Integrand size = 213, antiderivative size = 39 \[ \int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx=-x+\frac {\log (3)}{3 x}+(-5+2 x)^4 \left (x+\frac {\frac {x}{2}-\log (x)}{x}\right )^4 \] Output:
1/3*ln(3)/x-x+(x+(1/2*x-ln(x))/x)^4*(-5+2*x)^4
Leaf count is larger than twice the leaf count of optimal. \(252\) vs. \(2(39)=78\).
Time = 0.07 (sec) , antiderivative size = 252, normalized size of antiderivative = 6.46 \[ \int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx=249 x+475 x^2+40 x^3-554 x^4-32 x^5+304 x^6-128 x^7+16 x^8+\frac {\log (9)}{6 x}-1375 \log (x)-\frac {625 \log (x)}{2 x}-1050 x \log (x)+1780 x^2 \log (x)+872 x^3 \log (x)-1488 x^4 \log (x)+544 x^5 \log (x)-64 x^6 \log (x)-1350 \log ^2(x)+\frac {1875 \log ^2(x)}{2 x^2}+\frac {2250 \log ^2(x)}{x}-2640 x \log ^2(x)+2664 x^2 \log ^2(x)-864 x^3 \log ^2(x)+96 x^4 \log ^2(x)-2080 \log ^3(x)-\frac {1250 \log ^3(x)}{x^3}-\frac {500 \log ^3(x)}{x^2}+\frac {2800 \log ^3(x)}{x}+608 x \log ^3(x)-64 x^2 \log ^3(x)+16 \log ^4(x)+\frac {625 \log ^4(x)}{x^4}-\frac {1000 \log ^4(x)}{x^3}+\frac {600 \log ^4(x)}{x^2}-\frac {160 \log ^4(x)}{x} \] Input:
Integrate[(-1875*x^3 - 8250*x^4 - 4806*x^5 + 16380*x^6 + 5952*x^7 - 22224* x^8 + 2304*x^9 + 10560*x^10 - 5376*x^11 + 768*x^12 - 2*x^3*Log[3] + (11250 *x^2 + 28875*x^3 - 16200*x^4 - 37980*x^5 + 53328*x^6 + 5328*x^7 - 34560*x^ 8 + 16320*x^9 - 2304*x^10)*Log[x] + (-22500*x - 20250*x^2 + 36900*x^3 - 37 440*x^4 - 4896*x^5 + 30816*x^6 - 15552*x^7 + 2304*x^8)*Log[x]^2 + (15000 - 1500*x + 20400*x^2 - 20640*x^3 + 384*x^4 + 3648*x^5 - 768*x^6)*Log[x]^3 + (-15000 + 18000*x - 7200*x^2 + 960*x^3)*Log[x]^4)/(6*x^5),x]
Output:
249*x + 475*x^2 + 40*x^3 - 554*x^4 - 32*x^5 + 304*x^6 - 128*x^7 + 16*x^8 + Log[9]/(6*x) - 1375*Log[x] - (625*Log[x])/(2*x) - 1050*x*Log[x] + 1780*x^ 2*Log[x] + 872*x^3*Log[x] - 1488*x^4*Log[x] + 544*x^5*Log[x] - 64*x^6*Log[ x] - 1350*Log[x]^2 + (1875*Log[x]^2)/(2*x^2) + (2250*Log[x]^2)/x - 2640*x* Log[x]^2 + 2664*x^2*Log[x]^2 - 864*x^3*Log[x]^2 + 96*x^4*Log[x]^2 - 2080*L og[x]^3 - (1250*Log[x]^3)/x^3 - (500*Log[x]^3)/x^2 + (2800*Log[x]^3)/x + 6 08*x*Log[x]^3 - 64*x^2*Log[x]^3 + 16*Log[x]^4 + (625*Log[x]^4)/x^4 - (1000 *Log[x]^4)/x^3 + (600*Log[x]^4)/x^2 - (160*Log[x]^4)/x
Leaf count is larger than twice the leaf count of optimal. \(256\) vs. \(2(39)=78\).
Time = 1.42 (sec) , antiderivative size = 256, normalized size of antiderivative = 6.56, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6, 27, 25, 2010, 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.
| \(\displaystyle \int \frac {768 x^{12}-5376 x^{11}+10560 x^{10}+2304 x^9-22224 x^8+5952 x^7+16380 x^6-4806 x^5-8250 x^4-1875 x^3-2 x^3 \log (3)+\left (960 x^3-7200 x^2+18000 x-15000\right ) \log ^4(x)+\left (-768 x^6+3648 x^5+384 x^4-20640 x^3+20400 x^2-1500 x+15000\right ) \log ^3(x)+\left (2304 x^8-15552 x^7+30816 x^6-4896 x^5-37440 x^4+36900 x^3-20250 x^2-22500 x\right ) \log ^2(x)+\left (-2304 x^{10}+16320 x^9-34560 x^8+5328 x^7+53328 x^6-37980 x^5-16200 x^4+28875 x^3+11250 x^2\right ) \log (x)}{6 x^5} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {768 x^{12}-5376 x^{11}+10560 x^{10}+2304 x^9-22224 x^8+5952 x^7+16380 x^6-4806 x^5-8250 x^4+x^3 (-1875-2 \log (3))+\left (960 x^3-7200 x^2+18000 x-15000\right ) \log ^4(x)+\left (-768 x^6+3648 x^5+384 x^4-20640 x^3+20400 x^2-1500 x+15000\right ) \log ^3(x)+\left (2304 x^8-15552 x^7+30816 x^6-4896 x^5-37440 x^4+36900 x^3-20250 x^2-22500 x\right ) \log ^2(x)+\left (-2304 x^{10}+16320 x^9-34560 x^8+5328 x^7+53328 x^6-37980 x^5-16200 x^4+28875 x^3+11250 x^2\right ) \log (x)}{6 x^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{6} \int -\frac {-768 x^{12}+5376 x^{11}-10560 x^{10}-2304 x^9+22224 x^8-5952 x^7-16380 x^6+4806 x^5+8250 x^4+(1875+\log (9)) x^3+120 \left (-8 x^3+60 x^2-150 x+125\right ) \log ^4(x)-12 \left (-64 x^6+304 x^5+32 x^4-1720 x^3+1700 x^2-125 x+1250\right ) \log ^3(x)+18 \left (-128 x^8+864 x^7-1712 x^6+272 x^5+2080 x^4-2050 x^3+1125 x^2+1250 x\right ) \log ^2(x)-3 \left (-768 x^{10}+5440 x^9-11520 x^8+1776 x^7+17776 x^6-12660 x^5-5400 x^4+9625 x^3+3750 x^2\right ) \log (x)}{x^5}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{6} \int \frac {-768 x^{12}+5376 x^{11}-10560 x^{10}-2304 x^9+22224 x^8-5952 x^7-16380 x^6+4806 x^5+8250 x^4+(1875+\log (9)) x^3+120 \left (-8 x^3+60 x^2-150 x+125\right ) \log ^4(x)-12 \left (-64 x^6+304 x^5+32 x^4-1720 x^3+1700 x^2-125 x+1250\right ) \log ^3(x)+18 \left (-128 x^8+864 x^7-1712 x^6+272 x^5+2080 x^4-2050 x^3+1125 x^2+1250 x\right ) \log ^2(x)-3 \left (-768 x^{10}+5440 x^9-11520 x^8+1776 x^7+17776 x^6-12660 x^5-5400 x^4+9625 x^3+3750 x^2\right ) \log (x)}{x^5}dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle -\frac {1}{6} \int \left (-\frac {120 (2 x-5)^3 \log ^4(x)}{x^5}+\frac {12 (2 x-5)^3 \left (8 x^3+22 x^2+11 x+10\right ) \log ^3(x)}{x^5}-\frac {18 (2 x-5)^3 (2 x+1) \left (8 x^3+2 x^2+x+10\right ) \log ^2(x)}{x^4}+\frac {3 (2 x-5)^3 (2 x+1)^2 \left (24 x^3-14 x^2-7 x+30\right ) \log (x)}{x^3}+\frac {-768 x^9+5376 x^8-10560 x^7-2304 x^6+22224 x^5-5952 x^4-16380 x^3+4806 x^2+8250 x+1875 \left (1+\frac {2 \log (3)}{1875}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{6} \left (96 x^8-768 x^7+1824 x^6-384 x^6 \log (x)-192 x^5+3264 x^5 \log (x)-3324 x^4+\frac {3750 \log ^4(x)}{x^4}+576 x^4 \log ^2(x)-8928 x^4 \log (x)+240 x^3-\frac {6000 \log ^4(x)}{x^3}-\frac {7500 \log ^3(x)}{x^3}-5184 x^3 \log ^2(x)+5232 x^3 \log (x)+2850 x^2+\frac {3600 \log ^4(x)}{x^2}-384 x^2 \log ^3(x)-\frac {3000 \log ^3(x)}{x^2}+15984 x^2 \log ^2(x)+\frac {5625 \log ^2(x)}{x^2}+10680 x^2 \log (x)+1494 x-\frac {1875}{x}+96 \log ^4(x)-\frac {960 \log ^4(x)}{x}+3648 x \log ^3(x)-12480 \log ^3(x)+\frac {16800 \log ^3(x)}{x}-15840 x \log ^2(x)-8100 \log ^2(x)+\frac {13500 \log ^2(x)}{x}-6300 x \log (x)-8250 \log (x)-\frac {1875 \log (x)}{x}+\frac {1875+\log (9)}{x}\right )\) |
Input:
Int[(-1875*x^3 - 8250*x^4 - 4806*x^5 + 16380*x^6 + 5952*x^7 - 22224*x^8 + 2304*x^9 + 10560*x^10 - 5376*x^11 + 768*x^12 - 2*x^3*Log[3] + (11250*x^2 + 28875*x^3 - 16200*x^4 - 37980*x^5 + 53328*x^6 + 5328*x^7 - 34560*x^8 + 16 320*x^9 - 2304*x^10)*Log[x] + (-22500*x - 20250*x^2 + 36900*x^3 - 37440*x^ 4 - 4896*x^5 + 30816*x^6 - 15552*x^7 + 2304*x^8)*Log[x]^2 + (15000 - 1500* x + 20400*x^2 - 20640*x^3 + 384*x^4 + 3648*x^5 - 768*x^6)*Log[x]^3 + (-150 00 + 18000*x - 7200*x^2 + 960*x^3)*Log[x]^4)/(6*x^5),x]
Output:
(-1875/x + 1494*x + 2850*x^2 + 240*x^3 - 3324*x^4 - 192*x^5 + 1824*x^6 - 7 68*x^7 + 96*x^8 + (1875 + Log[9])/x - 8250*Log[x] - (1875*Log[x])/x - 6300 *x*Log[x] + 10680*x^2*Log[x] + 5232*x^3*Log[x] - 8928*x^4*Log[x] + 3264*x^ 5*Log[x] - 384*x^6*Log[x] - 8100*Log[x]^2 + (5625*Log[x]^2)/x^2 + (13500*L og[x]^2)/x - 15840*x*Log[x]^2 + 15984*x^2*Log[x]^2 - 5184*x^3*Log[x]^2 + 5 76*x^4*Log[x]^2 - 12480*Log[x]^3 - (7500*Log[x]^3)/x^3 - (3000*Log[x]^3)/x ^2 + (16800*Log[x]^3)/x + 3648*x*Log[x]^3 - 384*x^2*Log[x]^3 + 96*Log[x]^4 + (3750*Log[x]^4)/x^4 - (6000*Log[x]^4)/x^3 + (3600*Log[x]^4)/x^2 - (960* Log[x]^4)/x)/6
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Leaf count of result is larger than twice the leaf count of optimal. \(194\) vs. \(2(35)=70\).
Time = 156.87 (sec) , antiderivative size = 195, normalized size of antiderivative = 5.00
| method | result | size |
| risch | \(\frac {\left (16 x^{4}-160 x^{3}+600 x^{2}-1000 x +625\right ) \ln \left (x \right )^{4}}{x^{4}}-\frac {2 \left (32 x^{5}-304 x^{4}+1040 x^{3}-1400 x^{2}+250 x +625\right ) \ln \left (x \right )^{3}}{x^{3}}+\frac {3 \left (64 x^{6}-576 x^{5}+1776 x^{4}-1760 x^{3}-900 x^{2}+1500 x +625\right ) \ln \left (x \right )^{2}}{2 x^{2}}-\frac {\left (128 x^{7}-1088 x^{6}+2976 x^{5}-1744 x^{4}-3560 x^{3}+2100 x^{2}+625\right ) \ln \left (x \right )}{2 x}+\frac {48 x^{9}-384 x^{8}+912 x^{7}-96 x^{6}-1662 x^{5}+120 x^{4}+1425 x^{3}-4125 x \ln \left (x \right )+747 x^{2}+\ln \left (3\right )}{3 x}\) | \(195\) |
| default | \(249 x +96 x^{4} \ln \left (x \right )^{2}+544 x^{5} \ln \left (x \right )-64 x^{6} \ln \left (x \right )-1488 x^{4} \ln \left (x \right )-864 x^{3} \ln \left (x \right )^{2}-\frac {625 \ln \left (x \right )}{2 x}+2664 x^{2} \ln \left (x \right )^{2}-2640 x \ln \left (x \right )^{2}+\frac {\ln \left (3\right )}{3 x}+\frac {2800 \ln \left (x \right )^{3}}{x}-\frac {160 \ln \left (x \right )^{4}}{x}-\frac {500 \ln \left (x \right )^{3}}{x^{2}}+\frac {625 \ln \left (x \right )^{4}}{x^{4}}+\frac {600 \ln \left (x \right )^{4}}{x^{2}}-\frac {1250 \ln \left (x \right )^{3}}{x^{3}}-\frac {1000 \ln \left (x \right )^{4}}{x^{3}}+\frac {2250 \ln \left (x \right )^{2}}{x}+\frac {1875 \ln \left (x \right )^{2}}{2 x^{2}}+608 x \ln \left (x \right )^{3}+16 x^{8}-2080 \ln \left (x \right )^{3}+16 \ln \left (x \right )^{4}+304 x^{6}-128 x^{7}+872 x^{3} \ln \left (x \right )-64 x^{2} \ln \left (x \right )^{3}-1050 x \ln \left (x \right )+1780 x^{2} \ln \left (x \right )-1375 \ln \left (x \right )-1350 \ln \left (x \right )^{2}+475 x^{2}+40 x^{3}-554 x^{4}-32 x^{5}\) | \(247\) |
| parts | \(249 x +96 x^{4} \ln \left (x \right )^{2}+544 x^{5} \ln \left (x \right )-64 x^{6} \ln \left (x \right )-1488 x^{4} \ln \left (x \right )-864 x^{3} \ln \left (x \right )^{2}-\frac {625 \ln \left (x \right )}{2 x}+2664 x^{2} \ln \left (x \right )^{2}-2640 x \ln \left (x \right )^{2}+\frac {2800 \ln \left (x \right )^{3}}{x}-\frac {160 \ln \left (x \right )^{4}}{x}-\frac {500 \ln \left (x \right )^{3}}{x^{2}}+\frac {625 \ln \left (x \right )^{4}}{x^{4}}+\frac {600 \ln \left (x \right )^{4}}{x^{2}}-\frac {1250 \ln \left (x \right )^{3}}{x^{3}}-\frac {1000 \ln \left (x \right )^{4}}{x^{3}}+\frac {2250 \ln \left (x \right )^{2}}{x}+\frac {1875 \ln \left (x \right )^{2}}{2 x^{2}}+608 x \ln \left (x \right )^{3}+16 x^{8}-2080 \ln \left (x \right )^{3}+16 \ln \left (x \right )^{4}+304 x^{6}-128 x^{7}+872 x^{3} \ln \left (x \right )-64 x^{2} \ln \left (x \right )^{3}-1050 x \ln \left (x \right )+1780 x^{2} \ln \left (x \right )-\frac {625}{2 x}-1375 \ln \left (x \right )-1350 \ln \left (x \right )^{2}+475 x^{2}+40 x^{3}-554 x^{4}-32 x^{5}+\frac {2 \ln \left (3\right )+1875}{6 x}\) | \(256\) |
| parallelrisch | \(\frac {-5184 x^{7} \ln \left (x \right )^{2}+3264 x^{9} \ln \left (x \right )-8928 x^{8} \ln \left (x \right )+576 x^{8} \ln \left (x \right )^{2}+15984 x^{6} \ln \left (x \right )^{2}-8100 x^{4} \ln \left (x \right )^{2}-6300 x^{5} \ln \left (x \right )+10680 x^{6} \ln \left (x \right )+5232 x^{7} \ln \left (x \right )+3600 x^{2} \ln \left (x \right )^{4}-15840 x^{5} \ln \left (x \right )^{2}-8250 x^{4} \ln \left (x \right )+13500 x^{3} \ln \left (x \right )^{2}-384 x^{6} \ln \left (x \right )^{3}+16800 x^{3} \ln \left (x \right )^{3}-6000 x \ln \left (x \right )^{4}+5625 x^{2} \ln \left (x \right )^{2}+96 x^{4} \ln \left (x \right )^{4}-960 x^{3} \ln \left (x \right )^{4}-12480 x^{4} \ln \left (x \right )^{3}-384 \ln \left (x \right ) x^{10}+3648 \ln \left (x \right )^{3} x^{5}+2 x^{3} \ln \left (3\right )-7500 x \ln \left (x \right )^{3}+96 x^{12}-768 x^{11}-3324 x^{8}+3750 \ln \left (x \right )^{4}+2850 x^{6}-192 x^{9}+1824 x^{10}+240 x^{7}-1875 x^{3} \ln \left (x \right )-3000 x^{2} \ln \left (x \right )^{3}+1494 x^{5}}{6 x^{4}}\) | \(265\) |
Input:
int(1/6*((960*x^3-7200*x^2+18000*x-15000)*ln(x)^4+(-768*x^6+3648*x^5+384*x ^4-20640*x^3+20400*x^2-1500*x+15000)*ln(x)^3+(2304*x^8-15552*x^7+30816*x^6 -4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*ln(x)^2+(-2304*x^10+16320 *x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+11250*x^2) *ln(x)-2*x^3*ln(3)+768*x^12-5376*x^11+10560*x^10+2304*x^9-22224*x^8+5952*x ^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x,method=_RETURNVERBOSE)
Output:
(16*x^4-160*x^3+600*x^2-1000*x+625)/x^4*ln(x)^4-2*(32*x^5-304*x^4+1040*x^3 -1400*x^2+250*x+625)/x^3*ln(x)^3+3/2*(64*x^6-576*x^5+1776*x^4-1760*x^3-900 *x^2+1500*x+625)/x^2*ln(x)^2-1/2*(128*x^7-1088*x^6+2976*x^5-1744*x^4-3560* x^3+2100*x^2+625)/x*ln(x)+1/3*(48*x^9-384*x^8+912*x^7-96*x^6-1662*x^5+120* x^4+1425*x^3-4125*x*ln(x)+747*x^2+ln(3))/x
Leaf count of result is larger than twice the leaf count of optimal. 201 vs. \(2 (36) = 72\).
Time = 0.10 (sec) , antiderivative size = 201, normalized size of antiderivative = 5.15 \[ \int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx=\frac {96 \, x^{12} - 768 \, x^{11} + 1824 \, x^{10} - 192 \, x^{9} - 3324 \, x^{8} + 240 \, x^{7} + 2850 \, x^{6} + 1494 \, x^{5} + 6 \, {\left (16 \, x^{4} - 160 \, x^{3} + 600 \, x^{2} - 1000 \, x + 625\right )} \log \left (x\right )^{4} + 2 \, x^{3} \log \left (3\right ) - 12 \, {\left (32 \, x^{6} - 304 \, x^{5} + 1040 \, x^{4} - 1400 \, x^{3} + 250 \, x^{2} + 625 \, x\right )} \log \left (x\right )^{3} + 9 \, {\left (64 \, x^{8} - 576 \, x^{7} + 1776 \, x^{6} - 1760 \, x^{5} - 900 \, x^{4} + 1500 \, x^{3} + 625 \, x^{2}\right )} \log \left (x\right )^{2} - 3 \, {\left (128 \, x^{10} - 1088 \, x^{9} + 2976 \, x^{8} - 1744 \, x^{7} - 3560 \, x^{6} + 2100 \, x^{5} + 2750 \, x^{4} + 625 \, x^{3}\right )} \log \left (x\right )}{6 \, x^{4}} \] Input:
integrate(1/6*((960*x^3-7200*x^2+18000*x-15000)*log(x)^4+(-768*x^6+3648*x^ 5+384*x^4-20640*x^3+20400*x^2-1500*x+15000)*log(x)^3+(2304*x^8-15552*x^7+3 0816*x^6-4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*log(x)^2+(-2304*x ^10+16320*x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+1 1250*x^2)*log(x)-2*x^3*log(3)+768*x^12-5376*x^11+10560*x^10+2304*x^9-22224 *x^8+5952*x^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x, algorithm="fric as")
Output:
1/6*(96*x^12 - 768*x^11 + 1824*x^10 - 192*x^9 - 3324*x^8 + 240*x^7 + 2850* x^6 + 1494*x^5 + 6*(16*x^4 - 160*x^3 + 600*x^2 - 1000*x + 625)*log(x)^4 + 2*x^3*log(3) - 12*(32*x^6 - 304*x^5 + 1040*x^4 - 1400*x^3 + 250*x^2 + 625* x)*log(x)^3 + 9*(64*x^8 - 576*x^7 + 1776*x^6 - 1760*x^5 - 900*x^4 + 1500*x ^3 + 625*x^2)*log(x)^2 - 3*(128*x^10 - 1088*x^9 + 2976*x^8 - 1744*x^7 - 35 60*x^6 + 2100*x^5 + 2750*x^4 + 625*x^3)*log(x))/x^4
Leaf count of result is larger than twice the leaf count of optimal. 192 vs. \(2 (26) = 52\).
Time = 0.33 (sec) , antiderivative size = 192, normalized size of antiderivative = 4.92 \[ \int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx=16 x^{8} - 128 x^{7} + 304 x^{6} - 32 x^{5} - 554 x^{4} + 40 x^{3} + 475 x^{2} + 249 x - 1375 \log {\left (x \right )} + \frac {\left (- 128 x^{7} + 1088 x^{6} - 2976 x^{5} + 1744 x^{4} + 3560 x^{3} - 2100 x^{2} - 625\right ) \log {\left (x \right )}}{2 x} + \frac {\log {\left (3 \right )}}{3 x} + \frac {\left (192 x^{6} - 1728 x^{5} + 5328 x^{4} - 5280 x^{3} - 2700 x^{2} + 4500 x + 1875\right ) \log {\left (x \right )}^{2}}{2 x^{2}} + \frac {\left (- 64 x^{5} + 608 x^{4} - 2080 x^{3} + 2800 x^{2} - 500 x - 1250\right ) \log {\left (x \right )}^{3}}{x^{3}} + \frac {\left (16 x^{4} - 160 x^{3} + 600 x^{2} - 1000 x + 625\right ) \log {\left (x \right )}^{4}}{x^{4}} \] Input:
integrate(1/6*((960*x**3-7200*x**2+18000*x-15000)*ln(x)**4+(-768*x**6+3648 *x**5+384*x**4-20640*x**3+20400*x**2-1500*x+15000)*ln(x)**3+(2304*x**8-155 52*x**7+30816*x**6-4896*x**5-37440*x**4+36900*x**3-20250*x**2-22500*x)*ln( x)**2+(-2304*x**10+16320*x**9-34560*x**8+5328*x**7+53328*x**6-37980*x**5-1 6200*x**4+28875*x**3+11250*x**2)*ln(x)-2*x**3*ln(3)+768*x**12-5376*x**11+1 0560*x**10+2304*x**9-22224*x**8+5952*x**7+16380*x**6-4806*x**5-8250*x**4-1 875*x**3)/x**5,x)
Output:
16*x**8 - 128*x**7 + 304*x**6 - 32*x**5 - 554*x**4 + 40*x**3 + 475*x**2 + 249*x - 1375*log(x) + (-128*x**7 + 1088*x**6 - 2976*x**5 + 1744*x**4 + 356 0*x**3 - 2100*x**2 - 625)*log(x)/(2*x) + log(3)/(3*x) + (192*x**6 - 1728*x **5 + 5328*x**4 - 5280*x**3 - 2700*x**2 + 4500*x + 1875)*log(x)**2/(2*x**2 ) + (-64*x**5 + 608*x**4 - 2080*x**3 + 2800*x**2 - 500*x - 1250)*log(x)**3 /x**3 + (16*x**4 - 160*x**3 + 600*x**2 - 1000*x + 625)*log(x)**4/x**4
Leaf count of result is larger than twice the leaf count of optimal. 491 vs. \(2 (36) = 72\).
Time = 0.05 (sec) , antiderivative size = 491, normalized size of antiderivative = 12.59 \[ \int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx =\text {Too large to display} \] Input:
integrate(1/6*((960*x^3-7200*x^2+18000*x-15000)*log(x)^4+(-768*x^6+3648*x^ 5+384*x^4-20640*x^3+20400*x^2-1500*x+15000)*log(x)^3+(2304*x^8-15552*x^7+3 0816*x^6-4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*log(x)^2+(-2304*x ^10+16320*x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+1 1250*x^2)*log(x)-2*x^3*log(3)+768*x^12-5376*x^11+10560*x^10+2304*x^9-22224 *x^8+5952*x^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x, algorithm="maxi ma")
Output:
16*x^8 - 128*x^7 - 64*x^6*log(x) + 304*x^6 + 544*x^5*log(x) + 12*(8*log(x) ^2 - 4*log(x) + 1)*x^4 - 32*x^5 - 1440*x^4*log(x) - 96*(9*log(x)^2 - 6*log (x) + 2)*x^3 - 566*x^4 + 296*x^3*log(x) + 16*log(x)^4 - 16*(4*log(x)^3 - 6 *log(x)^2 + 6*log(x) - 3)*x^2 + 1284*(2*log(x)^2 - 2*log(x) + 1)*x^2 + 232 *x^3 + 4444*x^2*log(x) - 2080*log(x)^3 + 608*(log(x)^3 - 3*log(x)^2 + 6*lo g(x) - 6)*x - 816*(log(x)^2 - 2*log(x) + 2)*x - 857*x^2 - 6330*x*log(x) - 1350*log(x)^2 + 5529*x - 160*(log(x)^4 + 4*log(x)^3 + 12*log(x)^2 + 24*log (x) + 24)/x + 3440*(log(x)^3 + 3*log(x)^2 + 6*log(x) + 6)/x - 6150*(log(x) ^2 + 2*log(x) + 2)/x + 1/3*log(3)/x - 9625/2*log(x)/x + 300*(2*log(x)^4 + 4*log(x)^3 + 6*log(x)^2 + 6*log(x) + 3)/x^2 - 425*(4*log(x)^3 + 6*log(x)^2 + 6*log(x) + 3)/x^2 + 3375/4*(2*log(x)^2 + 2*log(x) + 1)/x^2 - 4500/x - 1 875/2*log(x)/x^2 - 1000/27*(27*log(x)^4 + 36*log(x)^3 + 36*log(x)^2 + 24*l og(x) + 8)/x^3 + 250/27*(9*log(x)^3 + 9*log(x)^2 + 6*log(x) + 2)/x^3 + 125 0/9*(9*log(x)^2 + 6*log(x) + 2)/x^3 - 1875/4/x^2 + 625/32*(32*log(x)^4 + 3 2*log(x)^3 + 24*log(x)^2 + 12*log(x) + 3)/x^4 - 625/32*(32*log(x)^3 + 24*l og(x)^2 + 12*log(x) + 3)/x^4 - 1375*log(x)
\[ \int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx=\int { \frac {768 \, x^{12} - 5376 \, x^{11} + 10560 \, x^{10} + 2304 \, x^{9} - 22224 \, x^{8} + 5952 \, x^{7} + 16380 \, x^{6} - 4806 \, x^{5} + 120 \, {\left (8 \, x^{3} - 60 \, x^{2} + 150 \, x - 125\right )} \log \left (x\right )^{4} - 8250 \, x^{4} - 2 \, x^{3} \log \left (3\right ) - 12 \, {\left (64 \, x^{6} - 304 \, x^{5} - 32 \, x^{4} + 1720 \, x^{3} - 1700 \, x^{2} + 125 \, x - 1250\right )} \log \left (x\right )^{3} - 1875 \, x^{3} + 18 \, {\left (128 \, x^{8} - 864 \, x^{7} + 1712 \, x^{6} - 272 \, x^{5} - 2080 \, x^{4} + 2050 \, x^{3} - 1125 \, x^{2} - 1250 \, x\right )} \log \left (x\right )^{2} - 3 \, {\left (768 \, x^{10} - 5440 \, x^{9} + 11520 \, x^{8} - 1776 \, x^{7} - 17776 \, x^{6} + 12660 \, x^{5} + 5400 \, x^{4} - 9625 \, x^{3} - 3750 \, x^{2}\right )} \log \left (x\right )}{6 \, x^{5}} \,d x } \] Input:
integrate(1/6*((960*x^3-7200*x^2+18000*x-15000)*log(x)^4+(-768*x^6+3648*x^ 5+384*x^4-20640*x^3+20400*x^2-1500*x+15000)*log(x)^3+(2304*x^8-15552*x^7+3 0816*x^6-4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*log(x)^2+(-2304*x ^10+16320*x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+1 1250*x^2)*log(x)-2*x^3*log(3)+768*x^12-5376*x^11+10560*x^10+2304*x^9-22224 *x^8+5952*x^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x, algorithm="giac ")
Output:
integrate(1/6*(768*x^12 - 5376*x^11 + 10560*x^10 + 2304*x^9 - 22224*x^8 + 5952*x^7 + 16380*x^6 - 4806*x^5 + 120*(8*x^3 - 60*x^2 + 150*x - 125)*log(x )^4 - 8250*x^4 - 2*x^3*log(3) - 12*(64*x^6 - 304*x^5 - 32*x^4 + 1720*x^3 - 1700*x^2 + 125*x - 1250)*log(x)^3 - 1875*x^3 + 18*(128*x^8 - 864*x^7 + 17 12*x^6 - 272*x^5 - 2080*x^4 + 2050*x^3 - 1125*x^2 - 1250*x)*log(x)^2 - 3*( 768*x^10 - 5440*x^9 + 11520*x^8 - 1776*x^7 - 17776*x^6 + 12660*x^5 + 5400* x^4 - 9625*x^3 - 3750*x^2)*log(x))/x^5, x)
Time = 6.24 (sec) , antiderivative size = 246, normalized size of antiderivative = 6.31 \[ \int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx=249\,x-1375\,\ln \left (x\right )-\frac {625\,\ln \left (x\right )}{2\,x}-2640\,x\,{\ln \left (x\right )}^2+1780\,x^2\,\ln \left (x\right )+608\,x\,{\ln \left (x\right )}^3+872\,x^3\,\ln \left (x\right )-1488\,x^4\,\ln \left (x\right )+544\,x^5\,\ln \left (x\right )-64\,x^6\,\ln \left (x\right )-1350\,{\ln \left (x\right )}^2-2080\,{\ln \left (x\right )}^3+16\,{\ln \left (x\right )}^4+\frac {2250\,{\ln \left (x\right )}^2}{x}+\frac {2800\,{\ln \left (x\right )}^3}{x}+\frac {1875\,{\ln \left (x\right )}^2}{2\,x^2}+2664\,x^2\,{\ln \left (x\right )}^2-\frac {160\,{\ln \left (x\right )}^4}{x}-\frac {500\,{\ln \left (x\right )}^3}{x^2}-64\,x^2\,{\ln \left (x\right )}^3-864\,x^3\,{\ln \left (x\right )}^2+\frac {600\,{\ln \left (x\right )}^4}{x^2}-\frac {1250\,{\ln \left (x\right )}^3}{x^3}+96\,x^4\,{\ln \left (x\right )}^2-\frac {1000\,{\ln \left (x\right )}^4}{x^3}+\frac {625\,{\ln \left (x\right )}^4}{x^4}+\frac {\ln \left (3\right )}{3\,x}-1050\,x\,\ln \left (x\right )+475\,x^2+40\,x^3-554\,x^4-32\,x^5+304\,x^6-128\,x^7+16\,x^8 \] Input:
int(((log(x)^4*(18000*x - 7200*x^2 + 960*x^3 - 15000))/6 - (log(x)^2*(2250 0*x + 20250*x^2 - 36900*x^3 + 37440*x^4 + 4896*x^5 - 30816*x^6 + 15552*x^7 - 2304*x^8))/6 + (log(x)*(11250*x^2 + 28875*x^3 - 16200*x^4 - 37980*x^5 + 53328*x^6 + 5328*x^7 - 34560*x^8 + 16320*x^9 - 2304*x^10))/6 - (x^3*log(3 ))/3 - (625*x^3)/2 - 1375*x^4 - 801*x^5 + 2730*x^6 + 992*x^7 - 3704*x^8 + 384*x^9 + 1760*x^10 - 896*x^11 + 128*x^12 + (log(x)^3*(20400*x^2 - 1500*x - 20640*x^3 + 384*x^4 + 3648*x^5 - 768*x^6 + 15000))/6)/x^5,x)
Output:
249*x - 1375*log(x) - (625*log(x))/(2*x) - 2640*x*log(x)^2 + 1780*x^2*log( x) + 608*x*log(x)^3 + 872*x^3*log(x) - 1488*x^4*log(x) + 544*x^5*log(x) - 64*x^6*log(x) - 1350*log(x)^2 - 2080*log(x)^3 + 16*log(x)^4 + (2250*log(x) ^2)/x + (2800*log(x)^3)/x + (1875*log(x)^2)/(2*x^2) + 2664*x^2*log(x)^2 - (160*log(x)^4)/x - (500*log(x)^3)/x^2 - 64*x^2*log(x)^3 - 864*x^3*log(x)^2 + (600*log(x)^4)/x^2 - (1250*log(x)^3)/x^3 + 96*x^4*log(x)^2 - (1000*log( x)^4)/x^3 + (625*log(x)^4)/x^4 + log(3)/(3*x) - 1050*x*log(x) + 475*x^2 + 40*x^3 - 554*x^4 - 32*x^5 + 304*x^6 - 128*x^7 + 16*x^8
Time = 0.17 (sec) , antiderivative size = 264, normalized size of antiderivative = 6.77 \[ \int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx=\frac {-8100 \mathrm {log}\left (x \right )^{2} x^{4}+13500 \mathrm {log}\left (x \right )^{2} x^{3}-12480 \mathrm {log}\left (x \right )^{3} x^{4}-15840 \mathrm {log}\left (x \right )^{2} x^{5}+1824 x^{10}-192 x^{9}+5625 \mathrm {log}\left (x \right )^{2} x^{2}-8250 \,\mathrm {log}\left (x \right ) x^{4}+3648 \mathrm {log}\left (x \right )^{3} x^{5}+5232 \,\mathrm {log}\left (x \right ) x^{7}+2 \,\mathrm {log}\left (3\right ) x^{3}+1494 x^{5}+15984 \mathrm {log}\left (x \right )^{2} x^{6}+240 x^{7}+3600 \mathrm {log}\left (x \right )^{4} x^{2}+96 \mathrm {log}\left (x \right )^{4} x^{4}-960 \mathrm {log}\left (x \right )^{4} x^{3}-3324 x^{8}+2850 x^{6}-6300 \,\mathrm {log}\left (x \right ) x^{5}+96 x^{12}-6000 \mathrm {log}\left (x \right )^{4} x -8928 \,\mathrm {log}\left (x \right ) x^{8}-1875 \,\mathrm {log}\left (x \right ) x^{3}-7500 \mathrm {log}\left (x \right )^{3} x +3750 \mathrm {log}\left (x \right )^{4}-384 \mathrm {log}\left (x \right )^{3} x^{6}+16800 \mathrm {log}\left (x \right )^{3} x^{3}+576 \mathrm {log}\left (x \right )^{2} x^{8}-5184 \mathrm {log}\left (x \right )^{2} x^{7}-384 \,\mathrm {log}\left (x \right ) x^{10}+3264 \,\mathrm {log}\left (x \right ) x^{9}-768 x^{11}-3000 \mathrm {log}\left (x \right )^{3} x^{2}+10680 \,\mathrm {log}\left (x \right ) x^{6}}{6 x^{4}} \] Input:
int(1/6*((960*x^3-7200*x^2+18000*x-15000)*log(x)^4+(-768*x^6+3648*x^5+384* x^4-20640*x^3+20400*x^2-1500*x+15000)*log(x)^3+(2304*x^8-15552*x^7+30816*x ^6-4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*log(x)^2+(-2304*x^10+16 320*x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+11250*x ^2)*log(x)-2*x^3*log(3)+768*x^12-5376*x^11+10560*x^10+2304*x^9-22224*x^8+5 952*x^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x)
Output:
(96*log(x)**4*x**4 - 960*log(x)**4*x**3 + 3600*log(x)**4*x**2 - 6000*log(x )**4*x + 3750*log(x)**4 - 384*log(x)**3*x**6 + 3648*log(x)**3*x**5 - 12480 *log(x)**3*x**4 + 16800*log(x)**3*x**3 - 3000*log(x)**3*x**2 - 7500*log(x) **3*x + 576*log(x)**2*x**8 - 5184*log(x)**2*x**7 + 15984*log(x)**2*x**6 - 15840*log(x)**2*x**5 - 8100*log(x)**2*x**4 + 13500*log(x)**2*x**3 + 5625*l og(x)**2*x**2 - 384*log(x)*x**10 + 3264*log(x)*x**9 - 8928*log(x)*x**8 + 5 232*log(x)*x**7 + 10680*log(x)*x**6 - 6300*log(x)*x**5 - 8250*log(x)*x**4 - 1875*log(x)*x**3 + 2*log(3)*x**3 + 96*x**12 - 768*x**11 + 1824*x**10 - 1 92*x**9 - 3324*x**8 + 240*x**7 + 2850*x**6 + 1494*x**5)/(6*x**4)