) \log ^3\left (\log ^2(6+x)\right )} \, dx=\frac {16 \mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right )^{3}-32 \mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right )^{2} \mathrm {log}\left (\mathrm {log}\left (x +6\right )\right )+16 \mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right )^{2} x^{2}+16 \mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right )^{2} x -4 \mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right )^{2}-32 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right ) \mathrm {log}\left (\mathrm {log}\left (x +6\right )\right ) x^{2}-32 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right ) \mathrm {log}\left (\mathrm {log}\left (x +6\right )\right ) x +4 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right ) x^{4}+8 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right ) x^{3}-4 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right ) x -8 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )\right ) x^{4}-16 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )\right ) x^{3}-8 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )\right ) x^{2}-x^{4}-2 x^{3}-2 x +1}{4 \mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right )^{2}+4 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right ) x^{2}+4 \,\mathrm {log}\left (\mathrm {log}\left (x +6\right )^{2}\right ) x +x^{4}+2 x^{3}+x^{2}} \] Input:
int(((4*x^2+20*x-24)*log(6+x)*log(log(6+x)^2)+(-2*x^4-6*x^3+34*x^2-14*x-12 )*log(6+x)-8*x^2+16*x-8)/((8*x+48)*log(6+x)*log(log(6+x)^2)^3+(12*x^3+84*x ^2+72*x)*log(6+x)*log(log(6+x)^2)^2+(6*x^5+48*x^4+78*x^3+36*x^2)*log(6+x)* log(log(6+x)^2)+(x^7+9*x^6+21*x^5+19*x^4+6*x^3)*log(6+x)),x)
Output:
(16*log(log(x + 6)**2)**3 - 32*log(log(x + 6)**2)**2*log(log(x + 6)) + 16* log(log(x + 6)**2)**2*x**2 + 16*log(log(x + 6)**2)**2*x - 4*log(log(x + 6) **2)**2 - 32*log(log(x + 6)**2)*log(log(x + 6))*x**2 - 32*log(log(x + 6)** 2)*log(log(x + 6))*x + 4*log(log(x + 6)**2)*x**4 + 8*log(log(x + 6)**2)*x* *3 - 4*log(log(x + 6)**2)*x - 8*log(log(x + 6))*x**4 - 16*log(log(x + 6))* x**3 - 8*log(log(x + 6))*x**2 - x**4 - 2*x**3 - 2*x + 1)/(4*log(log(x + 6) **2)**2 + 4*log(log(x + 6)**2)*x**2 + 4*log(log(x + 6)**2)*x + x**4 + 2*x* *3 + x**2)