Integrand size = 175, antiderivative size = 22 \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=x^2 \log \left (\left (x+\frac {5 x}{3 (25+x)}+\log (\log (x))\right )^2\right ) \] Output:
x^2*ln((x/(3/5*x+15)+x+ln(ln(x)))^2)
Time = 0.10 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.45 \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=x^2 \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right ) \] Input:
Integrate[(3750*x + 300*x^2 + 6*x^3 + (4000*x^2 + 300*x^3 + 6*x^4)*Log[x] + ((4000*x^2 + 310*x^3 + 6*x^4)*Log[x] + (3750*x + 300*x^2 + 6*x^3)*Log[x] *Log[Log[x]])*Log[(6400*x^2 + 480*x^3 + 9*x^4 + (12000*x + 930*x^2 + 18*x^ 3)*Log[Log[x]] + (5625 + 450*x + 9*x^2)*Log[Log[x]]^2)/(5625 + 450*x + 9*x ^2)])/((2000*x + 155*x^2 + 3*x^3)*Log[x] + (1875 + 150*x + 3*x^2)*Log[x]*L og[Log[x]]),x]
Output:
x^2*Log[(x*(80 + 3*x) + 3*(25 + x)*Log[Log[x]])^2/(9*(25 + x)^2)]
Time = 6.82 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.45, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {7239, 27, 7293, 2009}
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.
| \(\displaystyle \int \frac {6 x^3+300 x^2+\left (\left (6 x^3+300 x^2+3750 x\right ) \log (\log (x)) \log (x)+\left (6 x^4+310 x^3+4000 x^2\right ) \log (x)\right ) \log \left (\frac {9 x^4+480 x^3+6400 x^2+\left (9 x^2+450 x+5625\right ) \log ^2(\log (x))+\left (18 x^3+930 x^2+12000 x\right ) \log (\log (x))}{9 x^2+450 x+5625}\right )+\left (6 x^4+300 x^3+4000 x^2\right ) \log (x)+3750 x}{\left (3 x^2+150 x+1875\right ) \log (\log (x)) \log (x)+\left (3 x^3+155 x^2+2000 x\right ) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \left (3 x^2+\left (3 x^2+150 x+2000\right ) x \log (x)+150 x+(x+25) \log (x) (x (3 x+80)+3 (x+25) \log (\log (x))) \log \left (\frac {(x (3 x+80)+3 (x+25) \log (\log (x)))^2}{9 (x+25)^2}\right )+1875\right )}{(x+25) \log (x) (x (3 x+80)+3 (x+25) \log (\log (x)))}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {x \left (3 x^2+\left (3 x^2+150 x+2000\right ) \log (x) x+150 x+(x+25) \log (x) (x (3 x+80)+3 (x+25) \log (\log (x))) \log \left (\frac {(x (3 x+80)+3 (x+25) \log (\log (x)))^2}{9 (x+25)^2}\right )+1875\right )}{(x+25) \log (x) (x (3 x+80)+3 (x+25) \log (\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {3 x^3}{(x+25) \log (x) \left (3 x^2+3 \log (\log (x)) x+80 x+75 \log (\log (x))\right )}+\frac {\left (3 x^2+150 x+2000\right ) x^2}{(x+25) \left (3 x^2+3 \log (\log (x)) x+80 x+75 \log (\log (x))\right )}+\frac {150 x^2}{(x+25) \log (x) \left (3 x^2+3 \log (\log (x)) x+80 x+75 \log (\log (x))\right )}+\log \left (\frac {(x (3 x+80)+3 (x+25) \log (\log (x)))^2}{9 (x+25)^2}\right ) x+\frac {1875 x}{(x+25) \log (x) \left (3 x^2+3 \log (\log (x)) x+80 x+75 \log (\log (x))\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x^2 \log \left (\frac {(x (3 x+80)+3 (x+25) \log (\log (x)))^2}{9 (x+25)^2}\right )\) |
Input:
Int[(3750*x + 300*x^2 + 6*x^3 + (4000*x^2 + 300*x^3 + 6*x^4)*Log[x] + ((40 00*x^2 + 310*x^3 + 6*x^4)*Log[x] + (3750*x + 300*x^2 + 6*x^3)*Log[x]*Log[L og[x]])*Log[(6400*x^2 + 480*x^3 + 9*x^4 + (12000*x + 930*x^2 + 18*x^3)*Log [Log[x]] + (5625 + 450*x + 9*x^2)*Log[Log[x]]^2)/(5625 + 450*x + 9*x^2)])/ ((2000*x + 155*x^2 + 3*x^3)*Log[x] + (1875 + 150*x + 3*x^2)*Log[x]*Log[Log [x]]),x]
Output:
x^2*Log[(x*(80 + 3*x) + 3*(25 + x)*Log[Log[x]])^2/(9*(25 + x)^2)]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(21)=42\).
Time = 48.18 (sec) , antiderivative size = 68, normalized size of antiderivative = 3.09
| method | result | size |
| parallelrisch | \(\ln \left (\frac {\left (9 x^{2}+450 x +5625\right ) \ln \left (\ln \left (x \right )\right )^{2}+\left (18 x^{3}+930 x^{2}+12000 x \right ) \ln \left (\ln \left (x \right )\right )+9 x^{4}+480 x^{3}+6400 x^{2}}{9 x^{2}+450 x +5625}\right ) x^{2}\) | \(68\) |
| risch | \(2 x^{2} \ln \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )-2 x^{2} \ln \left (x +25\right )-\frac {i \pi \,x^{2} \operatorname {csgn}\left (\frac {i}{\left (x +25\right )^{2}}\right ) \operatorname {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}\right ) \operatorname {csgn}\left (\frac {i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}}{\left (x +25\right )^{2}}\right )}{2}+\frac {i \pi \,x^{2} \operatorname {csgn}\left (\frac {i}{\left (x +25\right )^{2}}\right ) {\operatorname {csgn}\left (\frac {i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}}{\left (x +25\right )^{2}}\right )}^{2}}{2}+\frac {i \pi \,x^{2} \operatorname {csgn}\left (i \left (x +25\right )\right )^{2} \operatorname {csgn}\left (i \left (x +25\right )^{2}\right )}{2}-i \pi \,x^{2} \operatorname {csgn}\left (i \left (x +25\right )\right ) \operatorname {csgn}\left (i \left (x +25\right )^{2}\right )^{2}+\frac {i \pi \,x^{2} \operatorname {csgn}\left (i \left (x +25\right )^{2}\right )^{3}}{2}-\frac {i \pi \,x^{2} {\operatorname {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )\right )}^{2} \operatorname {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}\right )}{2}+i \pi \,x^{2} \operatorname {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )\right ) {\operatorname {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}\right )}^{2}-\frac {i \pi \,x^{2} {\operatorname {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}\right )}^{3}}{2}+\frac {i \pi \,x^{2} \operatorname {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}\right ) {\operatorname {csgn}\left (\frac {i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}}{\left (x +25\right )^{2}}\right )}^{2}}{2}-\frac {i \pi \,x^{2} {\operatorname {csgn}\left (\frac {i \left (x^{2}+\left (\ln \left (\ln \left (x \right )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \left (x \right )\right )\right )^{2}}{\left (x +25\right )^{2}}\right )}^{3}}{2}\) | \(438\) |
Input:
int((((6*x^3+300*x^2+3750*x)*ln(x)*ln(ln(x))+(6*x^4+310*x^3+4000*x^2)*ln(x ))*ln(((9*x^2+450*x+5625)*ln(ln(x))^2+(18*x^3+930*x^2+12000*x)*ln(ln(x))+9 *x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3+4000*x^2)*ln(x)+ 6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*ln(x)*ln(ln(x))+(3*x^3+155*x^2+2 000*x)*ln(x)),x,method=_RETURNVERBOSE)
Output:
ln(1/9/(x^2+50*x+625)*((9*x^2+450*x+5625)*ln(ln(x))^2+(18*x^3+930*x^2+1200 0*x)*ln(ln(x))+9*x^4+480*x^3+6400*x^2))*x^2
Leaf count of result is larger than twice the leaf count of optimal. 67 vs. \(2 (26) = 52\).
Time = 0.08 (sec) , antiderivative size = 67, normalized size of antiderivative = 3.05 \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=x^{2} \log \left (\frac {9 \, x^{4} + 480 \, x^{3} + 9 \, {\left (x^{2} + 50 \, x + 625\right )} \log \left (\log \left (x\right )\right )^{2} + 6400 \, x^{2} + 6 \, {\left (3 \, x^{3} + 155 \, x^{2} + 2000 \, x\right )} \log \left (\log \left (x\right )\right )}{9 \, {\left (x^{2} + 50 \, x + 625\right )}}\right ) \] Input:
integrate((((6*x^3+300*x^2+3750*x)*log(x)*log(log(x))+(6*x^4+310*x^3+4000* x^2)*log(x))*log(((9*x^2+450*x+5625)*log(log(x))^2+(18*x^3+930*x^2+12000*x )*log(log(x))+9*x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3+4 000*x^2)*log(x)+6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*log(x)*log(log(x ))+(3*x^3+155*x^2+2000*x)*log(x)),x, algorithm="fricas")
Output:
x^2*log(1/9*(9*x^4 + 480*x^3 + 9*(x^2 + 50*x + 625)*log(log(x))^2 + 6400*x ^2 + 6*(3*x^3 + 155*x^2 + 2000*x)*log(log(x)))/(x^2 + 50*x + 625))
Exception generated. \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((6*x**3+300*x**2+3750*x)*ln(x)*ln(ln(x))+(6*x**4+310*x**3+4000 *x**2)*ln(x))*ln(((9*x**2+450*x+5625)*ln(ln(x))**2+(18*x**3+930*x**2+12000 *x)*ln(ln(x))+9*x**4+480*x**3+6400*x**2)/(9*x**2+450*x+5625))+(6*x**4+300* x**3+4000*x**2)*ln(x)+6*x**3+300*x**2+3750*x)/((3*x**2+150*x+1875)*ln(x)*l n(ln(x))+(3*x**3+155*x**2+2000*x)*ln(x)),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
Time = 0.17 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.82 \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=-2 \, x^{2} \log \left (3\right ) + 2 \, x^{2} \log \left (3 \, x^{2} + 3 \, {\left (x + 25\right )} \log \left (\log \left (x\right )\right ) + 80 \, x\right ) - 2 \, x^{2} \log \left (x + 25\right ) \] Input:
integrate((((6*x^3+300*x^2+3750*x)*log(x)*log(log(x))+(6*x^4+310*x^3+4000* x^2)*log(x))*log(((9*x^2+450*x+5625)*log(log(x))^2+(18*x^3+930*x^2+12000*x )*log(log(x))+9*x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3+4 000*x^2)*log(x)+6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*log(x)*log(log(x ))+(3*x^3+155*x^2+2000*x)*log(x)),x, algorithm="maxima")
Output:
-2*x^2*log(3) + 2*x^2*log(3*x^2 + 3*(x + 25)*log(log(x)) + 80*x) - 2*x^2*l og(x + 25)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (26) = 52\).
Time = 36.75 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.86 \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=x^{2} \log \left (9 \, x^{4} + 18 \, x^{3} \log \left (\log \left (x\right )\right ) + 9 \, x^{2} \log \left (\log \left (x\right )\right )^{2} + 480 \, x^{3} + 930 \, x^{2} \log \left (\log \left (x\right )\right ) + 450 \, x \log \left (\log \left (x\right )\right )^{2} + 6400 \, x^{2} + 12000 \, x \log \left (\log \left (x\right )\right ) + 5625 \, \log \left (\log \left (x\right )\right )^{2}\right ) - x^{2} \log \left (9 \, x^{2} + 450 \, x + 5625\right ) \] Input:
integrate((((6*x^3+300*x^2+3750*x)*log(x)*log(log(x))+(6*x^4+310*x^3+4000* x^2)*log(x))*log(((9*x^2+450*x+5625)*log(log(x))^2+(18*x^3+930*x^2+12000*x )*log(log(x))+9*x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3+4 000*x^2)*log(x)+6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*log(x)*log(log(x ))+(3*x^3+155*x^2+2000*x)*log(x)),x, algorithm="giac")
Output:
x^2*log(9*x^4 + 18*x^3*log(log(x)) + 9*x^2*log(log(x))^2 + 480*x^3 + 930*x ^2*log(log(x)) + 450*x*log(log(x))^2 + 6400*x^2 + 12000*x*log(log(x)) + 56 25*log(log(x))^2) - x^2*log(9*x^2 + 450*x + 5625)
Time = 1.02 (sec) , antiderivative size = 68, normalized size of antiderivative = 3.09 \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=x^2\,\ln \left (\frac {\ln \left (\ln \left (x\right )\right )\,\left (18\,x^3+930\,x^2+12000\,x\right )+{\ln \left (\ln \left (x\right )\right )}^2\,\left (9\,x^2+450\,x+5625\right )+6400\,x^2+480\,x^3+9\,x^4}{9\,x^2+450\,x+5625}\right ) \] Input:
int((3750*x + log(x)*(4000*x^2 + 300*x^3 + 6*x^4) + log((log(log(x))*(1200 0*x + 930*x^2 + 18*x^3) + log(log(x))^2*(450*x + 9*x^2 + 5625) + 6400*x^2 + 480*x^3 + 9*x^4)/(450*x + 9*x^2 + 5625))*(log(x)*(4000*x^2 + 310*x^3 + 6 *x^4) + log(log(x))*log(x)*(3750*x + 300*x^2 + 6*x^3)) + 300*x^2 + 6*x^3)/ (log(x)*(2000*x + 155*x^2 + 3*x^3) + log(log(x))*log(x)*(150*x + 3*x^2 + 1 875)),x)
Output:
x^2*log((log(log(x))*(12000*x + 930*x^2 + 18*x^3) + log(log(x))^2*(450*x + 9*x^2 + 5625) + 6400*x^2 + 480*x^3 + 9*x^4)/(450*x + 9*x^2 + 5625))
Time = 0.26 (sec) , antiderivative size = 81, normalized size of antiderivative = 3.68 \[ \int \frac {3750 x+300 x^2+6 x^3+\left (4000 x^2+300 x^3+6 x^4\right ) \log (x)+\left (\left (4000 x^2+310 x^3+6 x^4\right ) \log (x)+\left (3750 x+300 x^2+6 x^3\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {6400 x^2+480 x^3+9 x^4+\left (12000 x+930 x^2+18 x^3\right ) \log (\log (x))+\left (5625+450 x+9 x^2\right ) \log ^2(\log (x))}{5625+450 x+9 x^2}\right )}{\left (2000 x+155 x^2+3 x^3\right ) \log (x)+\left (1875+150 x+3 x^2\right ) \log (x) \log (\log (x))} \, dx=\mathrm {log}\left (\frac {9 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2} x^{2}+450 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2} x +5625 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2}+18 \,\mathrm {log}\left (\mathrm {log}\left (x \right )\right ) x^{3}+930 \,\mathrm {log}\left (\mathrm {log}\left (x \right )\right ) x^{2}+12000 \,\mathrm {log}\left (\mathrm {log}\left (x \right )\right ) x +9 x^{4}+480 x^{3}+6400 x^{2}}{9 x^{2}+450 x +5625}\right ) x^{2} \] Input:
int((((6*x^3+300*x^2+3750*x)*log(x)*log(log(x))+(6*x^4+310*x^3+4000*x^2)*l og(x))*log(((9*x^2+450*x+5625)*log(log(x))^2+(18*x^3+930*x^2+12000*x)*log( log(x))+9*x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3+4000*x^ 2)*log(x)+6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*log(x)*log(log(x))+(3* x^3+155*x^2+2000*x)*log(x)),x)
Output:
log((9*log(log(x))**2*x**2 + 450*log(log(x))**2*x + 5625*log(log(x))**2 + 18*log(log(x))*x**3 + 930*log(log(x))*x**2 + 12000*log(log(x))*x + 9*x**4 + 480*x**3 + 6400*x**2)/(9*x**2 + 450*x + 5625))*x**2