Integrand size = 194, antiderivative size = 27 \[ \int \frac {-60 x^4-36 x^5+40 x^6+e^6 \left (-12-20 x+8 x^2\right )+e^3 \left (72 x^2+56 x^3-48 x^4\right )+\left (-240 x^4-160 x^5+144 x^6+e^3 \left (144 x^2+128 x^3-80 x^4\right )\right ) \log (3-x)+\left (-360 x^4-264 x^5+192 x^6+e^3 \left (72 x^2+72 x^3-32 x^4\right )\right ) \log ^2(3-x)+\left (-240 x^4-192 x^5+112 x^6\right ) \log ^3(3-x)+\left (-60 x^4-52 x^5+24 x^6\right ) \log ^4(3-x)}{-3+x} \, dx=4 x (1+x) \left (e^3-x^2 (1+\log (3-x))^2\right )^2 \] Output:
4*x*(1+x)*(exp(3)-(ln(3-x)+1)^2*x^2)^2
Time = 0.06 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.48 \[ \int \frac {-60 x^4-36 x^5+40 x^6+e^6 \left (-12-20 x+8 x^2\right )+e^3 \left (72 x^2+56 x^3-48 x^4\right )+\left (-240 x^4-160 x^5+144 x^6+e^3 \left (144 x^2+128 x^3-80 x^4\right )\right ) \log (3-x)+\left (-360 x^4-264 x^5+192 x^6+e^3 \left (72 x^2+72 x^3-32 x^4\right )\right ) \log ^2(3-x)+\left (-240 x^4-192 x^5+112 x^6\right ) \log ^3(3-x)+\left (-60 x^4-52 x^5+24 x^6\right ) \log ^4(3-x)}{-3+x} \, dx=4 x (1+x) \left (-e^3+x^2+2 x^2 \log (3-x)+x^2 \log ^2(3-x)\right )^2 \] Input:
Integrate[(-60*x^4 - 36*x^5 + 40*x^6 + E^6*(-12 - 20*x + 8*x^2) + E^3*(72* x^2 + 56*x^3 - 48*x^4) + (-240*x^4 - 160*x^5 + 144*x^6 + E^3*(144*x^2 + 12 8*x^3 - 80*x^4))*Log[3 - x] + (-360*x^4 - 264*x^5 + 192*x^6 + E^3*(72*x^2 + 72*x^3 - 32*x^4))*Log[3 - x]^2 + (-240*x^4 - 192*x^5 + 112*x^6)*Log[3 - x]^3 + (-60*x^4 - 52*x^5 + 24*x^6)*Log[3 - x]^4)/(-3 + x),x]
Output:
4*x*(1 + x)*(-E^3 + x^2 + 2*x^2*Log[3 - x] + x^2*Log[3 - x]^2)^2
Leaf count is larger than twice the leaf count of optimal. \(1216\) vs. \(2(27)=54\).
Time = 6.14 (sec) , antiderivative size = 1216, normalized size of antiderivative = 45.04, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {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.
| \(\displaystyle \int \frac {40 x^6-36 x^5-60 x^4+e^6 \left (8 x^2-20 x-12\right )+\left (24 x^6-52 x^5-60 x^4\right ) \log ^4(3-x)+\left (112 x^6-192 x^5-240 x^4\right ) \log ^3(3-x)+e^3 \left (-48 x^4+56 x^3+72 x^2\right )+\left (192 x^6-264 x^5-360 x^4+e^3 \left (-32 x^4+72 x^3+72 x^2\right )\right ) \log ^2(3-x)+\left (144 x^6-160 x^5-240 x^4+e^3 \left (-80 x^4+128 x^3+144 x^2\right )\right ) \log (3-x)}{x-3} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (4 (6 x+5) x^4 \log ^4(3-x)+\frac {16 \left (7 x^2-12 x-15\right ) x^4 \log ^3(3-x)}{x-3}+\frac {8 \left (-24 x^4+33 x^3+\left (45+4 e^3\right ) x^2-9 e^3 x-9 e^3\right ) x^2 \log ^2(3-x)}{3-x}+\frac {16 \left (-9 x^4+10 x^3+5 \left (3+e^3\right ) x^2-8 e^3 x-9 e^3\right ) x^2 \log (3-x)}{3-x}+\frac {4 \left (-10 x^6+9 x^5+15 \left (1+\frac {4 e^3}{5}\right ) x^4-14 e^3 x^3-18 e^3 \left (1+\frac {e^3}{9}\right ) x^2+5 e^6 x+3 e^6\right )}{3-x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 \log ^4(3-x) (3-x)^6+16 \log ^3(3-x) (3-x)^6-8 \log ^2(3-x) (3-x)^6-8 \log (3-x) (3-x)^6+\frac {4}{3} (3-x)^6-76 \log ^4(3-x) (3-x)^5-304 \log ^3(3-x) (3-x)^5+\frac {912}{5} \log ^2(3-x) (3-x)^5+\frac {912}{5} \log (3-x) (3-x)^5-\frac {912}{25} (3-x)^5+600 \log ^4(3-x) (3-x)^4+2400 \log ^3(3-x) (3-x)^4-1800 \log ^2(3-x) (3-x)^4-4 \left (18-e^3\right ) \log (3-x) (3-x)^4-1728 \log (3-x) (3-x)^4+\left (18-e^3\right ) (3-x)^4+432 (3-x)^4-2520 \log ^4(3-x) (3-x)^3-10080 \log ^3(3-x) (3-x)^3+10080 \log ^2(3-x) (3-x)^3+\frac {16}{3} \left (72-e^3\right ) \log (3-x) (3-x)^3+64 \left (18-e^3\right ) \log (3-x) (3-x)^3+8544 \log (3-x) (3-x)^3-\frac {16}{9} \left (72-e^3\right ) (3-x)^3-\frac {64}{3} \left (18-e^3\right ) (3-x)^3-2848 (3-x)^3+5940 \log ^4(3-x) (3-x)^2+23760 \log ^3(3-x) (3-x)^2-33048 \log ^2(3-x) (3-x)^2-72 \left (72-e^3\right ) \log (3-x) (3-x)^2-432 \left (18-e^3\right ) \log (3-x) (3-x)^2-22680 \log (3-x) (3-x)^2+36 \left (72-e^3\right ) (3-x)^2+216 \left (18-e^3\right ) (3-x)^2+11340 (3-x)^2-7452 \log ^4(3-x) (3-x)-29808 \log ^3(3-x) (3-x)+58320 \log ^2(3-x) (3-x)+432 \left (72-e^3\right ) \log (3-x) (3-x)-576 \left (27-e^3\right ) \log (3-x) (3-x)+1728 \left (18-e^3\right ) \log (3-x) (3-x)+27216 \log (3-x) (3-x)+\frac {8 x^6}{3}-\frac {212 x^5}{25}+12 \left (4-e^3\right ) x^4-\left (36-5 e^3\right ) x^4-\frac {474 x^4}{5}+3888 \log ^4(3-x)-4 \left (36-5 e^3\right ) x^3-\frac {16}{9} \left (108-7 e^3\right ) x^3+\frac {8}{3} \left (72-11 e^3\right ) x^3-\frac {1896 x^3}{5}+15552 \log ^3(3-x)+4 \left (216-24 e^3+e^6\right ) x^2-48 \left (27-e^3\right ) x^2-18 \left (36-5 e^3\right ) x^2-8 \left (108-7 e^3\right ) x^2-\frac {8532 x^2}{5}+32 x^6 \log ^2(3-x)+\frac {312}{5} x^5 \log ^2(3-x)+8 \left (18-e^3\right ) x^4 \log ^2(3-x)+8 \left (72-e^3\right ) x^3 \log ^2(3-x)-216 \left (72-e^3\right ) \log ^2(3-x)+864 \left (27-e^3\right ) \log ^2(3-x)-648 \left (18-e^3\right ) \log ^2(3-x)-\frac {192456}{5} \log ^2(3-x)+4 \left (1296-144 e^3+e^6\right ) x+432 \left (72-e^3\right ) x-864 \left (27-e^3\right ) x+1728 \left (18-e^3\right ) x-108 \left (36-5 e^3\right ) x-48 \left (108-7 e^3\right ) x+\frac {84888 x}{5}+24 x^6 \log (3-x)+\frac {272}{5} x^5 \log (3-x)+4 \left (36-5 e^3\right ) x^4 \log (3-x)+\frac {16}{3} \left (108-7 e^3\right ) x^3 \log (3-x)+96 \left (27-e^3\right ) x^2 \log (3-x)-864 \left (27-e^3\right ) \log (3-x)+1728 \left (9-e^3\right ) \log (3-x)-324 \left (36-5 e^3\right ) \log (3-x)-144 \left (108-7 e^3\right ) \log (3-x)-\frac {153576}{5} \log (3-x)\) |
Input:
Int[(-60*x^4 - 36*x^5 + 40*x^6 + E^6*(-12 - 20*x + 8*x^2) + E^3*(72*x^2 + 56*x^3 - 48*x^4) + (-240*x^4 - 160*x^5 + 144*x^6 + E^3*(144*x^2 + 128*x^3 - 80*x^4))*Log[3 - x] + (-360*x^4 - 264*x^5 + 192*x^6 + E^3*(72*x^2 + 72*x ^3 - 32*x^4))*Log[3 - x]^2 + (-240*x^4 - 192*x^5 + 112*x^6)*Log[3 - x]^3 + (-60*x^4 - 52*x^5 + 24*x^6)*Log[3 - x]^4)/(-3 + x),x]
Output:
11340*(3 - x)^2 + 216*(18 - E^3)*(3 - x)^2 + 36*(72 - E^3)*(3 - x)^2 - 284 8*(3 - x)^3 - (64*(18 - E^3)*(3 - x)^3)/3 - (16*(72 - E^3)*(3 - x)^3)/9 + 432*(3 - x)^4 + (18 - E^3)*(3 - x)^4 - (912*(3 - x)^5)/25 + (4*(3 - x)^6)/ 3 + (84888*x)/5 - 48*(108 - 7*E^3)*x - 108*(36 - 5*E^3)*x + 1728*(18 - E^3 )*x - 864*(27 - E^3)*x + 432*(72 - E^3)*x + 4*(1296 - 144*E^3 + E^6)*x - ( 8532*x^2)/5 - 8*(108 - 7*E^3)*x^2 - 18*(36 - 5*E^3)*x^2 - 48*(27 - E^3)*x^ 2 + 4*(216 - 24*E^3 + E^6)*x^2 - (1896*x^3)/5 + (8*(72 - 11*E^3)*x^3)/3 - (16*(108 - 7*E^3)*x^3)/9 - 4*(36 - 5*E^3)*x^3 - (474*x^4)/5 - (36 - 5*E^3) *x^4 + 12*(4 - E^3)*x^4 - (212*x^5)/25 + (8*x^6)/3 - (153576*Log[3 - x])/5 - 144*(108 - 7*E^3)*Log[3 - x] - 324*(36 - 5*E^3)*Log[3 - x] + 1728*(9 - E^3)*Log[3 - x] - 864*(27 - E^3)*Log[3 - x] + 27216*(3 - x)*Log[3 - x] + 1 728*(18 - E^3)*(3 - x)*Log[3 - x] - 576*(27 - E^3)*(3 - x)*Log[3 - x] + 43 2*(72 - E^3)*(3 - x)*Log[3 - x] - 22680*(3 - x)^2*Log[3 - x] - 432*(18 - E ^3)*(3 - x)^2*Log[3 - x] - 72*(72 - E^3)*(3 - x)^2*Log[3 - x] + 8544*(3 - x)^3*Log[3 - x] + 64*(18 - E^3)*(3 - x)^3*Log[3 - x] + (16*(72 - E^3)*(3 - x)^3*Log[3 - x])/3 - 1728*(3 - x)^4*Log[3 - x] - 4*(18 - E^3)*(3 - x)^4*L og[3 - x] + (912*(3 - x)^5*Log[3 - x])/5 - 8*(3 - x)^6*Log[3 - x] + 96*(27 - E^3)*x^2*Log[3 - x] + (16*(108 - 7*E^3)*x^3*Log[3 - x])/3 + 4*(36 - 5*E ^3)*x^4*Log[3 - x] + (272*x^5*Log[3 - x])/5 + 24*x^6*Log[3 - x] - (192456* Log[3 - x]^2)/5 - 648*(18 - E^3)*Log[3 - x]^2 + 864*(27 - E^3)*Log[3 - ...
Leaf count of result is larger than twice the leaf count of optimal. \(534\) vs. \(2(26)=52\).
Time = 0.02 (sec) , antiderivative size = 535, normalized size of antiderivative = 19.81
\[-3888-8 x^{3} {\mathrm e}^{3}+3888 \ln \left (-x +3\right )^{4}+15552 \ln \left (-x +3\right )^{3}+23328 \ln \left (-x +3\right )^{2}-8 x^{4} {\mathrm e}^{3}+4 x^{2} {\mathrm e}^{6}+4 x \,{\mathrm e}^{6}-48 \,{\mathrm e}^{6}+15552 \ln \left (-x +3\right )+4 x^{6}+4 x^{5}+864 \,{\mathrm e}^{3}+4 \ln \left (-x +3\right )^{4} \left (-x +3\right )^{6}-76 \ln \left (-x +3\right )^{4} \left (-x +3\right )^{5}+16 \ln \left (-x +3\right )^{3} \left (-x +3\right )^{6}+600 \ln \left (-x +3\right )^{4} \left (-x +3\right )^{4}-304 \ln \left (-x +3\right )^{3} \left (-x +3\right )^{5}+24 \ln \left (-x +3\right )^{2} \left (-x +3\right )^{6}-2520 \ln \left (-x +3\right )^{4} \left (-x +3\right )^{3}-44712 \ln \left (-x +3\right )^{2} \left (-x +3\right )+23760 \ln \left (-x +3\right ) \left (-x +3\right )^{2}-29808 \ln \left (-x +3\right ) \left (-x +3\right )-29808 \ln \left (-x +3\right )^{3} \left (-x +3\right )+35640 \ln \left (-x +3\right )^{2} \left (-x +3\right )^{2}-10080 \ln \left (-x +3\right ) \left (-x +3\right )^{3}+2400 \ln \left (-x +3\right )^{3} \left (-x +3\right )^{4}-456 \ln \left (-x +3\right )^{2} \left (-x +3\right )^{5}+16 \ln \left (-x +3\right ) \left (-x +3\right )^{6}+5940 \ln \left (-x +3\right )^{4} \left (-x +3\right )^{2}-10080 \ln \left (-x +3\right )^{3} \left (-x +3\right )^{3}+3600 \ln \left (-x +3\right )^{2} \left (-x +3\right )^{4}-304 \ln \left (-x +3\right ) \left (-x +3\right )^{5}-7452 \ln \left (-x +3\right )^{4} \left (-x +3\right )+23760 \ln \left (-x +3\right )^{3} \left (-x +3\right )^{2}-15120 \ln \left (-x +3\right )^{2} \left (-x +3\right )^{3}+2400 \ln \left (-x +3\right ) \left (-x +3\right )^{4}-16 \,{\mathrm e}^{3} \ln \left (-x +3\right ) x^{3}-8 \,{\mathrm e}^{3} \ln \left (-x +3\right )^{2} x^{3}-16 \,{\mathrm e}^{3} \ln \left (-x +3\right ) x^{4}-8 \,{\mathrm e}^{3} \ln \left (-x +3\right )^{2} x^{4}\]
Input:
int(((24*x^6-52*x^5-60*x^4)*ln(-x+3)^4+(112*x^6-192*x^5-240*x^4)*ln(-x+3)^ 3+((-32*x^4+72*x^3+72*x^2)*exp(3)+192*x^6-264*x^5-360*x^4)*ln(-x+3)^2+((-8 0*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*ln(-x+3)+(8*x^2-20* x-12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/(-3+x) ,x)
Output:
-3888+4*x^2*exp(3)^2-8*x^3*exp(3)+3888*ln(-x+3)^4+15552*ln(-x+3)^3+23328*l n(-x+3)^2-8*x^4*exp(3)+4*x*exp(3)^2+15552*ln(-x+3)+4*x^6+4*x^5+864*exp(3)- 48*exp(3)^2+4*ln(-x+3)^4*(-x+3)^6-76*ln(-x+3)^4*(-x+3)^5+16*ln(-x+3)^3*(-x +3)^6+600*ln(-x+3)^4*(-x+3)^4-304*ln(-x+3)^3*(-x+3)^5+24*ln(-x+3)^2*(-x+3) ^6-2520*ln(-x+3)^4*(-x+3)^3-44712*ln(-x+3)^2*(-x+3)+23760*ln(-x+3)*(-x+3)^ 2-29808*ln(-x+3)*(-x+3)-29808*ln(-x+3)^3*(-x+3)+35640*ln(-x+3)^2*(-x+3)^2- 10080*ln(-x+3)*(-x+3)^3+2400*ln(-x+3)^3*(-x+3)^4-456*ln(-x+3)^2*(-x+3)^5+1 6*ln(-x+3)*(-x+3)^6+5940*ln(-x+3)^4*(-x+3)^2-10080*ln(-x+3)^3*(-x+3)^3+360 0*ln(-x+3)^2*(-x+3)^4-304*ln(-x+3)*(-x+3)^5-7452*ln(-x+3)^4*(-x+3)+23760*l n(-x+3)^3*(-x+3)^2-15120*ln(-x+3)^2*(-x+3)^3+2400*ln(-x+3)*(-x+3)^4-16*exp (3)*ln(-x+3)*x^3-8*exp(3)*ln(-x+3)^2*x^3-16*exp(3)*ln(-x+3)*x^4-8*exp(3)*l n(-x+3)^2*x^4
Leaf count of result is larger than twice the leaf count of optimal. 123 vs. \(2 (27) = 54\).
Time = 0.12 (sec) , antiderivative size = 123, normalized size of antiderivative = 4.56 \[ \int \frac {-60 x^4-36 x^5+40 x^6+e^6 \left (-12-20 x+8 x^2\right )+e^3 \left (72 x^2+56 x^3-48 x^4\right )+\left (-240 x^4-160 x^5+144 x^6+e^3 \left (144 x^2+128 x^3-80 x^4\right )\right ) \log (3-x)+\left (-360 x^4-264 x^5+192 x^6+e^3 \left (72 x^2+72 x^3-32 x^4\right )\right ) \log ^2(3-x)+\left (-240 x^4-192 x^5+112 x^6\right ) \log ^3(3-x)+\left (-60 x^4-52 x^5+24 x^6\right ) \log ^4(3-x)}{-3+x} \, dx=4 \, x^{6} + 4 \, x^{5} + 4 \, {\left (x^{6} + x^{5}\right )} \log \left (-x + 3\right )^{4} + 16 \, {\left (x^{6} + x^{5}\right )} \log \left (-x + 3\right )^{3} + 8 \, {\left (3 \, x^{6} + 3 \, x^{5} - {\left (x^{4} + x^{3}\right )} e^{3}\right )} \log \left (-x + 3\right )^{2} + 4 \, {\left (x^{2} + x\right )} e^{6} - 8 \, {\left (x^{4} + x^{3}\right )} e^{3} + 16 \, {\left (x^{6} + x^{5} - {\left (x^{4} + x^{3}\right )} e^{3}\right )} \log \left (-x + 3\right ) \] Input:
integrate(((24*x^6-52*x^5-60*x^4)*log(3-x)^4+(112*x^6-192*x^5-240*x^4)*log (3-x)^3+((-32*x^4+72*x^3+72*x^2)*exp(3)+192*x^6-264*x^5-360*x^4)*log(3-x)^ 2+((-80*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*log(3-x)+(8*x ^2-20*x-12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/ (-3+x),x, algorithm="fricas")
Output:
4*x^6 + 4*x^5 + 4*(x^6 + x^5)*log(-x + 3)^4 + 16*(x^6 + x^5)*log(-x + 3)^3 + 8*(3*x^6 + 3*x^5 - (x^4 + x^3)*e^3)*log(-x + 3)^2 + 4*(x^2 + x)*e^6 - 8 *(x^4 + x^3)*e^3 + 16*(x^6 + x^5 - (x^4 + x^3)*e^3)*log(-x + 3)
Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (22) = 44\).
Time = 0.18 (sec) , antiderivative size = 141, normalized size of antiderivative = 5.22 \[ \int \frac {-60 x^4-36 x^5+40 x^6+e^6 \left (-12-20 x+8 x^2\right )+e^3 \left (72 x^2+56 x^3-48 x^4\right )+\left (-240 x^4-160 x^5+144 x^6+e^3 \left (144 x^2+128 x^3-80 x^4\right )\right ) \log (3-x)+\left (-360 x^4-264 x^5+192 x^6+e^3 \left (72 x^2+72 x^3-32 x^4\right )\right ) \log ^2(3-x)+\left (-240 x^4-192 x^5+112 x^6\right ) \log ^3(3-x)+\left (-60 x^4-52 x^5+24 x^6\right ) \log ^4(3-x)}{-3+x} \, dx=4 x^{6} + 4 x^{5} - 8 x^{4} e^{3} - 8 x^{3} e^{3} + 4 x^{2} e^{6} + 4 x e^{6} + \left (4 x^{6} + 4 x^{5}\right ) \log {\left (3 - x \right )}^{4} + \left (16 x^{6} + 16 x^{5}\right ) \log {\left (3 - x \right )}^{3} + \left (16 x^{6} + 16 x^{5} - 16 x^{4} e^{3} - 16 x^{3} e^{3}\right ) \log {\left (3 - x \right )} + \left (24 x^{6} + 24 x^{5} - 8 x^{4} e^{3} - 8 x^{3} e^{3}\right ) \log {\left (3 - x \right )}^{2} \] Input:
integrate(((24*x**6-52*x**5-60*x**4)*ln(3-x)**4+(112*x**6-192*x**5-240*x** 4)*ln(3-x)**3+((-32*x**4+72*x**3+72*x**2)*exp(3)+192*x**6-264*x**5-360*x** 4)*ln(3-x)**2+((-80*x**4+128*x**3+144*x**2)*exp(3)+144*x**6-160*x**5-240*x **4)*ln(3-x)+(8*x**2-20*x-12)*exp(3)**2+(-48*x**4+56*x**3+72*x**2)*exp(3)+ 40*x**6-36*x**5-60*x**4)/(-3+x),x)
Output:
4*x**6 + 4*x**5 - 8*x**4*exp(3) - 8*x**3*exp(3) + 4*x**2*exp(6) + 4*x*exp( 6) + (4*x**6 + 4*x**5)*log(3 - x)**4 + (16*x**6 + 16*x**5)*log(3 - x)**3 + (16*x**6 + 16*x**5 - 16*x**4*exp(3) - 16*x**3*exp(3))*log(3 - x) + (24*x* *6 + 24*x**5 - 8*x**4*exp(3) - 8*x**3*exp(3))*log(3 - x)**2
Leaf count of result is larger than twice the leaf count of optimal. 1389 vs. \(2 (27) = 54\).
Time = 0.08 (sec) , antiderivative size = 1389, normalized size of antiderivative = 51.44 \[ \int \frac {-60 x^4-36 x^5+40 x^6+e^6 \left (-12-20 x+8 x^2\right )+e^3 \left (72 x^2+56 x^3-48 x^4\right )+\left (-240 x^4-160 x^5+144 x^6+e^3 \left (144 x^2+128 x^3-80 x^4\right )\right ) \log (3-x)+\left (-360 x^4-264 x^5+192 x^6+e^3 \left (72 x^2+72 x^3-32 x^4\right )\right ) \log ^2(3-x)+\left (-240 x^4-192 x^5+112 x^6\right ) \log ^3(3-x)+\left (-60 x^4-52 x^5+24 x^6\right ) \log ^4(3-x)}{-3+x} \, dx=\text {Too large to display} \] Input:
integrate(((24*x^6-52*x^5-60*x^4)*log(3-x)^4+(112*x^6-192*x^5-240*x^4)*log (3-x)^3+((-32*x^4+72*x^3+72*x^2)*exp(3)+192*x^6-264*x^5-360*x^4)*log(3-x)^ 2+((-80*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*log(3-x)+(8*x ^2-20*x-12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/ (-3+x),x, algorithm="maxima")
Output:
2/27*(54*log(-x + 3)^4 - 36*log(-x + 3)^3 + 18*log(-x + 3)^2 - 6*log(-x + 3) + 1)*(x - 3)^6 + 14/27*(36*log(-x + 3)^3 - 18*log(-x + 3)^2 + 6*log(-x + 3) - 1)*(x - 3)^6 + 16/9*(18*log(-x + 3)^2 - 6*log(-x + 3) + 1)*(x - 3)^ 6 + 76/625*(625*log(-x + 3)^4 - 500*log(-x + 3)^3 + 300*log(-x + 3)^2 - 12 0*log(-x + 3) + 24)*(x - 3)^5 + 1824/625*(125*log(-x + 3)^3 - 75*log(-x + 3)^2 + 30*log(-x + 3) - 6)*(x - 3)^5 + 3192/125*(25*log(-x + 3)^2 - 10*log (-x + 3) + 2)*(x - 3)^5 + 8/3*x^6 + 75/4*(32*log(-x + 3)^4 - 32*log(-x + 3 )^3 + 24*log(-x + 3)^2 - 12*log(-x + 3) + 3)*(x - 3)^4 + 375/4*(32*log(-x + 3)^3 - 24*log(-x + 3)^2 + 12*log(-x + 3) - 3)*(x - 3)^4 + 675*(8*log(-x + 3)^2 - 4*log(-x + 3) + 1)*(x - 3)^4 - 212/25*x^5 + 280/3*(27*log(-x + 3) ^4 - 36*log(-x + 3)^3 + 36*log(-x + 3)^2 - 24*log(-x + 3) + 8)*(x - 3)^3 + 4480/3*(9*log(-x + 3)^3 - 9*log(-x + 3)^2 + 6*log(-x + 3) - 2)*(x - 3)^3 + 2800*(9*log(-x + 3)^2 - 6*log(-x + 3) + 2)*(x - 3)^3 - 414/5*x^4 + 3888* log(-x + 3)^4 + 2970*(2*log(-x + 3)^4 - 4*log(-x + 3)^3 + 6*log(-x + 3)^2 - 6*log(-x + 3) + 3)*(x - 3)^2 + 8910*(4*log(-x + 3)^3 - 6*log(-x + 3)^2 + 6*log(-x + 3) - 3)*(x - 3)^2 + 35640*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1 )*(x - 3)^2 - 2616/5*x^3 - 20*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x - 3))*e^3*log(-x + 3) + 64/3*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^3*log (-x + 3) + 72*(x^2 + 6*x + 18*log(x - 3))*e^3*log(-x + 3) + 15552*log(-x + 3)^3 + 7452*(log(-x + 3)^4 - 4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*l...
Leaf count of result is larger than twice the leaf count of optimal. 614 vs. \(2 (27) = 54\).
Time = 0.14 (sec) , antiderivative size = 614, normalized size of antiderivative = 22.74 \[ \int \frac {-60 x^4-36 x^5+40 x^6+e^6 \left (-12-20 x+8 x^2\right )+e^3 \left (72 x^2+56 x^3-48 x^4\right )+\left (-240 x^4-160 x^5+144 x^6+e^3 \left (144 x^2+128 x^3-80 x^4\right )\right ) \log (3-x)+\left (-360 x^4-264 x^5+192 x^6+e^3 \left (72 x^2+72 x^3-32 x^4\right )\right ) \log ^2(3-x)+\left (-240 x^4-192 x^5+112 x^6\right ) \log ^3(3-x)+\left (-60 x^4-52 x^5+24 x^6\right ) \log ^4(3-x)}{-3+x} \, dx =\text {Too large to display} \] Input:
integrate(((24*x^6-52*x^5-60*x^4)*log(3-x)^4+(112*x^6-192*x^5-240*x^4)*log (3-x)^3+((-32*x^4+72*x^3+72*x^2)*exp(3)+192*x^6-264*x^5-360*x^4)*log(3-x)^ 2+((-80*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*log(3-x)+(8*x ^2-20*x-12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/ (-3+x),x, algorithm="giac")
Output:
4*(x - 3)^6*log(-x + 3)^4 + 16*(x - 3)^6*log(-x + 3)^3 + 76*(x - 3)^5*log( -x + 3)^4 + 24*(x - 3)^6*log(-x + 3)^2 + 304*(x - 3)^5*log(-x + 3)^3 + 600 *(x - 3)^4*log(-x + 3)^4 + 16*(x - 3)^6*log(-x + 3) + 456*(x - 3)^5*log(-x + 3)^2 - 8*(x - 3)^4*e^3*log(-x + 3)^2 + 2400*(x - 3)^4*log(-x + 3)^3 + 2 520*(x - 3)^3*log(-x + 3)^4 + 4*(x - 3)^6 + 304*(x - 3)^5*log(-x + 3) - 16 *(x - 3)^4*e^3*log(-x + 3) + 3600*(x - 3)^4*log(-x + 3)^2 - 104*(x - 3)^3* e^3*log(-x + 3)^2 + 10080*(x - 3)^3*log(-x + 3)^3 + 5940*(x - 3)^2*log(-x + 3)^4 + 76*(x - 3)^5 - 8*(x - 3)^4*e^3 + 2400*(x - 3)^4*log(-x + 3) - 208 *(x - 3)^3*e^3*log(-x + 3) + 15120*(x - 3)^3*log(-x + 3)^2 - 504*(x - 3)^2 *e^3*log(-x + 3)^2 + 23760*(x - 3)^2*log(-x + 3)^3 + 7452*(x - 3)*log(-x + 3)^4 + 600*(x - 3)^4 - 104*(x - 3)^3*e^3 + 10080*(x - 3)^3*log(-x + 3) - 1008*(x - 3)^2*e^3*log(-x + 3) + 35640*(x - 3)^2*log(-x + 3)^2 - 1080*(x - 3)*e^3*log(-x + 3)^2 + 29808*(x - 3)*log(-x + 3)^3 + 3888*log(-x + 3)^4 + 2520*(x - 3)^3 + 4*(x - 3)^2*e^6 - 504*(x - 3)^2*e^3 + 23760*(x - 3)^2*lo g(-x + 3) - 2160*(x - 3)*e^3*log(-x + 3) + 44712*(x - 3)*log(-x + 3)^2 - 8 64*e^3*log(-x + 3)^2 + 15552*log(-x + 3)^3 + 5940*(x - 3)^2 + 28*(x - 3)*e ^6 - 1080*(x - 3)*e^3 + 29808*(x - 3)*log(-x + 3) - 1728*e^3*log(-x + 3) + 23328*log(-x + 3)^2 + 7452*x + 15552*log(-x + 3) - 22356
Time = 3.74 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.44 \[ \int \frac {-60 x^4-36 x^5+40 x^6+e^6 \left (-12-20 x+8 x^2\right )+e^3 \left (72 x^2+56 x^3-48 x^4\right )+\left (-240 x^4-160 x^5+144 x^6+e^3 \left (144 x^2+128 x^3-80 x^4\right )\right ) \log (3-x)+\left (-360 x^4-264 x^5+192 x^6+e^3 \left (72 x^2+72 x^3-32 x^4\right )\right ) \log ^2(3-x)+\left (-240 x^4-192 x^5+112 x^6\right ) \log ^3(3-x)+\left (-60 x^4-52 x^5+24 x^6\right ) \log ^4(3-x)}{-3+x} \, dx=4\,x\,\left (x+1\right )\,{\left (x^2\,{\ln \left (3-x\right )}^2+2\,x^2\,\ln \left (3-x\right )+x^2-{\mathrm {e}}^3\right )}^2 \] Input:
int(-(exp(6)*(20*x - 8*x^2 + 12) - log(3 - x)^2*(exp(3)*(72*x^2 + 72*x^3 - 32*x^4) - 360*x^4 - 264*x^5 + 192*x^6) + log(3 - x)^4*(60*x^4 + 52*x^5 - 24*x^6) + log(3 - x)^3*(240*x^4 + 192*x^5 - 112*x^6) - exp(3)*(72*x^2 + 56 *x^3 - 48*x^4) - log(3 - x)*(exp(3)*(144*x^2 + 128*x^3 - 80*x^4) - 240*x^4 - 160*x^5 + 144*x^6) + 60*x^4 + 36*x^5 - 40*x^6)/(x - 3),x)
Output:
4*x*(x + 1)*(x^2*log(3 - x)^2 - exp(3) + x^2 + 2*x^2*log(3 - x))^2
Time = 0.18 (sec) , antiderivative size = 235, normalized size of antiderivative = 8.70 \[ \int \frac {-60 x^4-36 x^5+40 x^6+e^6 \left (-12-20 x+8 x^2\right )+e^3 \left (72 x^2+56 x^3-48 x^4\right )+\left (-240 x^4-160 x^5+144 x^6+e^3 \left (144 x^2+128 x^3-80 x^4\right )\right ) \log (3-x)+\left (-360 x^4-264 x^5+192 x^6+e^3 \left (72 x^2+72 x^3-32 x^4\right )\right ) \log ^2(3-x)+\left (-240 x^4-192 x^5+112 x^6\right ) \log ^3(3-x)+\left (-60 x^4-52 x^5+24 x^6\right ) \log ^4(3-x)}{-3+x} \, dx=4 \mathrm {log}\left (-x +3\right )^{4} x^{6}+4 \mathrm {log}\left (-x +3\right )^{4} x^{5}+16 \mathrm {log}\left (-x +3\right )^{3} x^{6}+16 \mathrm {log}\left (-x +3\right )^{3} x^{5}-8 \mathrm {log}\left (-x +3\right )^{2} e^{3} x^{4}-8 \mathrm {log}\left (-x +3\right )^{2} e^{3} x^{3}+24 \mathrm {log}\left (-x +3\right )^{2} x^{6}+24 \mathrm {log}\left (-x +3\right )^{2} x^{5}-16 \,\mathrm {log}\left (-x +3\right ) e^{3} x^{4}-16 \,\mathrm {log}\left (-x +3\right ) e^{3} x^{3}+1728 \,\mathrm {log}\left (-x +3\right ) e^{3}+16 \,\mathrm {log}\left (-x +3\right ) x^{6}+16 \,\mathrm {log}\left (-x +3\right ) x^{5}-15552 \,\mathrm {log}\left (-x +3\right )-1728 \,\mathrm {log}\left (x -3\right ) e^{3}+15552 \,\mathrm {log}\left (x -3\right )+4 e^{6} x^{2}+4 e^{6} x -8 e^{3} x^{4}-8 e^{3} x^{3}+4 x^{6}+4 x^{5} \] Input:
int(((24*x^6-52*x^5-60*x^4)*log(3-x)^4+(112*x^6-192*x^5-240*x^4)*log(3-x)^ 3+((-32*x^4+72*x^3+72*x^2)*exp(3)+192*x^6-264*x^5-360*x^4)*log(3-x)^2+((-8 0*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*log(3-x)+(8*x^2-20* x-12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/(-3+x) ,x)
Output:
4*(log( - x + 3)**4*x**6 + log( - x + 3)**4*x**5 + 4*log( - x + 3)**3*x**6 + 4*log( - x + 3)**3*x**5 - 2*log( - x + 3)**2*e**3*x**4 - 2*log( - x + 3 )**2*e**3*x**3 + 6*log( - x + 3)**2*x**6 + 6*log( - x + 3)**2*x**5 - 4*log ( - x + 3)*e**3*x**4 - 4*log( - x + 3)*e**3*x**3 + 432*log( - x + 3)*e**3 + 4*log( - x + 3)*x**6 + 4*log( - x + 3)*x**5 - 3888*log( - x + 3) - 432*l og(x - 3)*e**3 + 3888*log(x - 3) + e**6*x**2 + e**6*x - 2*e**3*x**4 - 2*e* *3*x**3 + x**6 + x**5)