Integrand size = 38, antiderivative size = 588 \[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx=\frac {\left (5 d^2-2 d e+3 e^2\right )^3 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right ) (d+e x)^{1+m}}{e^{11} (1+m)}-\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (200 d^5+169 d^4 e+108 d^3 e^2-20 d^2 e^3+86 d e^4-15 e^5\right ) (d+e x)^{2+m}}{e^{11} (2+m)}+\frac {3 \left (5 d^2-2 d e+3 e^2\right ) \left (1500 d^6+660 d^5 e+792 d^4 e^2+58 d^3 e^3+547 d^2 e^4-156 d e^5+53 e^6\right ) (d+e x)^{3+m}}{e^{11} (3+m)}-\frac {2 \left (30000 d^7+1050 d^6 e+21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+2218 d e^6-287 e^7\right ) (d+e x)^{4+m}}{e^{11} (4+m)}+\frac {\left (105000 d^6+3150 d^5 e+53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4-2550 d e^5+1109 e^6\right ) (d+e x)^{5+m}}{e^{11} (5+m)}-\frac {6 \left (21000 d^5+525 d^4 e+7140 d^3 e^2+343 d^2 e^3+999 d e^4-85 e^5\right ) (d+e x)^{6+m}}{e^{11} (6+m)}+\frac {\left (105000 d^4+2100 d^3 e+21420 d^2 e^2+686 d e^3+999 e^4\right ) (d+e x)^{7+m}}{e^{11} (7+m)}-\frac {2 \left (30000 d^3+450 d^2 e+3060 d e^2+49 e^3\right ) (d+e x)^{8+m}}{e^{11} (8+m)}+\frac {45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^{9+m}}{e^{11} (9+m)}-\frac {25 (200 d+e) (d+e x)^{10+m}}{e^{11} (10+m)}+\frac {500 (d+e x)^{11+m}}{e^{11} (11+m)} \]
(5*d^2-2*d*e+3*e^2)^3*(4*d^4+5*d^3*e+3*d^2*e^2-d*e^3+2*e^4)*(e*x+d)^(1+m)/ e^11/(1+m)-(5*d^2-2*d*e+3*e^2)^2*(200*d^5+169*d^4*e+108*d^3*e^2-20*d^2*e^3 +86*d*e^4-15*e^5)*(e*x+d)^(2+m)/e^11/(2+m)+3*(5*d^2-2*d*e+3*e^2)*(1500*d^6 +660*d^5*e+792*d^4*e^2+58*d^3*e^3+547*d^2*e^4-156*d*e^5+53*e^6)*(e*x+d)^(3 +m)/e^11/(3+m)-2*(30000*d^7+1050*d^6*e+21420*d^5*e^2+1715*d^4*e^3+9990*d^3 *e^4-2550*d^2*e^5+2218*d*e^6-287*e^7)*(e*x+d)^(4+m)/e^11/(4+m)+(105000*d^6 +3150*d^5*e+53550*d^4*e^2+3430*d^3*e^3+14985*d^2*e^4-2550*d*e^5+1109*e^6)* (e*x+d)^(5+m)/e^11/(5+m)-6*(21000*d^5+525*d^4*e+7140*d^3*e^2+343*d^2*e^3+9 99*d*e^4-85*e^5)*(e*x+d)^(6+m)/e^11/(6+m)+(105000*d^4+2100*d^3*e+21420*d^2 *e^2+686*d*e^3+999*e^4)*(e*x+d)^(7+m)/e^11/(7+m)-2*(30000*d^3+450*d^2*e+30 60*d*e^2+49*e^3)*(e*x+d)^(8+m)/e^11/(8+m)+45*(500*d^2+5*d*e+17*e^2)*(e*x+d )^(9+m)/e^11/(9+m)-25*(200*d+e)*(e*x+d)^(10+m)/e^11/(10+m)+500*(e*x+d)^(11 +m)/e^11/(11+m)
Time = 0.40 (sec) , antiderivative size = 537, normalized size of antiderivative = 0.91 \[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx=\frac {(d+e x)^{1+m} \left (\frac {\left (5 d^2-2 d e+3 e^2\right )^3 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right )}{1+m}-\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (200 d^5+169 d^4 e+108 d^3 e^2-20 d^2 e^3+86 d e^4-15 e^5\right ) (d+e x)}{2+m}+\frac {3 \left (5 d^2-2 d e+3 e^2\right ) \left (1500 d^6+660 d^5 e+792 d^4 e^2+58 d^3 e^3+547 d^2 e^4-156 d e^5+53 e^6\right ) (d+e x)^2}{3+m}-\frac {2 \left (30000 d^7+1050 d^6 e+21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+2218 d e^6-287 e^7\right ) (d+e x)^3}{4+m}+\frac {\left (105000 d^6+3150 d^5 e+53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4-2550 d e^5+1109 e^6\right ) (d+e x)^4}{5+m}-\frac {6 \left (21000 d^5+525 d^4 e+7140 d^3 e^2+343 d^2 e^3+999 d e^4-85 e^5\right ) (d+e x)^5}{6+m}+\frac {\left (105000 d^4+2100 d^3 e+21420 d^2 e^2+686 d e^3+999 e^4\right ) (d+e x)^6}{7+m}-\frac {2 \left (30000 d^3+450 d^2 e+3060 d e^2+49 e^3\right ) (d+e x)^7}{8+m}+\frac {45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^8}{9+m}-\frac {25 (200 d+e) (d+e x)^9}{10+m}+\frac {500 (d+e x)^{10}}{11+m}\right )}{e^{11}} \]
((d + e*x)^(1 + m)*(((5*d^2 - 2*d*e + 3*e^2)^3*(4*d^4 + 5*d^3*e + 3*d^2*e^ 2 - d*e^3 + 2*e^4))/(1 + m) - ((5*d^2 - 2*d*e + 3*e^2)^2*(200*d^5 + 169*d^ 4*e + 108*d^3*e^2 - 20*d^2*e^3 + 86*d*e^4 - 15*e^5)*(d + e*x))/(2 + m) + ( 3*(5*d^2 - 2*d*e + 3*e^2)*(1500*d^6 + 660*d^5*e + 792*d^4*e^2 + 58*d^3*e^3 + 547*d^2*e^4 - 156*d*e^5 + 53*e^6)*(d + e*x)^2)/(3 + m) - (2*(30000*d^7 + 1050*d^6*e + 21420*d^5*e^2 + 1715*d^4*e^3 + 9990*d^3*e^4 - 2550*d^2*e^5 + 2218*d*e^6 - 287*e^7)*(d + e*x)^3)/(4 + m) + ((105000*d^6 + 3150*d^5*e + 53550*d^4*e^2 + 3430*d^3*e^3 + 14985*d^2*e^4 - 2550*d*e^5 + 1109*e^6)*(d + e*x)^4)/(5 + m) - (6*(21000*d^5 + 525*d^4*e + 7140*d^3*e^2 + 343*d^2*e^3 + 999*d*e^4 - 85*e^5)*(d + e*x)^5)/(6 + m) + ((105000*d^4 + 2100*d^3*e + 21420*d^2*e^2 + 686*d*e^3 + 999*e^4)*(d + e*x)^6)/(7 + m) - (2*(30000*d^3 + 450*d^2*e + 3060*d*e^2 + 49*e^3)*(d + e*x)^7)/(8 + m) + (45*(500*d^2 + 5 *d*e + 17*e^2)*(d + e*x)^8)/(9 + m) - (25*(200*d + e)*(d + e*x)^9)/(10 + m ) + (500*(d + e*x)^10)/(11 + m)))/e^11
Time = 0.82 (sec) , antiderivative size = 588, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2159, 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.
| \(\displaystyle \int \left (5 x^2+2 x+3\right )^3 \left (4 x^4-5 x^3+3 x^2+x+2\right ) (d+e x)^m \, dx\) |
| \(\Big \downarrow \) 2159 |
| \(\displaystyle \int \left (\frac {45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^{m+8}}{e^{10}}-\frac {2 \left (30000 d^3+450 d^2 e+3060 d e^2+49 e^3\right ) (d+e x)^{m+7}}{e^{10}}+\frac {\left (5 d^2-2 d e+3 e^2\right )^3 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right ) (d+e x)^m}{e^{10}}+\frac {\left (105000 d^4+2100 d^3 e+21420 d^2 e^2+686 d e^3+999 e^4\right ) (d+e x)^{m+6}}{e^{10}}+\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (-200 d^5-169 d^4 e-108 d^3 e^2+20 d^2 e^3-86 d e^4+15 e^5\right ) (d+e x)^{m+1}}{e^{10}}+\frac {6 \left (-21000 d^5-525 d^4 e-7140 d^3 e^2-343 d^2 e^3-999 d e^4+85 e^5\right ) (d+e x)^{m+5}}{e^{10}}+\frac {\left (105000 d^6+3150 d^5 e+53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4-2550 d e^5+1109 e^6\right ) (d+e x)^{m+4}}{e^{10}}+\frac {2 \left (-30000 d^7-1050 d^6 e-21420 d^5 e^2-1715 d^4 e^3-9990 d^3 e^4+2550 d^2 e^5-2218 d e^6+287 e^7\right ) (d+e x)^{m+3}}{e^{10}}+\frac {3 \left (7500 d^8+300 d^7 e+7140 d^6 e^2+686 d^5 e^3+4995 d^4 e^4-1700 d^3 e^5+2218 d^2 e^6-574 d e^7+159 e^8\right ) (d+e x)^{m+2}}{e^{10}}-\frac {25 (200 d+e) (d+e x)^{m+9}}{e^{10}}+\frac {500 (d+e x)^{m+10}}{e^{10}}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^{m+9}}{e^{11} (m+9)}-\frac {2 \left (30000 d^3+450 d^2 e+3060 d e^2+49 e^3\right ) (d+e x)^{m+8}}{e^{11} (m+8)}+\frac {\left (5 d^2-2 d e+3 e^2\right )^3 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right ) (d+e x)^{m+1}}{e^{11} (m+1)}+\frac {\left (105000 d^4+2100 d^3 e+21420 d^2 e^2+686 d e^3+999 e^4\right ) (d+e x)^{m+7}}{e^{11} (m+7)}-\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (200 d^5+169 d^4 e+108 d^3 e^2-20 d^2 e^3+86 d e^4-15 e^5\right ) (d+e x)^{m+2}}{e^{11} (m+2)}-\frac {6 \left (21000 d^5+525 d^4 e+7140 d^3 e^2+343 d^2 e^3+999 d e^4-85 e^5\right ) (d+e x)^{m+6}}{e^{11} (m+6)}+\frac {3 \left (5 d^2-2 d e+3 e^2\right ) \left (1500 d^6+660 d^5 e+792 d^4 e^2+58 d^3 e^3+547 d^2 e^4-156 d e^5+53 e^6\right ) (d+e x)^{m+3}}{e^{11} (m+3)}+\frac {\left (105000 d^6+3150 d^5 e+53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4-2550 d e^5+1109 e^6\right ) (d+e x)^{m+5}}{e^{11} (m+5)}-\frac {2 \left (30000 d^7+1050 d^6 e+21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+2218 d e^6-287 e^7\right ) (d+e x)^{m+4}}{e^{11} (m+4)}-\frac {25 (200 d+e) (d+e x)^{m+10}}{e^{11} (m+10)}+\frac {500 (d+e x)^{m+11}}{e^{11} (m+11)}\) |
((5*d^2 - 2*d*e + 3*e^2)^3*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*( d + e*x)^(1 + m))/(e^11*(1 + m)) - ((5*d^2 - 2*d*e + 3*e^2)^2*(200*d^5 + 1 69*d^4*e + 108*d^3*e^2 - 20*d^2*e^3 + 86*d*e^4 - 15*e^5)*(d + e*x)^(2 + m) )/(e^11*(2 + m)) + (3*(5*d^2 - 2*d*e + 3*e^2)*(1500*d^6 + 660*d^5*e + 792* d^4*e^2 + 58*d^3*e^3 + 547*d^2*e^4 - 156*d*e^5 + 53*e^6)*(d + e*x)^(3 + m) )/(e^11*(3 + m)) - (2*(30000*d^7 + 1050*d^6*e + 21420*d^5*e^2 + 1715*d^4*e ^3 + 9990*d^3*e^4 - 2550*d^2*e^5 + 2218*d*e^6 - 287*e^7)*(d + e*x)^(4 + m) )/(e^11*(4 + m)) + ((105000*d^6 + 3150*d^5*e + 53550*d^4*e^2 + 3430*d^3*e^ 3 + 14985*d^2*e^4 - 2550*d*e^5 + 1109*e^6)*(d + e*x)^(5 + m))/(e^11*(5 + m )) - (6*(21000*d^5 + 525*d^4*e + 7140*d^3*e^2 + 343*d^2*e^3 + 999*d*e^4 - 85*e^5)*(d + e*x)^(6 + m))/(e^11*(6 + m)) + ((105000*d^4 + 2100*d^3*e + 21 420*d^2*e^2 + 686*d*e^3 + 999*e^4)*(d + e*x)^(7 + m))/(e^11*(7 + m)) - (2* (30000*d^3 + 450*d^2*e + 3060*d*e^2 + 49*e^3)*(d + e*x)^(8 + m))/(e^11*(8 + m)) + (45*(500*d^2 + 5*d*e + 17*e^2)*(d + e*x)^(9 + m))/(e^11*(9 + m)) - (25*(200*d + e)*(d + e*x)^(10 + m))/(e^11*(10 + m)) + (500*(d + e*x)^(11 + m))/(e^11*(11 + m))
3.4.67.3.1 Defintions of rubi rules used
Int[(Pq_)*((d_.) + (e_.)*(x_))^(m_.)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p _.), x_Symbol] :> Int[ExpandIntegrand[(d + e*x)^m*Pq*(a + b*x + c*x^2)^p, x ], x] /; FreeQ[{a, b, c, d, e, m}, x] && PolyQ[Pq, x] && IGtQ[p, -2]
Leaf count of result is larger than twice the leaf count of optimal. \(5923\) vs. \(2(588)=1176\).
Time = 0.45 (sec) , antiderivative size = 5924, normalized size of antiderivative = 10.07
| method | result | size |
| gosper | \(\text {Expression too large to display}\) | \(5924\) |
| risch | \(\text {Expression too large to display}\) | \(6934\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(11277\) |
Leaf count of result is larger than twice the leaf count of optimal. 4795 vs. \(2 (588) = 1176\).
Time = 0.35 (sec) , antiderivative size = 4795, normalized size of antiderivative = 8.15 \[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx=\text {Too large to display} \]
(54*d*e^10*m^10 + 500*(e^11*m^10 + 55*e^11*m^9 + 1320*e^11*m^8 + 18150*e^1 1*m^7 + 157773*e^11*m^6 + 902055*e^11*m^5 + 3416930*e^11*m^4 + 8409500*e^1 1*m^3 + 12753576*e^11*m^2 + 10628640*e^11*m + 3628800*e^11)*x^11 + 1814400 000*d^11 + 99792000*d^10*e + 3392928000*d^9*e^2 + 488980800*d^8*e^3 + 5696 697600*d^7*e^4 - 3392928000*d^6*e^5 + 8853546240*d^5*e^6 - 5728060800*d^4* e^7 + 6346771200*d^3*e^8 - 2694384000*d^2*e^9 + 2155507200*d*e^10 - 25*(39 91680*e^11 - (20*d*e^10 - e^11)*m^10 - 4*(225*d*e^10 - 14*e^11)*m^9 - 15*( 1160*d*e^10 - 91*e^11)*m^8 - 60*(3150*d*e^10 - 317*e^11)*m^7 - 21*(60260*d *e^10 - 7963*e^11)*m^6 - 84*(64125*d*e^10 - 11492*e^11)*m^5 - 5*(2894720*d *e^10 - 737251*e^11)*m^4 - 20*(1172700*d*e^10 - 456659*e^11)*m^3 - 36*(570 320*d*e^10 - 386841*e^11)*m^2 - 144*(50400*d*e^10 - 80939*e^11)*m)*x^10 - 135*(d^2*e^9 - 26*d*e^10)*m^9 + 5*(678585600*e^11 - (5*d*e^10 - 153*e^11)* m^10 - (1000*d^2*e^9 + 235*d*e^10 - 8721*e^11)*m^9 - 6*(6000*d^2*e^9 + 785 *d*e^10 - 36006*e^11)*m^8 - 6*(91000*d^2*e^9 + 8785*d*e^10 - 509031*e^11)* m^7 - 105*(43200*d^2*e^9 + 3445*d*e^10 - 259029*e^11)*m^6 - 21*(1069000*d^ 2*e^9 + 74815*d*e^10 - 7560189*e^11)*m^5 - 2*(33642000*d^2*e^9 + 2145620*d *e^10 - 306036567*e^11)*m^4 - 4*(29531000*d^2*e^9 + 1761185*d*e^10 - 38217 2121*e^11)*m^3 - 72*(1522000*d^2*e^9 + 86510*d*e^10 - 32587351*e^11)*m^2 - 1440*(28000*d^2*e^9 + 1540*d*e^10 - 1370727*e^11)*m)*x^9 + 9*(106*d^3*e^8 - 945*d^2*e^9 + 11160*d*e^10)*m^8 - (488980800*e^11 - (765*d*e^10 - 98...
Leaf count of result is larger than twice the leaf count of optimal. 136733 vs. \(2 (564) = 1128\).
Time = 38.08 (sec) , antiderivative size = 136733, normalized size of antiderivative = 232.54 \[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx=\text {Too large to display} \]
Piecewise((d**m*(500*x**11/11 - 5*x**10/2 + 85*x**9 - 49*x**8/4 + 999*x**7 /7 + 85*x**6 + 1109*x**5/5 + 287*x**4/2 + 159*x**3 + 135*x**2/2 + 54*x), E q(e, 0)), (1260000*d**10*log(d/e + x)/(2520*d**10*e**11 + 25200*d**9*e**12 *x + 113400*d**8*e**13*x**2 + 302400*d**7*e**14*x**3 + 529200*d**6*e**15*x **4 + 635040*d**5*e**16*x**5 + 529200*d**4*e**17*x**6 + 302400*d**3*e**18* x**7 + 113400*d**2*e**19*x**8 + 25200*d*e**20*x**9 + 2520*e**21*x**10) + 3 690500*d**10/(2520*d**10*e**11 + 25200*d**9*e**12*x + 113400*d**8*e**13*x* *2 + 302400*d**7*e**14*x**3 + 529200*d**6*e**15*x**4 + 635040*d**5*e**16*x **5 + 529200*d**4*e**17*x**6 + 302400*d**3*e**18*x**7 + 113400*d**2*e**19* x**8 + 25200*d*e**20*x**9 + 2520*e**21*x**10) + 12600000*d**9*e*x*log(d/e + x)/(2520*d**10*e**11 + 25200*d**9*e**12*x + 113400*d**8*e**13*x**2 + 302 400*d**7*e**14*x**3 + 529200*d**6*e**15*x**4 + 635040*d**5*e**16*x**5 + 52 9200*d**4*e**17*x**6 + 302400*d**3*e**18*x**7 + 113400*d**2*e**19*x**8 + 2 5200*d*e**20*x**9 + 2520*e**21*x**10) + 35645000*d**9*e*x/(2520*d**10*e**1 1 + 25200*d**9*e**12*x + 113400*d**8*e**13*x**2 + 302400*d**7*e**14*x**3 + 529200*d**6*e**15*x**4 + 635040*d**5*e**16*x**5 + 529200*d**4*e**17*x**6 + 302400*d**3*e**18*x**7 + 113400*d**2*e**19*x**8 + 25200*d*e**20*x**9 + 2 520*e**21*x**10) + 6300*d**9*e/(2520*d**10*e**11 + 25200*d**9*e**12*x + 11 3400*d**8*e**13*x**2 + 302400*d**7*e**14*x**3 + 529200*d**6*e**15*x**4 + 6 35040*d**5*e**16*x**5 + 529200*d**4*e**17*x**6 + 302400*d**3*e**18*x**7...
Leaf count of result is larger than twice the leaf count of optimal. 2292 vs. \(2 (588) = 1176\).
Time = 0.27 (sec) , antiderivative size = 2292, normalized size of antiderivative = 3.90 \[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx=\text {Too large to display} \]
135*(e^2*(m + 1)*x^2 + d*e*m*x - d^2)*(e*x + d)^m/((m^2 + 3*m + 2)*e^2) + 54*(e*x + d)^(m + 1)/(e*(m + 1)) + 477*((m^2 + 3*m + 2)*e^3*x^3 + (m^2 + m )*d*e^2*x^2 - 2*d^2*e*m*x + 2*d^3)*(e*x + d)^m/((m^3 + 6*m^2 + 11*m + 6)*e ^3) + 574*((m^3 + 6*m^2 + 11*m + 6)*e^4*x^4 + (m^3 + 3*m^2 + 2*m)*d*e^3*x^ 3 - 3*(m^2 + m)*d^2*e^2*x^2 + 6*d^3*e*m*x - 6*d^4)*(e*x + d)^m/((m^4 + 10* m^3 + 35*m^2 + 50*m + 24)*e^4) + 1109*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24) *e^5*x^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*d*e^4*x^4 - 4*(m^3 + 3*m^2 + 2*m)* d^2*e^3*x^3 + 12*(m^2 + m)*d^3*e^2*x^2 - 24*d^4*e*m*x + 24*d^5)*(e*x + d)^ m/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^5) + 510*((m^5 + 15*m ^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^6*x^6 + (m^5 + 10*m^4 + 35*m^3 + 50 *m^2 + 24*m)*d*e^5*x^5 - 5*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^2*e^4*x^4 + 20*( m^3 + 3*m^2 + 2*m)*d^3*e^3*x^3 - 60*(m^2 + m)*d^4*e^2*x^2 + 120*d^5*e*m*x - 120*d^6)*(e*x + d)^m/((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 176 4*m + 720)*e^6) + 999*((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764 *m + 720)*e^7*x^7 + (m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d* e^6*x^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^2*e^5*x^5 + 30*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^3*e^4*x^4 - 120*(m^3 + 3*m^2 + 2*m)*d^4*e^3*x^3 + 360*(m^2 + m)*d^5*e^2*x^2 - 720*d^6*e*m*x + 720*d^7)*(e*x + d)^m/((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*e^7) - 98*((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 1306...
Leaf count of result is larger than twice the leaf count of optimal. 10965 vs. \(2 (588) = 1176\).
Time = 0.39 (sec) , antiderivative size = 10965, normalized size of antiderivative = 18.65 \[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx=\text {Too large to display} \]
(500*(e*x + d)^m*e^11*m^10*x^11 + 500*(e*x + d)^m*d*e^10*m^10*x^10 - 25*(e *x + d)^m*e^11*m^10*x^10 + 27500*(e*x + d)^m*e^11*m^9*x^11 - 25*(e*x + d)^ m*d*e^10*m^10*x^9 + 765*(e*x + d)^m*e^11*m^10*x^9 + 22500*(e*x + d)^m*d*e^ 10*m^9*x^10 - 1400*(e*x + d)^m*e^11*m^9*x^10 + 660000*(e*x + d)^m*e^11*m^8 *x^11 + 765*(e*x + d)^m*d*e^10*m^10*x^8 - 98*(e*x + d)^m*e^11*m^10*x^8 - 5 000*(e*x + d)^m*d^2*e^9*m^9*x^9 - 1175*(e*x + d)^m*d*e^10*m^9*x^9 + 43605* (e*x + d)^m*e^11*m^9*x^9 + 435000*(e*x + d)^m*d*e^10*m^8*x^10 - 34125*(e*x + d)^m*e^11*m^8*x^10 + 9075000*(e*x + d)^m*e^11*m^7*x^11 - 98*(e*x + d)^m *d*e^10*m^10*x^7 + 999*(e*x + d)^m*e^11*m^10*x^7 + 225*(e*x + d)^m*d^2*e^9 *m^9*x^8 + 37485*(e*x + d)^m*d*e^10*m^9*x^8 - 5684*(e*x + d)^m*e^11*m^9*x^ 8 - 180000*(e*x + d)^m*d^2*e^9*m^8*x^9 - 23550*(e*x + d)^m*d*e^10*m^8*x^9 + 1080180*(e*x + d)^m*e^11*m^8*x^9 + 4725000*(e*x + d)^m*d*e^10*m^7*x^10 - 475500*(e*x + d)^m*e^11*m^7*x^10 + 78886500*(e*x + d)^m*e^11*m^6*x^11 + 9 99*(e*x + d)^m*d*e^10*m^10*x^6 + 510*(e*x + d)^m*e^11*m^10*x^6 - 6120*(e*x + d)^m*d^2*e^9*m^9*x^7 - 4998*(e*x + d)^m*d*e^10*m^9*x^7 + 58941*(e*x + d )^m*e^11*m^9*x^7 + 45000*(e*x + d)^m*d^3*e^8*m^8*x^8 + 8775*(e*x + d)^m*d^ 2*e^9*m^8*x^8 + 780300*(e*x + d)^m*d*e^10*m^8*x^8 - 143178*(e*x + d)^m*e^1 1*m^8*x^8 - 2730000*(e*x + d)^m*d^2*e^9*m^7*x^9 - 263550*(e*x + d)^m*d*e^1 0*m^7*x^9 + 15270930*(e*x + d)^m*e^11*m^7*x^9 + 31636500*(e*x + d)^m*d*e^1 0*m^6*x^10 - 4180575*(e*x + d)^m*e^11*m^6*x^10 + 451027500*(e*x + d)^m*...
Time = 18.10 (sec) , antiderivative size = 4341, normalized size of antiderivative = 7.38 \[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx=\text {Too large to display} \]
(500*x^11*(d + e*x)^m*(10628640*m + 12753576*m^2 + 8409500*m^3 + 3416930*m ^4 + 902055*m^5 + 157773*m^6 + 18150*m^7 + 1320*m^8 + 55*m^9 + m^10 + 3628 800))/(120543840*m + 150917976*m^2 + 105258076*m^3 + 45995730*m^4 + 133395 35*m^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 39916800) + ((d + e*x)^m*(2155507200*d*e^10 + 99792000*d^10*e + 18144000 00*d^11 - 2694384000*d^2*e^9 + 6346771200*d^3*e^8 - 5728060800*d^4*e^7 + 8 853546240*d^5*e^6 - 3392928000*d^6*e^5 + 5696697600*d^7*e^4 + 488980800*d^ 8*e^3 + 3392928000*d^9*e^2 - 4095133200*d^2*e^9*m + 7530723360*d^3*e^8*m - 5364581040*d^4*e^7*m + 6521026464*d^5*e^6*m - 1933552800*d^6*e^5*m + 2432 604960*d^7*e^4*m + 147682080*d^8*e^3*m + 647740800*d^9*e^2*m + 3795710544* d*e^10*m^2 + 1888225560*d*e^10*m^3 + 595543860*d*e^10*m^4 + 124791030*d*e^ 10*m^5 + 17637102*d*e^10*m^6 + 1663740*d*e^10*m^7 + 100440*d*e^10*m^8 + 35 10*d*e^10*m^9 + 54*d*e^10*m^10 - 2697071580*d^2*e^9*m^2 + 3842860824*d^3*e ^8*m^2 - 2127097056*d^4*e^7*m^2 + 1983530784*d^5*e^6*m^2 - 437886000*d^6*e ^5*m^2 + 387691920*d^7*e^4*m^2 + 14817600*d^8*e^3*m^2 + 30844800*d^9*e^2*m ^2 - 1011746160*d^2*e^9*m^3 + 1102270680*d^3*e^8*m^3 - 463042356*d^4*e^7*m ^3 + 318992760*d^5*e^6*m^3 - 49266000*d^6*e^5*m^3 + 27332640*d^7*e^4*m^3 + 493920*d^8*e^3*m^3 - 238556745*d^2*e^9*m^4 + 194510106*d^3*e^8*m^4 - 5978 7840*d^4*e^7*m^4 + 28612200*d^5*e^6*m^4 - 2754000*d^6*e^5*m^4 + 719280*d^7 *e^4*m^4 - 36710415*d^2*e^9*m^5 + 21636720*d^3*e^8*m^5 - 4580520*d^4*e^...