Integrand size = 159, antiderivative size = 23 \[ \int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+\left (-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}\right ) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx=\frac {x}{(-1+x)^8}-2 \left (-x+x^2 (2+x)\right ) \log (x) \] Output:
x/(-1+x)^8-2*ln(x)*(x^2*(2+x)-x)
Time = 0.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+\left (-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}\right ) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx=x \left (\frac {1}{(-1+x)^8}-2 \left (-1+2 x+x^2\right ) \log (x)\right ) \] Input:
Integrate[(-3 + 15*x - 106*x^2 + 294*x^3 - 516*x^4 + 588*x^5 - 420*x^6 + 1 56*x^7 + 6*x^8 - 34*x^9 + 14*x^10 - 2*x^11 + (-2 + 26*x - 138*x^2 + 402*x^ 3 - 708*x^4 + 756*x^5 - 420*x^6 - 12*x^7 + 198*x^8 - 142*x^9 + 46*x^10 - 6 *x^11)*Log[x])/(-1 + 9*x - 36*x^2 + 84*x^3 - 126*x^4 + 126*x^5 - 84*x^6 + 36*x^7 - 9*x^8 + x^9),x]
Output:
x*((-1 + x)^(-8) - 2*(-1 + 2*x + x^2)*Log[x])
Leaf count is larger than twice the leaf count of optimal. \(176\) vs. \(2(23)=46\).
Time = 0.95 (sec) , antiderivative size = 176, normalized size of antiderivative = 7.65, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {2007, 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.
| \(\displaystyle \int \frac {-2 x^{11}+14 x^{10}-34 x^9+6 x^8+156 x^7-420 x^6+588 x^5-516 x^4+294 x^3-106 x^2+15 x+\left (-6 x^{11}+46 x^{10}-142 x^9+198 x^8-12 x^7-420 x^6+756 x^5-708 x^4+402 x^3-138 x^2+26 x-2\right ) \log (x)-3}{x^9-9 x^8+36 x^7-84 x^6+126 x^5-126 x^4+84 x^3-36 x^2+9 x-1} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {-2 x^{11}+14 x^{10}-34 x^9+6 x^8+156 x^7-420 x^6+588 x^5-516 x^4+294 x^3-106 x^2+15 x+\left (-6 x^{11}+46 x^{10}-142 x^9+198 x^8-12 x^7-420 x^6+756 x^5-708 x^4+402 x^3-138 x^2+26 x-2\right ) \log (x)-3}{(x-1)^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2 x^{11}}{(x-1)^9}+\frac {14 x^{10}}{(x-1)^9}-\frac {34 x^9}{(x-1)^9}+\frac {6 x^8}{(x-1)^9}+\frac {156 x^7}{(x-1)^9}-\frac {420 x^6}{(x-1)^9}+\frac {588 x^5}{(x-1)^9}-\frac {516 x^4}{(x-1)^9}+\frac {294 x^3}{(x-1)^9}-\frac {106 x^2}{(x-1)^9}-2 \left (3 x^2+4 x-1\right ) \log (x)+\frac {15 x}{(x-1)^9}-\frac {3}{(x-1)^9}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {39 x^8}{2 (1-x)^8}+\frac {15 x^7}{2 (1-x)^7}+\frac {105 x^7}{2 (1-x)^8}-\frac {7 x^6}{2 (1-x)^6}-\frac {21 x^6}{(1-x)^7}-\frac {147 x^6}{2 (1-x)^8}-2 x^3 \log (x)-4 x^2 \log (x)-\frac {156}{1-x}+\frac {336}{(1-x)^2}-\frac {448}{(1-x)^3}+\frac {525}{(1-x)^4}-\frac {588}{(1-x)^5}+\frac {476}{(1-x)^6}-\frac {217}{(1-x)^7}+\frac {83}{2 (1-x)^8}+2 x \log (x)\) |
Input:
Int[(-3 + 15*x - 106*x^2 + 294*x^3 - 516*x^4 + 588*x^5 - 420*x^6 + 156*x^7 + 6*x^8 - 34*x^9 + 14*x^10 - 2*x^11 + (-2 + 26*x - 138*x^2 + 402*x^3 - 70 8*x^4 + 756*x^5 - 420*x^6 - 12*x^7 + 198*x^8 - 142*x^9 + 46*x^10 - 6*x^11) *Log[x])/(-1 + 9*x - 36*x^2 + 84*x^3 - 126*x^4 + 126*x^5 - 84*x^6 + 36*x^7 - 9*x^8 + x^9),x]
Output:
83/(2*(1 - x)^8) - 217/(1 - x)^7 + 476/(1 - x)^6 - 588/(1 - x)^5 + 525/(1 - x)^4 - 448/(1 - x)^3 + 336/(1 - x)^2 - 156/(1 - x) - (147*x^6)/(2*(1 - x )^8) - (21*x^6)/(1 - x)^7 - (7*x^6)/(2*(1 - x)^6) + (105*x^7)/(2*(1 - x)^8 ) + (15*x^7)/(2*(1 - x)^7) - (39*x^8)/(2*(1 - x)^8) + 2*x*Log[x] - 4*x^2*L og[x] - 2*x^3*Log[x]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Time = 4.20 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.35
| method | result | size |
| default | \(-2 x^{3} \ln \left (x \right )-4 x^{2} \ln \left (x \right )+2 x \ln \left (x \right )+\frac {1}{\left (-1+x \right )^{7}}+\frac {1}{\left (-1+x \right )^{8}}\) | \(31\) |
| parts | \(-2 x^{3} \ln \left (x \right )-4 x^{2} \ln \left (x \right )+2 x \ln \left (x \right )+\frac {1}{\left (-1+x \right )^{7}}+\frac {1}{\left (-1+x \right )^{8}}\) | \(31\) |
| risch | \(\left (-2 x^{3}-4 x^{2}+2 x \right ) \ln \left (x \right )+\frac {x}{x^{8}-8 x^{7}+28 x^{6}-56 x^{5}+70 x^{4}-56 x^{3}+28 x^{2}-8 x +1}\) | \(61\) |
| norman | \(\frac {x +2 x \ln \left (x \right )-20 x^{2} \ln \left (x \right )+86 x^{3} \ln \left (x \right )-208 x^{4} \ln \left (x \right )+308 x^{5} \ln \left (x \right )+140 x^{7} \ln \left (x \right )-22 x^{9} \ln \left (x \right )+12 x^{10} \ln \left (x \right )-2 x^{11} \ln \left (x \right )-280 \ln \left (x \right ) x^{6}-16 \ln \left (x \right ) x^{8}}{\left (-1+x \right )^{8}}\) | \(84\) |
| parallelrisch | \(-\frac {-70 x +19600 \ln \left (x \right ) x^{6}-9800 x^{7} \ln \left (x \right )-21560 x^{5} \ln \left (x \right )-6020 x^{3} \ln \left (x \right )+14560 x^{4} \ln \left (x \right )-140 x \ln \left (x \right )+1400 x^{2} \ln \left (x \right )+1540 x^{9} \ln \left (x \right )+140 x^{11} \ln \left (x \right )-840 x^{10} \ln \left (x \right )+1120 \ln \left (x \right ) x^{8}}{70 \left (x^{8}-8 x^{7}+28 x^{6}-56 x^{5}+70 x^{4}-56 x^{3}+28 x^{2}-8 x +1\right )}\) | \(122\) |
| orering | \(\frac {x \left (15 x^{14}-102 x^{13}+213 x^{12}-72 x^{11}+571 x^{10}-5710 x^{9}+18369 x^{8}-31296 x^{7}+30909 x^{6}-15522 x^{5}-780 x^{4}+6204 x^{3}-4134 x^{2}+1268 x -149\right ) \left (\left (-6 x^{11}+46 x^{10}-142 x^{9}+198 x^{8}-12 x^{7}-420 x^{6}+756 x^{5}-708 x^{4}+402 x^{3}-138 x^{2}+26 x -2\right ) \ln \left (x \right )-2 x^{11}+14 x^{10}-34 x^{9}+6 x^{8}+156 x^{7}-420 x^{6}+588 x^{5}-516 x^{4}+294 x^{3}-106 x^{2}+15 x -3\right )}{3 \left (9 x^{14}-68 x^{13}+199 x^{12}-236 x^{11}-59 x^{10}+392 x^{9}+51 x^{8}-1368 x^{7}+2427 x^{6}-2292 x^{5}+1244 x^{4}-640 x^{3}+130 x^{2}-6 x +1\right ) \left (x^{9}-9 x^{8}+36 x^{7}-84 x^{6}+126 x^{5}-126 x^{4}+84 x^{3}-36 x^{2}+9 x -1\right )}-\frac {\left (3 x^{14}-15 x^{13}+6 x^{12}+571 x^{10}-2527 x^{9}+4374 x^{8}-1848 x^{7}-5991 x^{6}+12867 x^{5}-12711 x^{4}+7440 x^{3}-2598 x^{2}+491 x -38\right ) \left (-1+x \right ) x \left (\frac {\left (-66 x^{10}+460 x^{9}-1278 x^{8}+1584 x^{7}-84 x^{6}-2520 x^{5}+3780 x^{4}-2832 x^{3}+1206 x^{2}-276 x +26\right ) \ln \left (x \right )+\frac {-6 x^{11}+46 x^{10}-142 x^{9}+198 x^{8}-12 x^{7}-420 x^{6}+756 x^{5}-708 x^{4}+402 x^{3}-138 x^{2}+26 x -2}{x}-22 x^{10}+140 x^{9}-306 x^{8}+48 x^{7}+1092 x^{6}-2520 x^{5}+2940 x^{4}-2064 x^{3}+882 x^{2}-212 x +15}{x^{9}-9 x^{8}+36 x^{7}-84 x^{6}+126 x^{5}-126 x^{4}+84 x^{3}-36 x^{2}+9 x -1}-\frac {\left (\left (-6 x^{11}+46 x^{10}-142 x^{9}+198 x^{8}-12 x^{7}-420 x^{6}+756 x^{5}-708 x^{4}+402 x^{3}-138 x^{2}+26 x -2\right ) \ln \left (x \right )-2 x^{11}+14 x^{10}-34 x^{9}+6 x^{8}+156 x^{7}-420 x^{6}+588 x^{5}-516 x^{4}+294 x^{3}-106 x^{2}+15 x -3\right ) \left (9 x^{8}-72 x^{7}+252 x^{6}-504 x^{5}+630 x^{4}-504 x^{3}+252 x^{2}-72 x +9\right )}{\left (x^{9}-9 x^{8}+36 x^{7}-84 x^{6}+126 x^{5}-126 x^{4}+84 x^{3}-36 x^{2}+9 x -1\right )^{2}}\right )}{3 \left (9 x^{14}-68 x^{13}+199 x^{12}-236 x^{11}-59 x^{10}+392 x^{9}+51 x^{8}-1368 x^{7}+2427 x^{6}-2292 x^{5}+1244 x^{4}-640 x^{3}+130 x^{2}-6 x +1\right )}\) | \(857\) |
Input:
int(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4+402*x ^3-138*x^2+26*x-2)*ln(x)-2*x^11+14*x^10-34*x^9+6*x^8+156*x^7-420*x^6+588*x ^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x^5-126*x^ 4+84*x^3-36*x^2+9*x-1),x,method=_RETURNVERBOSE)
Output:
-2*x^3*ln(x)-4*x^2*ln(x)+2*x*ln(x)+1/(-1+x)^7+1/(-1+x)^8
Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (23) = 46\).
Time = 0.09 (sec) , antiderivative size = 102, normalized size of antiderivative = 4.43 \[ \int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+\left (-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}\right ) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx=-\frac {2 \, {\left (x^{11} - 6 \, x^{10} + 11 \, x^{9} + 8 \, x^{8} - 70 \, x^{7} + 140 \, x^{6} - 154 \, x^{5} + 104 \, x^{4} - 43 \, x^{3} + 10 \, x^{2} - x\right )} \log \left (x\right ) - x}{x^{8} - 8 \, x^{7} + 28 \, x^{6} - 56 \, x^{5} + 70 \, x^{4} - 56 \, x^{3} + 28 \, x^{2} - 8 \, x + 1} \] Input:
integrate(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4 +402*x^3-138*x^2+26*x-2)*log(x)-2*x^11+14*x^10-34*x^9+6*x^8+156*x^7-420*x^ 6+588*x^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x^5 -126*x^4+84*x^3-36*x^2+9*x-1),x, algorithm="fricas")
Output:
-(2*(x^11 - 6*x^10 + 11*x^9 + 8*x^8 - 70*x^7 + 140*x^6 - 154*x^5 + 104*x^4 - 43*x^3 + 10*x^2 - x)*log(x) - x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^ 4 - 56*x^3 + 28*x^2 - 8*x + 1)
Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (19) = 38\).
Time = 0.11 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.43 \[ \int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+\left (-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}\right ) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx=\frac {x}{x^{8} - 8 x^{7} + 28 x^{6} - 56 x^{5} + 70 x^{4} - 56 x^{3} + 28 x^{2} - 8 x + 1} + \left (- 2 x^{3} - 4 x^{2} + 2 x\right ) \log {\left (x \right )} \] Input:
integrate(((-6*x**11+46*x**10-142*x**9+198*x**8-12*x**7-420*x**6+756*x**5- 708*x**4+402*x**3-138*x**2+26*x-2)*ln(x)-2*x**11+14*x**10-34*x**9+6*x**8+1 56*x**7-420*x**6+588*x**5-516*x**4+294*x**3-106*x**2+15*x-3)/(x**9-9*x**8+ 36*x**7-84*x**6+126*x**5-126*x**4+84*x**3-36*x**2+9*x-1),x)
Output:
x/(x**8 - 8*x**7 + 28*x**6 - 56*x**5 + 70*x**4 - 56*x**3 + 28*x**2 - 8*x + 1) + (-2*x**3 - 4*x**2 + 2*x)*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 1945 vs. \(2 (23) = 46\).
Time = 0.15 (sec) , antiderivative size = 1945, normalized size of antiderivative = 84.57 \[ \int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+\left (-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}\right ) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx=\text {Too large to display} \] Input:
integrate(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4 +402*x^3-138*x^2+26*x-2)*log(x)-2*x^11+14*x^10-34*x^9+6*x^8+156*x^7-420*x^ 6+588*x^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x^5 -126*x^4+84*x^3-36*x^2+9*x-1),x, algorithm="maxima")
Output:
-2/3*x^3 - 2*x^2 + 2*x + 3/2*(8*x^7 - 28*x^6 + 56*x^5 - 70*x^4 + 56*x^3 - 28*x^2 + 8*x - 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 15/2*(28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8 *x + 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 9/2*(56*x^5 - 70*x^4 + 56*x^3 - 28*x^2 + 8*x - 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 177/70*( 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 201/140*(56*x^3 - 28*x^2 + 8*x - 1 )*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 23/28*(28*x^2 - 8*x + 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70* x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 13/28*(8*x - 1)*log(x)/(x^8 - 8*x^7 + 2 8*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 2/105*(35*x^11 - 17 5*x^10 + 35*x^9 + 1820*x^8 - 7840*x^7 + 15680*x^6 - 15680*x^5 + 4900*x^4 + 5488*x^3 - 6664*x^2 - 105*(x^11 - 6*x^10 + 11*x^9)*log(x) + 2864*x - 463) /(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 1/ 84*(55440*x^7 - 349272*x^6 + 957264*x^5 - 1473780*x^4 + 1373064*x^3 - 7727 72*x^2 + 242968*x - 32891)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^ 3 + 28*x^2 - 8*x + 1) + 17/140*(10080*x^7 - 58800*x^6 + 152880*x^5 - 22638 0*x^4 + 204624*x^3 - 112392*x^2 + 34632*x - 4609)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 1/140*(6720*x^7 - 35280*...
Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (23) = 46\).
Time = 0.12 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.57 \[ \int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+\left (-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}\right ) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx=-2 \, {\left (x^{3} + 2 \, x^{2} - x\right )} \log \left (x\right ) + \frac {x}{x^{8} - 8 \, x^{7} + 28 \, x^{6} - 56 \, x^{5} + 70 \, x^{4} - 56 \, x^{3} + 28 \, x^{2} - 8 \, x + 1} \] Input:
integrate(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4 +402*x^3-138*x^2+26*x-2)*log(x)-2*x^11+14*x^10-34*x^9+6*x^8+156*x^7-420*x^ 6+588*x^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x^5 -126*x^4+84*x^3-36*x^2+9*x-1),x, algorithm="giac")
Output:
-2*(x^3 + 2*x^2 - x)*log(x) + x/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1)
Time = 4.41 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.65 \[ \int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+\left (-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}\right ) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx=\frac {x}{x^8-8\,x^7+28\,x^6-56\,x^5+70\,x^4-56\,x^3+28\,x^2-8\,x+1}-\ln \left (x\right )\,\left (2\,x^3+4\,x^2-2\,x\right ) \] Input:
int(-(log(x)*(138*x^2 - 26*x - 402*x^3 + 708*x^4 - 756*x^5 + 420*x^6 + 12* x^7 - 198*x^8 + 142*x^9 - 46*x^10 + 6*x^11 + 2) - 15*x + 106*x^2 - 294*x^3 + 516*x^4 - 588*x^5 + 420*x^6 - 156*x^7 - 6*x^8 + 34*x^9 - 14*x^10 + 2*x^ 11 + 3)/(9*x - 36*x^2 + 84*x^3 - 126*x^4 + 126*x^5 - 84*x^6 + 36*x^7 - 9*x ^8 + x^9 - 1),x)
Output:
x/(28*x^2 - 8*x - 56*x^3 + 70*x^4 - 56*x^5 + 28*x^6 - 8*x^7 + x^8 + 1) - l og(x)*(4*x^2 - 2*x + 2*x^3)
Time = 0.16 (sec) , antiderivative size = 158, normalized size of antiderivative = 6.87 \[ \int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+\left (-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}\right ) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx=\frac {-12 \,\mathrm {log}\left (x \right ) x^{11}+72 \,\mathrm {log}\left (x \right ) x^{10}-132 \,\mathrm {log}\left (x \right ) x^{9}-96 \,\mathrm {log}\left (x \right ) x^{8}+840 \,\mathrm {log}\left (x \right ) x^{7}-1680 \,\mathrm {log}\left (x \right ) x^{6}+1848 \,\mathrm {log}\left (x \right ) x^{5}-1248 \,\mathrm {log}\left (x \right ) x^{4}+516 \,\mathrm {log}\left (x \right ) x^{3}-120 \,\mathrm {log}\left (x \right ) x^{2}+12 \,\mathrm {log}\left (x \right ) x +91 x^{8}-728 x^{7}+2548 x^{6}-5096 x^{5}+6370 x^{4}-5096 x^{3}+2548 x^{2}-722 x +91}{6 x^{8}-48 x^{7}+168 x^{6}-336 x^{5}+420 x^{4}-336 x^{3}+168 x^{2}-48 x +6} \] Input:
int(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4+402*x ^3-138*x^2+26*x-2)*log(x)-2*x^11+14*x^10-34*x^9+6*x^8+156*x^7-420*x^6+588* x^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x^5-126*x ^4+84*x^3-36*x^2+9*x-1),x)
Output:
( - 12*log(x)*x**11 + 72*log(x)*x**10 - 132*log(x)*x**9 - 96*log(x)*x**8 + 840*log(x)*x**7 - 1680*log(x)*x**6 + 1848*log(x)*x**5 - 1248*log(x)*x**4 + 516*log(x)*x**3 - 120*log(x)*x**2 + 12*log(x)*x + 91*x**8 - 728*x**7 + 2 548*x**6 - 5096*x**5 + 6370*x**4 - 5096*x**3 + 2548*x**2 - 722*x + 91)/(6* (x**8 - 8*x**7 + 28*x**6 - 56*x**5 + 70*x**4 - 56*x**3 + 28*x**2 - 8*x + 1 ))