Integrand size = 190, antiderivative size = 28 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=x^2 \left (-x^2+\left (5+\frac {\log (x) \log ^2(12 x)}{x}\right )^2\right )^2 \] Output:
((5+ln(x)/x*ln(12*x)^2)^2-x^2)^2*x^2
Time = 0.47 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.39 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\frac {\left (25 x^2-x^4+10 x \log (x) \log ^2(12 x)+\log ^2(x) \log ^4(12 x)\right )^2}{x^2} \] Input:
Integrate[(1250*x^4 - 200*x^6 + 6*x^8 + (1000*x^3 - 40*x^5)*Log[x]*Log[12* x] + (500*x^3 - 20*x^5 + (500*x^3 - 60*x^5)*Log[x])*Log[12*x]^2 + (600*x^2 - 8*x^4)*Log[x]^2*Log[12*x]^3 + ((300*x^2 - 4*x^4)*Log[x] - 4*x^4*Log[x]^ 2)*Log[12*x]^4 + 120*x*Log[x]^3*Log[12*x]^5 + (60*x*Log[x]^2 - 20*x*Log[x] ^3)*Log[12*x]^6 + 8*Log[x]^4*Log[12*x]^7 + (4*Log[x]^3 - 2*Log[x]^4)*Log[1 2*x]^8)/x^3,x]
Output:
(25*x^2 - x^4 + 10*x*Log[x]*Log[12*x]^2 + Log[x]^2*Log[12*x]^4)^2/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.
| \(\displaystyle \int \frac {6 x^8-200 x^6+1250 x^4+\left (-20 x^5+500 x^3+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+8 \log ^4(x) \log ^7(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)}{x^3} \, dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \int \left (-\frac {2 (\log (x)-2) \log ^3(x) \log ^8(12 x)}{x^3}+\frac {8 \log ^4(x) \log ^7(12 x)}{x^3}-\frac {4 \log (x) \left (x^2+x^2 \log (x)-75\right ) \log ^4(12 x)}{x}-20 \left (x^2+3 x^2 \log (x)-25 \log (x)-25\right ) \log ^2(12 x)-\frac {20 (\log (x)-3) \log ^2(x) \log ^6(12 x)}{x^2}+\frac {120 \log ^3(x) \log ^5(12 x)}{x^2}-\frac {8 \left (x^2-75\right ) \log ^2(x) \log ^3(12 x)}{x}+2 x \left (3 x^4-100 x^2+625\right )-40 (x-5) (x+5) \log (x) \log (12 x)\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (-\frac {2 (\log (x)-2) \log ^3(x) \log ^8(12 x)}{x^3}+\frac {8 \log ^4(x) \log ^7(12 x)}{x^3}-\frac {4 \log (x) \left (x^2+x^2 \log (x)-75\right ) \log ^4(12 x)}{x}-20 \left (x^2+3 x^2 \log (x)-25 \log (x)-25\right ) \log ^2(12 x)-\frac {20 (\log (x)-3) \log ^2(x) \log ^6(12 x)}{x^2}+\frac {120 \log ^3(x) \log ^5(12 x)}{x^2}-\frac {8 \left (x^2-75\right ) \log ^2(x) \log ^3(12 x)}{x}+2 x \left (3 x^4-100 x^2+625\right )-40 (x-5) (x+5) \log (x) \log (12 x)\right )dx\) |
Input:
Int[(1250*x^4 - 200*x^6 + 6*x^8 + (1000*x^3 - 40*x^5)*Log[x]*Log[12*x] + ( 500*x^3 - 20*x^5 + (500*x^3 - 60*x^5)*Log[x])*Log[12*x]^2 + (600*x^2 - 8*x ^4)*Log[x]^2*Log[12*x]^3 + ((300*x^2 - 4*x^4)*Log[x] - 4*x^4*Log[x]^2)*Log [12*x]^4 + 120*x*Log[x]^3*Log[12*x]^5 + (60*x*Log[x]^2 - 20*x*Log[x]^3)*Lo g[12*x]^6 + 8*Log[x]^4*Log[12*x]^7 + (4*Log[x]^3 - 2*Log[x]^4)*Log[12*x]^8 )/x^3,x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(367\) vs. \(2(28)=56\).
Time = 0.02 (sec) , antiderivative size = 368, normalized size of antiderivative = 13.14
\[\frac {\ln \left (x \right )^{12}}{x^{2}}+\frac {20 \ln \left (x \right )^{9}}{x}+150 \ln \left (12\right )^{4} \ln \left (x \right )^{2}+600 \ln \left (12\right )^{3} \ln \left (x \right )^{3}+900 \ln \left (12\right )^{2} \ln \left (x \right )^{4}+600 \ln \left (12\right ) \ln \left (x \right )^{5}-20 x^{3} \ln \left (x \right )^{3}-2 x^{2} \ln \left (x \right )^{6}+500 x \ln \left (x \right )^{3}+x^{6}+150 \ln \left (x \right )^{6}+625 x^{2}-50 x^{4}-20 x^{3} \ln \left (x \right ) \ln \left (12\right )^{2}-40 x^{3} \ln \left (x \right )^{2} \ln \left (12\right )+\frac {56 \ln \left (12\right )^{3} \ln \left (x \right )^{9}}{x^{2}}-8 \ln \left (12\right )^{3} x^{2} \ln \left (x \right )^{3}+\frac {120 \ln \left (12\right )^{5} \ln \left (x \right )^{4}}{x}+\frac {300 \ln \left (12\right )^{4} \ln \left (x \right )^{5}}{x}+500 \ln \left (12\right )^{2} \ln \left (x \right ) x +1000 \ln \left (12\right ) \ln \left (x \right )^{2} x +\frac {300 \ln \left (12\right )^{2} \ln \left (x \right )^{7}}{x}-12 \ln \left (12\right )^{2} x^{2} \ln \left (x \right )^{4}+\frac {400 \ln \left (12\right )^{3} \ln \left (x \right )^{6}}{x}-8 \ln \left (12\right ) x^{2} \ln \left (x \right )^{5}+\frac {20 \ln \left (12\right )^{6} \ln \left (x \right )^{3}}{x}+\frac {120 \ln \left (12\right ) \ln \left (x \right )^{8}}{x}-2 \ln \left (12\right )^{4} \ln \left (x \right )^{2} x^{2}+\frac {8 \ln \left (12\right ) \ln \left (x \right )^{11}}{x^{2}}+\frac {70 \ln \left (12\right )^{4} \ln \left (x \right )^{8}}{x^{2}}+\frac {8 \ln \left (12\right )^{7} \ln \left (x \right )^{5}}{x^{2}}+\frac {28 \ln \left (12\right )^{6} \ln \left (x \right )^{6}}{x^{2}}+\frac {56 \ln \left (12\right )^{5} \ln \left (x \right )^{7}}{x^{2}}+\frac {28 \ln \left (12\right )^{2} \ln \left (x \right )^{10}}{x^{2}}+\frac {\ln \left (12\right )^{8} \ln \left (x \right )^{4}}{x^{2}}\]
Input:
int(((-2*ln(x)^4+4*ln(x)^3)*ln(12*x)^8+8*ln(x)^4*ln(12*x)^7+(-20*x*ln(x)^3 +60*x*ln(x)^2)*ln(12*x)^6+120*x*ln(x)^3*ln(12*x)^5+(-4*x^4*ln(x)^2+(-4*x^4 +300*x^2)*ln(x))*ln(12*x)^4+(-8*x^4+600*x^2)*ln(x)^2*ln(12*x)^3+((-60*x^5+ 500*x^3)*ln(x)-20*x^5+500*x^3)*ln(12*x)^2+(-40*x^5+1000*x^3)*ln(x)*ln(12*x )+6*x^8-200*x^6+1250*x^4)/x^3,x)
Output:
1/x^2*ln(x)^12+20/x*ln(x)^9+150*ln(12)^4*ln(x)^2+600*ln(12)^3*ln(x)^3+900* ln(12)^2*ln(x)^4+600*ln(12)*ln(x)^5-20*x^3*ln(x)^3-2*x^2*ln(x)^6+500*x*ln( x)^3+x^6+150*ln(x)^6+625*x^2-50*x^4-20*x^3*ln(x)*ln(12)^2-40*x^3*ln(x)^2*l n(12)+56*ln(12)^3/x^2*ln(x)^9-8*ln(12)^3*x^2*ln(x)^3+120*ln(12)^5/x*ln(x)^ 4+300*ln(12)^4/x*ln(x)^5+500*ln(12)^2*ln(x)*x+1000*ln(12)*ln(x)^2*x+300*ln (12)^2/x*ln(x)^7-12*ln(12)^2*x^2*ln(x)^4+400*ln(12)^3/x*ln(x)^6-8*ln(12)*x ^2*ln(x)^5+20*ln(12)^6/x*ln(x)^3+120*ln(12)/x*ln(x)^8-2*ln(12)^4*ln(x)^2*x ^2+8*ln(12)/x^2*ln(x)^11+70*ln(12)^4/x^2*ln(x)^8+8*ln(12)^7/x^2*ln(x)^5+28 *ln(12)^6/x^2*ln(x)^6+56*ln(12)^5/x^2*ln(x)^7+28*ln(12)^2/x^2*ln(x)^10+ln( 12)^8/x^2*ln(x)^4
Leaf count of result is larger than twice the leaf count of optimal. 279 vs. \(2 (28) = 56\).
Time = 0.09 (sec) , antiderivative size = 279, normalized size of antiderivative = 9.96 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\frac {28 \, \log \left (12\right )^{2} \log \left (x\right )^{10} + 8 \, \log \left (12\right ) \log \left (x\right )^{11} + \log \left (x\right )^{12} + 4 \, {\left (14 \, \log \left (12\right )^{3} + 5 \, x\right )} \log \left (x\right )^{9} + 10 \, {\left (7 \, \log \left (12\right )^{4} + 12 \, x \log \left (12\right )\right )} \log \left (x\right )^{8} + x^{8} + 4 \, {\left (14 \, \log \left (12\right )^{5} + 75 \, x \log \left (12\right )^{2}\right )} \log \left (x\right )^{7} + 2 \, {\left (14 \, \log \left (12\right )^{6} - x^{4} + 200 \, x \log \left (12\right )^{3} + 75 \, x^{2}\right )} \log \left (x\right )^{6} - 50 \, x^{6} + 4 \, {\left (2 \, \log \left (12\right )^{7} + 75 \, x \log \left (12\right )^{4} - 2 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )\right )} \log \left (x\right )^{5} + {\left (\log \left (12\right )^{8} + 120 \, x \log \left (12\right )^{5} - 12 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{2}\right )} \log \left (x\right )^{4} + 625 \, x^{4} - 20 \, {\left (x^{5} - 25 \, x^{3}\right )} \log \left (12\right )^{2} \log \left (x\right ) + 4 \, {\left (5 \, x \log \left (12\right )^{6} - 5 \, x^{5} - 2 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{3} + 125 \, x^{3}\right )} \log \left (x\right )^{3} - 2 \, {\left ({\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{4} + 20 \, {\left (x^{5} - 25 \, x^{3}\right )} \log \left (12\right )\right )} \log \left (x\right )^{2}}{x^{2}} \] Input:
integrate(((-2*log(x)^4+4*log(x)^3)*log(12*x)^8+8*log(x)^4*log(12*x)^7+(-2 0*x*log(x)^3+60*x*log(x)^2)*log(12*x)^6+120*x*log(x)^3*log(12*x)^5+(-4*x^4 *log(x)^2+(-4*x^4+300*x^2)*log(x))*log(12*x)^4+(-8*x^4+600*x^2)*log(x)^2*l og(12*x)^3+((-60*x^5+500*x^3)*log(x)-20*x^5+500*x^3)*log(12*x)^2+(-40*x^5+ 1000*x^3)*log(x)*log(12*x)+6*x^8-200*x^6+1250*x^4)/x^3,x, algorithm="frica s")
Output:
(28*log(12)^2*log(x)^10 + 8*log(12)*log(x)^11 + log(x)^12 + 4*(14*log(12)^ 3 + 5*x)*log(x)^9 + 10*(7*log(12)^4 + 12*x*log(12))*log(x)^8 + x^8 + 4*(14 *log(12)^5 + 75*x*log(12)^2)*log(x)^7 + 2*(14*log(12)^6 - x^4 + 200*x*log( 12)^3 + 75*x^2)*log(x)^6 - 50*x^6 + 4*(2*log(12)^7 + 75*x*log(12)^4 - 2*(x ^4 - 75*x^2)*log(12))*log(x)^5 + (log(12)^8 + 120*x*log(12)^5 - 12*(x^4 - 75*x^2)*log(12)^2)*log(x)^4 + 625*x^4 - 20*(x^5 - 25*x^3)*log(12)^2*log(x) + 4*(5*x*log(12)^6 - 5*x^5 - 2*(x^4 - 75*x^2)*log(12)^3 + 125*x^3)*log(x) ^3 - 2*((x^4 - 75*x^2)*log(12)^4 + 20*(x^5 - 25*x^3)*log(12))*log(x)^2)/x^ 2
Leaf count of result is larger than twice the leaf count of optimal. 333 vs. \(2 (22) = 44\).
Time = 0.60 (sec) , antiderivative size = 333, normalized size of antiderivative = 11.89 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=x^{6} - 50 x^{4} + 625 x^{2} + \left (- 20 x^{3} \log {\left (12 \right )}^{2} + 500 x \log {\left (12 \right )}^{2}\right ) \log {\left (x \right )} + \left (- 40 x^{3} \log {\left (12 \right )} - 2 x^{2} \log {\left (12 \right )}^{4} + 1000 x \log {\left (12 \right )} + 150 \log {\left (12 \right )}^{4}\right ) \log {\left (x \right )}^{2} + \frac {\left (- 20 x^{4} - 8 x^{3} \log {\left (12 \right )}^{3} + 500 x^{2} + 600 x \log {\left (12 \right )}^{3} + 20 \log {\left (12 \right )}^{6}\right ) \log {\left (x \right )}^{3}}{x} + \frac {\left (20 x + 56 \log {\left (12 \right )}^{3}\right ) \log {\left (x \right )}^{9}}{x^{2}} + \frac {\left (120 x \log {\left (12 \right )} + 70 \log {\left (12 \right )}^{4}\right ) \log {\left (x \right )}^{8}}{x^{2}} + \frac {\left (300 x \log {\left (12 \right )}^{2} + 56 \log {\left (12 \right )}^{5}\right ) \log {\left (x \right )}^{7}}{x^{2}} + \frac {\left (- 2 x^{4} + 150 x^{2} + 400 x \log {\left (12 \right )}^{3} + 28 \log {\left (12 \right )}^{6}\right ) \log {\left (x \right )}^{6}}{x^{2}} + \frac {\left (- 8 x^{4} \log {\left (12 \right )} + 600 x^{2} \log {\left (12 \right )} + 300 x \log {\left (12 \right )}^{4} + 8 \log {\left (12 \right )}^{7}\right ) \log {\left (x \right )}^{5}}{x^{2}} + \frac {\left (- 12 x^{4} \log {\left (12 \right )}^{2} + 900 x^{2} \log {\left (12 \right )}^{2} + 120 x \log {\left (12 \right )}^{5} + \log {\left (12 \right )}^{8}\right ) \log {\left (x \right )}^{4}}{x^{2}} + \frac {\log {\left (x \right )}^{12}}{x^{2}} + \frac {8 \log {\left (12 \right )} \log {\left (x \right )}^{11}}{x^{2}} + \frac {28 \log {\left (12 \right )}^{2} \log {\left (x \right )}^{10}}{x^{2}} \] Input:
integrate(((-2*ln(x)**4+4*ln(x)**3)*ln(12*x)**8+8*ln(x)**4*ln(12*x)**7+(-2 0*x*ln(x)**3+60*x*ln(x)**2)*ln(12*x)**6+120*x*ln(x)**3*ln(12*x)**5+(-4*x** 4*ln(x)**2+(-4*x**4+300*x**2)*ln(x))*ln(12*x)**4+(-8*x**4+600*x**2)*ln(x)* *2*ln(12*x)**3+((-60*x**5+500*x**3)*ln(x)-20*x**5+500*x**3)*ln(12*x)**2+(- 40*x**5+1000*x**3)*ln(x)*ln(12*x)+6*x**8-200*x**6+1250*x**4)/x**3,x)
Output:
x**6 - 50*x**4 + 625*x**2 + (-20*x**3*log(12)**2 + 500*x*log(12)**2)*log(x ) + (-40*x**3*log(12) - 2*x**2*log(12)**4 + 1000*x*log(12) + 150*log(12)** 4)*log(x)**2 + (-20*x**4 - 8*x**3*log(12)**3 + 500*x**2 + 600*x*log(12)**3 + 20*log(12)**6)*log(x)**3/x + (20*x + 56*log(12)**3)*log(x)**9/x**2 + (1 20*x*log(12) + 70*log(12)**4)*log(x)**8/x**2 + (300*x*log(12)**2 + 56*log( 12)**5)*log(x)**7/x**2 + (-2*x**4 + 150*x**2 + 400*x*log(12)**3 + 28*log(1 2)**6)*log(x)**6/x**2 + (-8*x**4*log(12) + 600*x**2*log(12) + 300*x*log(12 )**4 + 8*log(12)**7)*log(x)**5/x**2 + (-12*x**4*log(12)**2 + 900*x**2*log( 12)**2 + 120*x*log(12)**5 + log(12)**8)*log(x)**4/x**2 + log(x)**12/x**2 + 8*log(12)*log(x)**11/x**2 + 28*log(12)**2*log(x)**10/x**2
Leaf count of result is larger than twice the leaf count of optimal. 1994 vs. \(2 (28) = 56\).
Time = 0.20 (sec) , antiderivative size = 1994, normalized size of antiderivative = 71.21 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\text {Too large to display} \] Input:
integrate(((-2*log(x)^4+4*log(x)^3)*log(12*x)^8+8*log(x)^4*log(12*x)^7+(-2 0*x*log(x)^3+60*x*log(x)^2)*log(12*x)^6+120*x*log(x)^3*log(12*x)^5+(-4*x^4 *log(x)^2+(-4*x^4+300*x^2)*log(x))*log(12*x)^4+(-8*x^4+600*x^2)*log(x)^2*l og(12*x)^3+((-60*x^5+500*x^3)*log(x)-20*x^5+500*x^3)*log(12*x)^2+(-40*x^5+ 1000*x^3)*log(x)*log(12*x)+6*x^8-200*x^6+1250*x^4)/x^3,x, algorithm="maxim a")
Output:
x^6 + 150*log(12*x)^4*log(x)^2 - 20/9*(9*log(12*x)^2 - 6*log(12*x) + 2)*x^ 3*log(x) - (2*log(12*x)^4 - 4*log(12*x)^3 + 6*log(12*x)^2 - 6*log(12*x) + 3)*x^2*log(x)^2 - (4*log(12*x)^3 - 6*log(12*x)^2 + 6*log(12*x) - 3)*x^2*lo g(x)^2 - 20/27*(9*log(12*x)^2 - 6*log(12*x) + 2)*x^3 + 20/9*(3*log(12*x)^2 - 4*log(12*x) + 2)*x^3 - 50*x^4 + 40/27*x^3*(3*log(3) + 6*log(2) - 2) - ( 2*log(12*x)^4 - 4*log(12*x)^3 + 6*log(12*x)^2 - 6*log(12*x) + 3)*x^2*log(x ) + (2*log(12*x)^4 - 8*log(12*x)^3 + 18*log(12*x)^2 - 24*log(12*x) + 15)*x ^2*log(x) + 2*(2*log(12*x)^3 - 6*log(12*x)^2 + 9*log(12*x) - 6)*x^2*log(x) + 40/9*x^3*log(x) + 1/2*(2*log(12*x)^4 - 8*log(12*x)^3 + 18*log(12*x)^2 - 24*log(12*x) + 15)*x^2 - 1/2*(2*log(12*x)^4 - 12*log(12*x)^3 + 36*log(12* x)^2 - 60*log(12*x) + 45)*x^2 - (2*log(12*x)^3 - 9*log(12*x)^2 + 18*log(12 *x) - 15)*x^2 + 500*(log(12*x)^2 - 2*log(12*x) + 2)*x*log(x) + 20*(log(12* x)^6 + 6*log(12*x)^5 + 30*log(12*x)^4 + 120*log(12*x)^3 + 360*log(12*x)^2 + 720*log(12*x) + 720)*log(x)^3/x - 120*(log(12*x)^5 + 5*log(12*x)^4 + 20* log(12*x)^3 + 60*log(12*x)^2 + 120*log(12*x) + 120)*log(x)^3/x + 1/2*(2*lo g(12*x)^8 + 8*log(12*x)^7 + 28*log(12*x)^6 + 84*log(12*x)^5 + 210*log(12*x )^4 + 420*log(12*x)^3 + 630*log(12*x)^2 + 630*log(12*x) + 315)*log(x)^4/x^ 2 - 1/2*(8*log(12*x)^7 + 28*log(12*x)^6 + 84*log(12*x)^5 + 210*log(12*x)^4 + 420*log(12*x)^3 + 630*log(12*x)^2 + 630*log(12*x) + 315)*log(x)^4/x^2 + 625*x^2 - 1000*x*(log(3) + 2*log(2) - 2) + 1000*x*log(12*x) - 40/9*(3*...
Leaf count of result is larger than twice the leaf count of optimal. 2318 vs. \(2 (28) = 56\).
Time = 0.73 (sec) , antiderivative size = 2318, normalized size of antiderivative = 82.79 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\text {Too large to display} \] Input:
integrate(((-2*log(x)^4+4*log(x)^3)*log(12*x)^8+8*log(x)^4*log(12*x)^7+(-2 0*x*log(x)^3+60*x*log(x)^2)*log(12*x)^6+120*x*log(x)^3*log(12*x)^5+(-4*x^4 *log(x)^2+(-4*x^4+300*x^2)*log(x))*log(12*x)^4+(-8*x^4+600*x^2)*log(x)^2*l og(12*x)^3+((-60*x^5+500*x^3)*log(x)-20*x^5+500*x^3)*log(12*x)^2+(-40*x^5+ 1000*x^3)*log(x)*log(12*x)+6*x^8-200*x^6+1250*x^4)/x^3,x, algorithm="giac" )
Output:
log(x)^12/x^2 + 1/2*(2*log(x)^4/x^2 + 4*log(x)^3/x^2 + 6*log(x)^2/x^2 + 6* log(x)/x^2 + 3/x^2)*log(12)^8 - 1/2*(4*log(x)^3/x^2 + 6*log(x)^2/x^2 + 6*l og(x)/x^2 + 3/x^2)*log(12)^8 + 2*(4*log(x)^5/x^2 + 10*log(x)^4/x^2 + 20*lo g(x)^3/x^2 + 30*log(x)^2/x^2 + 30*log(x)/x^2 + 15/x^2)*log(12)^7 - 10*(2*l og(x)^4/x^2 + 4*log(x)^3/x^2 + 6*log(x)^2/x^2 + 6*log(x)/x^2 + 3/x^2)*log( 12)^7 - 2*x^2*log(x)^6 + 20*log(x)^9/x + 7*(4*log(x)^6/x^2 + 12*log(x)^5/x ^2 + 30*log(x)^4/x^2 + 60*log(x)^3/x^2 + 90*log(x)^2/x^2 + 90*log(x)/x^2 + 45/x^2)*log(12)^6 - 21*(4*log(x)^5/x^2 + 10*log(x)^4/x^2 + 20*log(x)^3/x^ 2 + 30*log(x)^2/x^2 + 30*log(x)/x^2 + 15/x^2)*log(12)^6 + 20*(log(x)^3/x + 3*log(x)^2/x + 6*log(x)/x + 6/x)*log(12)^6 - 60*(log(x)^2/x + 2*log(x)/x + 2/x)*log(12)^6 + x^6 + 7*(8*log(x)^7/x^2 + 28*log(x)^6/x^2 + 84*log(x)^5 /x^2 + 210*log(x)^4/x^2 + 420*log(x)^3/x^2 + 630*log(x)^2/x^2 + 630*log(x) /x^2 + 315/x^2)*log(12)^5 - 49*(4*log(x)^6/x^2 + 12*log(x)^5/x^2 + 30*log( x)^4/x^2 + 60*log(x)^3/x^2 + 90*log(x)^2/x^2 + 90*log(x)/x^2 + 45/x^2)*log (12)^5 + 120*(log(x)^4/x + 4*log(x)^3/x + 12*log(x)^2/x + 24*log(x)/x + 24 /x)*log(12)^5 - 480*(log(x)^3/x + 3*log(x)^2/x + 6*log(x)/x + 6/x)*log(12) ^5 + 150*log(12)^4*log(x)^2 - 20*x^3*log(x)^3 + 600*log(12)^3*log(x)^3 + 9 00*log(12)^2*log(x)^4 + 600*log(12)*log(x)^5 + 150*log(x)^6 - 20/3*x^3*log (12)^2 + 35*(2*log(x)^8/x^2 + 8*log(x)^7/x^2 + 28*log(x)^6/x^2 + 84*log(x) ^5/x^2 + 210*log(x)^4/x^2 + 420*log(x)^3/x^2 + 630*log(x)^2/x^2 + 630*l...
Time = 4.78 (sec) , antiderivative size = 367, normalized size of antiderivative = 13.11 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=600\,\ln \left (12\right )\,{\ln \left (x\right )}^5+500\,x\,{\ln \left (x\right )}^3+150\,{\ln \left (x\right )}^6+900\,{\ln \left (12\right )}^2\,{\ln \left (x\right )}^4+600\,{\ln \left (12\right )}^3\,{\ln \left (x\right )}^3+150\,{\ln \left (12\right )}^4\,{\ln \left (x\right )}^2-20\,x^3\,{\ln \left (x\right )}^3-2\,x^2\,{\ln \left (x\right )}^6+\frac {20\,{\ln \left (x\right )}^9}{x}+\frac {{\ln \left (x\right )}^{12}}{x^2}+625\,x^2-50\,x^4+x^6-12\,x^2\,{\ln \left (12\right )}^2\,{\ln \left (x\right )}^4-8\,x^2\,{\ln \left (12\right )}^3\,{\ln \left (x\right )}^3-2\,x^2\,{\ln \left (12\right )}^4\,{\ln \left (x\right )}^2+\frac {300\,{\ln \left (12\right )}^2\,{\ln \left (x\right )}^7}{x}+\frac {400\,{\ln \left (12\right )}^3\,{\ln \left (x\right )}^6}{x}+\frac {300\,{\ln \left (12\right )}^4\,{\ln \left (x\right )}^5}{x}+\frac {120\,{\ln \left (12\right )}^5\,{\ln \left (x\right )}^4}{x}+\frac {20\,{\ln \left (12\right )}^6\,{\ln \left (x\right )}^3}{x}+\frac {28\,{\ln \left (12\right )}^2\,{\ln \left (x\right )}^{10}}{x^2}+\frac {56\,{\ln \left (12\right )}^3\,{\ln \left (x\right )}^9}{x^2}+\frac {70\,{\ln \left (12\right )}^4\,{\ln \left (x\right )}^8}{x^2}+\frac {56\,{\ln \left (12\right )}^5\,{\ln \left (x\right )}^7}{x^2}+\frac {28\,{\ln \left (12\right )}^6\,{\ln \left (x\right )}^6}{x^2}+\frac {8\,{\ln \left (12\right )}^7\,{\ln \left (x\right )}^5}{x^2}+\frac {{\ln \left (12\right )}^8\,{\ln \left (x\right )}^4}{x^2}+1000\,x\,\ln \left (12\right )\,{\ln \left (x\right )}^2+500\,x\,{\ln \left (12\right )}^2\,\ln \left (x\right )-40\,x^3\,\ln \left (12\right )\,{\ln \left (x\right )}^2-20\,x^3\,{\ln \left (12\right )}^2\,\ln \left (x\right )-8\,x^2\,\ln \left (12\right )\,{\ln \left (x\right )}^5+\frac {120\,\ln \left (12\right )\,{\ln \left (x\right )}^8}{x}+\frac {8\,\ln \left (12\right )\,{\ln \left (x\right )}^{11}}{x^2} \] Input:
int((8*log(12*x)^7*log(x)^4 + log(12*x)^6*(60*x*log(x)^2 - 20*x*log(x)^3) + log(12*x)^8*(4*log(x)^3 - 2*log(x)^4) + 1250*x^4 - 200*x^6 + 6*x^8 + log (12*x)^2*(log(x)*(500*x^3 - 60*x^5) + 500*x^3 - 20*x^5) + log(12*x)^4*(log (x)*(300*x^2 - 4*x^4) - 4*x^4*log(x)^2) + log(12*x)^3*log(x)^2*(600*x^2 - 8*x^4) + log(12*x)*log(x)*(1000*x^3 - 40*x^5) + 120*x*log(12*x)^5*log(x)^3 )/x^3,x)
Output:
600*log(12)*log(x)^5 + 500*x*log(x)^3 + 150*log(x)^6 + 900*log(12)^2*log(x )^4 + 600*log(12)^3*log(x)^3 + 150*log(12)^4*log(x)^2 - 20*x^3*log(x)^3 - 2*x^2*log(x)^6 + (20*log(x)^9)/x + log(x)^12/x^2 + 625*x^2 - 50*x^4 + x^6 - 12*x^2*log(12)^2*log(x)^4 - 8*x^2*log(12)^3*log(x)^3 - 2*x^2*log(12)^4*l og(x)^2 + (300*log(12)^2*log(x)^7)/x + (400*log(12)^3*log(x)^6)/x + (300*l og(12)^4*log(x)^5)/x + (120*log(12)^5*log(x)^4)/x + (20*log(12)^6*log(x)^3 )/x + (28*log(12)^2*log(x)^10)/x^2 + (56*log(12)^3*log(x)^9)/x^2 + (70*log (12)^4*log(x)^8)/x^2 + (56*log(12)^5*log(x)^7)/x^2 + (28*log(12)^6*log(x)^ 6)/x^2 + (8*log(12)^7*log(x)^5)/x^2 + (log(12)^8*log(x)^4)/x^2 + 1000*x*lo g(12)*log(x)^2 + 500*x*log(12)^2*log(x) - 40*x^3*log(12)*log(x)^2 - 20*x^3 *log(12)^2*log(x) - 8*x^2*log(12)*log(x)^5 + (120*log(12)*log(x)^8)/x + (8 *log(12)*log(x)^11)/x^2
Time = 0.18 (sec) , antiderivative size = 98, normalized size of antiderivative = 3.50 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\frac {\mathrm {log}\left (12 x \right )^{8} \mathrm {log}\left (x \right )^{4}+20 \mathrm {log}\left (12 x \right )^{6} \mathrm {log}\left (x \right )^{3} x -2 \mathrm {log}\left (12 x \right )^{4} \mathrm {log}\left (x \right )^{2} x^{4}+150 \mathrm {log}\left (12 x \right )^{4} \mathrm {log}\left (x \right )^{2} x^{2}-20 \mathrm {log}\left (12 x \right )^{2} \mathrm {log}\left (x \right ) x^{5}+500 \mathrm {log}\left (12 x \right )^{2} \mathrm {log}\left (x \right ) x^{3}+x^{8}-50 x^{6}+625 x^{4}}{x^{2}} \] Input:
int(((-2*log(x)^4+4*log(x)^3)*log(12*x)^8+8*log(x)^4*log(12*x)^7+(-20*x*lo g(x)^3+60*x*log(x)^2)*log(12*x)^6+120*x*log(x)^3*log(12*x)^5+(-4*x^4*log(x )^2+(-4*x^4+300*x^2)*log(x))*log(12*x)^4+(-8*x^4+600*x^2)*log(x)^2*log(12* x)^3+((-60*x^5+500*x^3)*log(x)-20*x^5+500*x^3)*log(12*x)^2+(-40*x^5+1000*x ^3)*log(x)*log(12*x)+6*x^8-200*x^6+1250*x^4)/x^3,x)
Output:
(log(12*x)**8*log(x)**4 + 20*log(12*x)**6*log(x)**3*x - 2*log(12*x)**4*log (x)**2*x**4 + 150*log(12*x)**4*log(x)**2*x**2 - 20*log(12*x)**2*log(x)*x** 5 + 500*log(12*x)**2*log(x)*x**3 + x**8 - 50*x**6 + 625*x**4)/x**2