Integrand size = 26, antiderivative size = 210 \[ \int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^4 \, dx=\frac {a^4 x^3}{3}+8 a^3 x^4+\frac {32}{5} (12-a) a^2 x^5+\frac {8}{3} a \left (128-48 a+a^2\right ) x^6+\frac {4}{7} \left (1024-1536 a+192 a^2-a^3\right ) x^7-4 \left (512-288 a+15 a^2\right ) x^8+\frac {64}{9} (128-3 a) (4-a) x^9-\frac {24}{5} \left (896-128 a+a^2\right ) x^{10}+\frac {2}{11} \left (20480-1536 a+3 a^2\right ) x^{11}-\frac {8}{3} (928-35 a) x^{12}+\frac {32}{13} (524-9 a) x^{13}-\frac {8}{7} (464-3 a) x^{14}+\frac {4}{15} (640-a) x^{15}-42 x^{16}+\frac {128 x^{17}}{17}-\frac {8 x^{18}}{9}+\frac {x^{19}}{19} \]
1/3*a^4*x^3+8*a^3*x^4+32/5*(12-a)*a^2*x^5+8/3*a*(a^2-48*a+128)*x^6+4/7*(-a ^3+192*a^2-1536*a+1024)*x^7-4*(15*a^2-288*a+512)*x^8+64/9*(128-3*a)*(4-a)* x^9-24/5*(a^2-128*a+896)*x^10+2/11*(3*a^2-1536*a+20480)*x^11-8/3*(928-35*a )*x^12+32/13*(524-9*a)*x^13-8/7*(464-3*a)*x^14+4/15*(640-a)*x^15-42*x^16+1 28/17*x^17-8/9*x^18+1/19*x^19
Time = 0.02 (sec) , antiderivative size = 204, normalized size of antiderivative = 0.97 \[ \int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^4 \, dx=\frac {a^4 x^3}{3}+8 a^3 x^4-\frac {32}{5} (-12+a) a^2 x^5+\frac {8}{3} a \left (128-48 a+a^2\right ) x^6-\frac {4}{7} \left (-1024+1536 a-192 a^2+a^3\right ) x^7-4 \left (512-288 a+15 a^2\right ) x^8+\frac {64}{9} \left (512-140 a+3 a^2\right ) x^9-\frac {24}{5} \left (896-128 a+a^2\right ) x^{10}+\frac {2}{11} \left (20480-1536 a+3 a^2\right ) x^{11}+\frac {8}{3} (-928+35 a) x^{12}-\frac {32}{13} (-524+9 a) x^{13}+\frac {8}{7} (-464+3 a) x^{14}-\frac {4}{15} (-640+a) x^{15}-42 x^{16}+\frac {128 x^{17}}{17}-\frac {8 x^{18}}{9}+\frac {x^{19}}{19} \]
(a^4*x^3)/3 + 8*a^3*x^4 - (32*(-12 + a)*a^2*x^5)/5 + (8*a*(128 - 48*a + a^ 2)*x^6)/3 - (4*(-1024 + 1536*a - 192*a^2 + a^3)*x^7)/7 - 4*(512 - 288*a + 15*a^2)*x^8 + (64*(512 - 140*a + 3*a^2)*x^9)/9 - (24*(896 - 128*a + a^2)*x ^10)/5 + (2*(20480 - 1536*a + 3*a^2)*x^11)/11 + (8*(-928 + 35*a)*x^12)/3 - (32*(-524 + 9*a)*x^13)/13 + (8*(-464 + 3*a)*x^14)/7 - (4*(-640 + a)*x^15) /15 - 42*x^16 + (128*x^17)/17 - (8*x^18)/9 + x^19/19
Time = 0.41 (sec) , antiderivative size = 210, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2465, 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.
| \(\displaystyle \int x^2 \left (a-x^4+4 x^3-8 x^2+8 x\right )^4 \, dx\) |
| \(\Big \downarrow \) 2465 |
| \(\displaystyle \int \left (a^4 x^2+32 a^3 x^3+2 \left (3 a^2-1536 a+20480\right ) x^{10}-48 \left (a^2-128 a+896\right ) x^9-32 \left (15 a^2-288 a+512\right ) x^7+16 a \left (a^2-48 a+128\right ) x^5+32 (12-a) a^2 x^4+4 \left (-a^3+192 a^2-1536 a+1024\right ) x^6+4 (640-a) x^{14}-16 (464-3 a) x^{13}+32 (524-9 a) x^{12}-32 (928-35 a) x^{11}+64 (128-3 a) (4-a) x^8+x^{18}-16 x^{17}+128 x^{16}-672 x^{15}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {a^4 x^3}{3}+8 a^3 x^4+\frac {2}{11} \left (3 a^2-1536 a+20480\right ) x^{11}-\frac {24}{5} \left (a^2-128 a+896\right ) x^{10}-4 \left (15 a^2-288 a+512\right ) x^8+\frac {8}{3} a \left (a^2-48 a+128\right ) x^6+\frac {32}{5} (12-a) a^2 x^5+\frac {4}{7} \left (-a^3+192 a^2-1536 a+1024\right ) x^7+\frac {4}{15} (640-a) x^{15}-\frac {8}{7} (464-3 a) x^{14}+\frac {32}{13} (524-9 a) x^{13}-\frac {8}{3} (928-35 a) x^{12}+\frac {64}{9} (128-3 a) (4-a) x^9+\frac {x^{19}}{19}-\frac {8 x^{18}}{9}+\frac {128 x^{17}}{17}-42 x^{16}\) |
(a^4*x^3)/3 + 8*a^3*x^4 + (32*(12 - a)*a^2*x^5)/5 + (8*a*(128 - 48*a + a^2 )*x^6)/3 + (4*(1024 - 1536*a + 192*a^2 - a^3)*x^7)/7 - 4*(512 - 288*a + 15 *a^2)*x^8 + (64*(128 - 3*a)*(4 - a)*x^9)/9 - (24*(896 - 128*a + a^2)*x^10) /5 + (2*(20480 - 1536*a + 3*a^2)*x^11)/11 - (8*(928 - 35*a)*x^12)/3 + (32* (524 - 9*a)*x^13)/13 - (8*(464 - 3*a)*x^14)/7 + (4*(640 - a)*x^15)/15 - 42 *x^16 + (128*x^17)/17 - (8*x^18)/9 + x^19/19
3.2.30.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> Int[ExpandToSum[u, Px^p, x], x] /; PolyQ [Px, x] && GtQ[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x ] && IGtQ[p, 0]
Time = 0.12 (sec) , antiderivative size = 182, normalized size of antiderivative = 0.87
| method | result | size |
| norman | \(\frac {a^{4} x^{3}}{3}+8 a^{3} x^{4}+\left (-\frac {32}{5} a^{3}+\frac {384}{5} a^{2}\right ) x^{5}+\left (\frac {8}{3} a^{3}-128 a^{2}+\frac {1024}{3} a \right ) x^{6}+\left (-\frac {4}{7} a^{3}+\frac {768}{7} a^{2}-\frac {6144}{7} a +\frac {4096}{7}\right ) x^{7}+\left (-60 a^{2}+1152 a -2048\right ) x^{8}+\left (\frac {64}{3} a^{2}-\frac {8960}{9} a +\frac {32768}{9}\right ) x^{9}+\left (-\frac {24}{5} a^{2}+\frac {3072}{5} a -\frac {21504}{5}\right ) x^{10}+\left (\frac {6}{11} a^{2}-\frac {3072}{11} a +\frac {40960}{11}\right ) x^{11}+\left (\frac {280 a}{3}-\frac {7424}{3}\right ) x^{12}+\left (-\frac {288 a}{13}+\frac {16768}{13}\right ) x^{13}+\left (\frac {24 a}{7}-\frac {3712}{7}\right ) x^{14}+\left (-\frac {4 a}{15}+\frac {512}{3}\right ) x^{15}-42 x^{16}+\frac {128 x^{17}}{17}-\frac {8 x^{18}}{9}+\frac {x^{19}}{19}\) | \(182\) |
| gosper | \(-\frac {21504}{5} x^{10}+\frac {40960}{11} x^{11}-\frac {7424}{3} x^{12}+\frac {16768}{13} x^{13}+\frac {32768}{9} x^{9}+\frac {4096}{7} x^{7}+\frac {24}{7} x^{14} a -\frac {24}{5} x^{10} a^{2}+\frac {8}{3} x^{6} a^{3}-\frac {3712}{7} x^{14}-2048 x^{8}+\frac {1}{3} a^{4} x^{3}-\frac {4}{7} a^{3} x^{7}-\frac {6144}{7} a \,x^{7}+\frac {1024}{3} a \,x^{6}-\frac {32}{5} x^{5} a^{3}+\frac {1}{19} x^{19}-\frac {8}{9} x^{18}+\frac {128}{17} x^{17}-42 x^{16}+\frac {512}{3} x^{15}+8 a^{3} x^{4}-\frac {288}{13} x^{13} a -60 a^{2} x^{8}+\frac {64}{3} x^{9} a^{2}-\frac {8960}{9} x^{9} a +\frac {3072}{5} x^{10} a -\frac {3072}{11} x^{11} a +\frac {280}{3} x^{12} a +1152 a \,x^{8}-\frac {4}{15} x^{15} a +\frac {6}{11} x^{11} a^{2}+\frac {768}{7} a^{2} x^{7}-128 a^{2} x^{6}+\frac {384}{5} a^{2} x^{5}\) | \(223\) |
| risch | \(-\frac {21504}{5} x^{10}+\frac {40960}{11} x^{11}-\frac {7424}{3} x^{12}+\frac {16768}{13} x^{13}+\frac {32768}{9} x^{9}+\frac {4096}{7} x^{7}+\frac {24}{7} x^{14} a -\frac {24}{5} x^{10} a^{2}+\frac {8}{3} x^{6} a^{3}-\frac {3712}{7} x^{14}-2048 x^{8}+\frac {1}{3} a^{4} x^{3}-\frac {4}{7} a^{3} x^{7}-\frac {6144}{7} a \,x^{7}+\frac {1024}{3} a \,x^{6}-\frac {32}{5} x^{5} a^{3}+\frac {1}{19} x^{19}-\frac {8}{9} x^{18}+\frac {128}{17} x^{17}-42 x^{16}+\frac {512}{3} x^{15}+8 a^{3} x^{4}-\frac {288}{13} x^{13} a -60 a^{2} x^{8}+\frac {64}{3} x^{9} a^{2}-\frac {8960}{9} x^{9} a +\frac {3072}{5} x^{10} a -\frac {3072}{11} x^{11} a +\frac {280}{3} x^{12} a +1152 a \,x^{8}-\frac {4}{15} x^{15} a +\frac {6}{11} x^{11} a^{2}+\frac {768}{7} a^{2} x^{7}-128 a^{2} x^{6}+\frac {384}{5} a^{2} x^{5}\) | \(223\) |
| parallelrisch | \(-\frac {21504}{5} x^{10}+\frac {40960}{11} x^{11}-\frac {7424}{3} x^{12}+\frac {16768}{13} x^{13}+\frac {32768}{9} x^{9}+\frac {4096}{7} x^{7}+\frac {24}{7} x^{14} a -\frac {24}{5} x^{10} a^{2}+\frac {8}{3} x^{6} a^{3}-\frac {3712}{7} x^{14}-2048 x^{8}+\frac {1}{3} a^{4} x^{3}-\frac {4}{7} a^{3} x^{7}-\frac {6144}{7} a \,x^{7}+\frac {1024}{3} a \,x^{6}-\frac {32}{5} x^{5} a^{3}+\frac {1}{19} x^{19}-\frac {8}{9} x^{18}+\frac {128}{17} x^{17}-42 x^{16}+\frac {512}{3} x^{15}+8 a^{3} x^{4}-\frac {288}{13} x^{13} a -60 a^{2} x^{8}+\frac {64}{3} x^{9} a^{2}-\frac {8960}{9} x^{9} a +\frac {3072}{5} x^{10} a -\frac {3072}{11} x^{11} a +\frac {280}{3} x^{12} a +1152 a \,x^{8}-\frac {4}{15} x^{15} a +\frac {6}{11} x^{11} a^{2}+\frac {768}{7} a^{2} x^{7}-128 a^{2} x^{6}+\frac {384}{5} a^{2} x^{5}\) | \(223\) |
| default | \(\frac {x^{19}}{19}-\frac {8 x^{18}}{9}+\frac {128 x^{17}}{17}-42 x^{16}+\frac {\left (-4 a +2560\right ) x^{15}}{15}+\frac {\left (48 a -7424\right ) x^{14}}{14}+\frac {\left (-288 a +16768\right ) x^{13}}{13}+\frac {\left (1120 a -29696\right ) x^{12}}{12}+\frac {\left (2 a^{2}-2560 a +24576+\left (-2 a +128\right )^{2}\right ) x^{11}}{11}+\frac {\left (-16 a^{2}+3584 a -10240+2 \left (8 a -128\right ) \left (-2 a +128\right )\right ) x^{10}}{10}+\frac {\left (64 a^{2}-2560 a +2 \left (-16 a +64\right ) \left (-2 a +128\right )+\left (8 a -128\right )^{2}\right ) x^{9}}{9}+\frac {\left (-160 a^{2}+32 a \left (-2 a +128\right )+2 \left (-16 a +64\right ) \left (8 a -128\right )\right ) x^{8}}{8}+\frac {\left (2 a^{2} \left (-2 a +128\right )+32 a \left (8 a -128\right )+\left (-16 a +64\right )^{2}\right ) x^{7}}{7}+\frac {\left (2 a^{2} \left (8 a -128\right )+32 a \left (-16 a +64\right )\right ) x^{6}}{6}+\frac {\left (2 a^{2} \left (-16 a +64\right )+256 a^{2}\right ) x^{5}}{5}+8 a^{3} x^{4}+\frac {a^{4} x^{3}}{3}\) | \(267\) |
1/3*a^4*x^3+8*a^3*x^4+(-32/5*a^3+384/5*a^2)*x^5+(8/3*a^3-128*a^2+1024/3*a) *x^6+(-4/7*a^3+768/7*a^2-6144/7*a+4096/7)*x^7+(-60*a^2+1152*a-2048)*x^8+(6 4/3*a^2-8960/9*a+32768/9)*x^9+(-24/5*a^2+3072/5*a-21504/5)*x^10+(6/11*a^2- 3072/11*a+40960/11)*x^11+(280/3*a-7424/3)*x^12+(-288/13*a+16768/13)*x^13+( 24/7*a-3712/7)*x^14+(-4/15*a+512/3)*x^15-42*x^16+128/17*x^17-8/9*x^18+1/19 *x^19
Time = 0.24 (sec) , antiderivative size = 182, normalized size of antiderivative = 0.87 \[ \int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^4 \, dx=\frac {1}{19} \, x^{19} - \frac {8}{9} \, x^{18} + \frac {128}{17} \, x^{17} - \frac {4}{15} \, {\left (a - 640\right )} x^{15} - 42 \, x^{16} + \frac {8}{7} \, {\left (3 \, a - 464\right )} x^{14} - \frac {32}{13} \, {\left (9 \, a - 524\right )} x^{13} + \frac {8}{3} \, {\left (35 \, a - 928\right )} x^{12} + \frac {2}{11} \, {\left (3 \, a^{2} - 1536 \, a + 20480\right )} x^{11} - \frac {24}{5} \, {\left (a^{2} - 128 \, a + 896\right )} x^{10} + \frac {64}{9} \, {\left (3 \, a^{2} - 140 \, a + 512\right )} x^{9} - 4 \, {\left (15 \, a^{2} - 288 \, a + 512\right )} x^{8} - \frac {4}{7} \, {\left (a^{3} - 192 \, a^{2} + 1536 \, a - 1024\right )} x^{7} + \frac {1}{3} \, a^{4} x^{3} + 8 \, a^{3} x^{4} + \frac {8}{3} \, {\left (a^{3} - 48 \, a^{2} + 128 \, a\right )} x^{6} - \frac {32}{5} \, {\left (a^{3} - 12 \, a^{2}\right )} x^{5} \]
1/19*x^19 - 8/9*x^18 + 128/17*x^17 - 4/15*(a - 640)*x^15 - 42*x^16 + 8/7*( 3*a - 464)*x^14 - 32/13*(9*a - 524)*x^13 + 8/3*(35*a - 928)*x^12 + 2/11*(3 *a^2 - 1536*a + 20480)*x^11 - 24/5*(a^2 - 128*a + 896)*x^10 + 64/9*(3*a^2 - 140*a + 512)*x^9 - 4*(15*a^2 - 288*a + 512)*x^8 - 4/7*(a^3 - 192*a^2 + 1 536*a - 1024)*x^7 + 1/3*a^4*x^3 + 8*a^3*x^4 + 8/3*(a^3 - 48*a^2 + 128*a)*x ^6 - 32/5*(a^3 - 12*a^2)*x^5
Time = 0.04 (sec) , antiderivative size = 219, normalized size of antiderivative = 1.04 \[ \int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^4 \, dx=\frac {a^{4} x^{3}}{3} + 8 a^{3} x^{4} + \frac {x^{19}}{19} - \frac {8 x^{18}}{9} + \frac {128 x^{17}}{17} - 42 x^{16} + x^{15} \cdot \left (\frac {512}{3} - \frac {4 a}{15}\right ) + x^{14} \cdot \left (\frac {24 a}{7} - \frac {3712}{7}\right ) + x^{13} \cdot \left (\frac {16768}{13} - \frac {288 a}{13}\right ) + x^{12} \cdot \left (\frac {280 a}{3} - \frac {7424}{3}\right ) + x^{11} \cdot \left (\frac {6 a^{2}}{11} - \frac {3072 a}{11} + \frac {40960}{11}\right ) + x^{10} \left (- \frac {24 a^{2}}{5} + \frac {3072 a}{5} - \frac {21504}{5}\right ) + x^{9} \cdot \left (\frac {64 a^{2}}{3} - \frac {8960 a}{9} + \frac {32768}{9}\right ) + x^{8} \left (- 60 a^{2} + 1152 a - 2048\right ) + x^{7} \left (- \frac {4 a^{3}}{7} + \frac {768 a^{2}}{7} - \frac {6144 a}{7} + \frac {4096}{7}\right ) + x^{6} \cdot \left (\frac {8 a^{3}}{3} - 128 a^{2} + \frac {1024 a}{3}\right ) + x^{5} \left (- \frac {32 a^{3}}{5} + \frac {384 a^{2}}{5}\right ) \]
a**4*x**3/3 + 8*a**3*x**4 + x**19/19 - 8*x**18/9 + 128*x**17/17 - 42*x**16 + x**15*(512/3 - 4*a/15) + x**14*(24*a/7 - 3712/7) + x**13*(16768/13 - 28 8*a/13) + x**12*(280*a/3 - 7424/3) + x**11*(6*a**2/11 - 3072*a/11 + 40960/ 11) + x**10*(-24*a**2/5 + 3072*a/5 - 21504/5) + x**9*(64*a**2/3 - 8960*a/9 + 32768/9) + x**8*(-60*a**2 + 1152*a - 2048) + x**7*(-4*a**3/7 + 768*a**2 /7 - 6144*a/7 + 4096/7) + x**6*(8*a**3/3 - 128*a**2 + 1024*a/3) + x**5*(-3 2*a**3/5 + 384*a**2/5)
Time = 0.19 (sec) , antiderivative size = 182, normalized size of antiderivative = 0.87 \[ \int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^4 \, dx=\frac {1}{19} \, x^{19} - \frac {8}{9} \, x^{18} + \frac {128}{17} \, x^{17} - \frac {4}{15} \, {\left (a - 640\right )} x^{15} - 42 \, x^{16} + \frac {8}{7} \, {\left (3 \, a - 464\right )} x^{14} - \frac {32}{13} \, {\left (9 \, a - 524\right )} x^{13} + \frac {8}{3} \, {\left (35 \, a - 928\right )} x^{12} + \frac {2}{11} \, {\left (3 \, a^{2} - 1536 \, a + 20480\right )} x^{11} - \frac {24}{5} \, {\left (a^{2} - 128 \, a + 896\right )} x^{10} + \frac {64}{9} \, {\left (3 \, a^{2} - 140 \, a + 512\right )} x^{9} - 4 \, {\left (15 \, a^{2} - 288 \, a + 512\right )} x^{8} - \frac {4}{7} \, {\left (a^{3} - 192 \, a^{2} + 1536 \, a - 1024\right )} x^{7} + \frac {1}{3} \, a^{4} x^{3} + 8 \, a^{3} x^{4} + \frac {8}{3} \, {\left (a^{3} - 48 \, a^{2} + 128 \, a\right )} x^{6} - \frac {32}{5} \, {\left (a^{3} - 12 \, a^{2}\right )} x^{5} \]
1/19*x^19 - 8/9*x^18 + 128/17*x^17 - 4/15*(a - 640)*x^15 - 42*x^16 + 8/7*( 3*a - 464)*x^14 - 32/13*(9*a - 524)*x^13 + 8/3*(35*a - 928)*x^12 + 2/11*(3 *a^2 - 1536*a + 20480)*x^11 - 24/5*(a^2 - 128*a + 896)*x^10 + 64/9*(3*a^2 - 140*a + 512)*x^9 - 4*(15*a^2 - 288*a + 512)*x^8 - 4/7*(a^3 - 192*a^2 + 1 536*a - 1024)*x^7 + 1/3*a^4*x^3 + 8*a^3*x^4 + 8/3*(a^3 - 48*a^2 + 128*a)*x ^6 - 32/5*(a^3 - 12*a^2)*x^5
Time = 0.29 (sec) , antiderivative size = 222, normalized size of antiderivative = 1.06 \[ \int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^4 \, dx=\frac {1}{19} \, x^{19} - \frac {8}{9} \, x^{18} + \frac {128}{17} \, x^{17} - \frac {4}{15} \, a x^{15} - 42 \, x^{16} + \frac {24}{7} \, a x^{14} + \frac {512}{3} \, x^{15} - \frac {288}{13} \, a x^{13} - \frac {3712}{7} \, x^{14} + \frac {6}{11} \, a^{2} x^{11} + \frac {280}{3} \, a x^{12} + \frac {16768}{13} \, x^{13} - \frac {24}{5} \, a^{2} x^{10} - \frac {3072}{11} \, a x^{11} - \frac {7424}{3} \, x^{12} + \frac {64}{3} \, a^{2} x^{9} + \frac {3072}{5} \, a x^{10} + \frac {40960}{11} \, x^{11} - \frac {4}{7} \, a^{3} x^{7} - 60 \, a^{2} x^{8} - \frac {8960}{9} \, a x^{9} - \frac {21504}{5} \, x^{10} + \frac {8}{3} \, a^{3} x^{6} + \frac {768}{7} \, a^{2} x^{7} + 1152 \, a x^{8} + \frac {32768}{9} \, x^{9} - \frac {32}{5} \, a^{3} x^{5} - 128 \, a^{2} x^{6} - \frac {6144}{7} \, a x^{7} - 2048 \, x^{8} + \frac {1}{3} \, a^{4} x^{3} + 8 \, a^{3} x^{4} + \frac {384}{5} \, a^{2} x^{5} + \frac {1024}{3} \, a x^{6} + \frac {4096}{7} \, x^{7} \]
1/19*x^19 - 8/9*x^18 + 128/17*x^17 - 4/15*a*x^15 - 42*x^16 + 24/7*a*x^14 + 512/3*x^15 - 288/13*a*x^13 - 3712/7*x^14 + 6/11*a^2*x^11 + 280/3*a*x^12 + 16768/13*x^13 - 24/5*a^2*x^10 - 3072/11*a*x^11 - 7424/3*x^12 + 64/3*a^2*x ^9 + 3072/5*a*x^10 + 40960/11*x^11 - 4/7*a^3*x^7 - 60*a^2*x^8 - 8960/9*a*x ^9 - 21504/5*x^10 + 8/3*a^3*x^6 + 768/7*a^2*x^7 + 1152*a*x^8 + 32768/9*x^9 - 32/5*a^3*x^5 - 128*a^2*x^6 - 6144/7*a*x^7 - 2048*x^8 + 1/3*a^4*x^3 + 8* a^3*x^4 + 384/5*a^2*x^5 + 1024/3*a*x^6 + 4096/7*x^7
Time = 9.27 (sec) , antiderivative size = 178, normalized size of antiderivative = 0.85 \[ \int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^4 \, dx=x^{14}\,\left (\frac {24\,a}{7}-\frac {3712}{7}\right )-x^{15}\,\left (\frac {4\,a}{15}-\frac {512}{3}\right )+x^{12}\,\left (\frac {280\,a}{3}-\frac {7424}{3}\right )-x^{13}\,\left (\frac {288\,a}{13}-\frac {16768}{13}\right )-x^8\,\left (60\,a^2-1152\,a+2048\right )-x^{10}\,\left (\frac {24\,a^2}{5}-\frac {3072\,a}{5}+\frac {21504}{5}\right )+x^9\,\left (\frac {64\,a^2}{3}-\frac {8960\,a}{9}+\frac {32768}{9}\right )+x^{11}\,\left (\frac {6\,a^2}{11}-\frac {3072\,a}{11}+\frac {40960}{11}\right )-x^7\,\left (\frac {4\,a^3}{7}-\frac {768\,a^2}{7}+\frac {6144\,a}{7}-\frac {4096}{7}\right )-42\,x^{16}+\frac {128\,x^{17}}{17}-\frac {8\,x^{18}}{9}+\frac {x^{19}}{19}+8\,a^3\,x^4+\frac {a^4\,x^3}{3}+\frac {8\,a\,x^6\,\left (a^2-48\,a+128\right )}{3}-\frac {32\,a^2\,x^5\,\left (a-12\right )}{5} \]
x^14*((24*a)/7 - 3712/7) - x^15*((4*a)/15 - 512/3) + x^12*((280*a)/3 - 742 4/3) - x^13*((288*a)/13 - 16768/13) - x^8*(60*a^2 - 1152*a + 2048) - x^10* ((24*a^2)/5 - (3072*a)/5 + 21504/5) + x^9*((64*a^2)/3 - (8960*a)/9 + 32768 /9) + x^11*((6*a^2)/11 - (3072*a)/11 + 40960/11) - x^7*((6144*a)/7 - (768* a^2)/7 + (4*a^3)/7 - 4096/7) - 42*x^16 + (128*x^17)/17 - (8*x^18)/9 + x^19 /19 + 8*a^3*x^4 + (a^4*x^3)/3 + (8*a*x^6*(a^2 - 48*a + 128))/3 - (32*a^2*x ^5*(a - 12))/5