3.1067 \(\int (a+b x)^{10} (A+B x) (d+e x)^4 \, dx\)
Optimal. Leaf size=204 \[ \frac{e^3 (a+b x)^{15} (-5 a B e+A b e+4 b B d)}{15 b^6}+\frac{e^2 (a+b x)^{14} (b d-a e) (-5 a B e+2 A b e+3 b B d)}{7 b^6}+\frac{2 e (a+b x)^{13} (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{13 b^6}+\frac{(a+b x)^{12} (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{12 b^6}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^4}{11 b^6}+\frac{B e^4 (a+b x)^{16}}{16 b^6} \]
[Out]
((A*b - a*B)*(b*d - a*e)^4*(a + b*x)^11)/(11*b^6) + ((b*d - a*e)^3*(b*B*d + 4*A*
b*e - 5*a*B*e)*(a + b*x)^12)/(12*b^6) + (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e -
5*a*B*e)*(a + b*x)^13)/(13*b^6) + (e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)
*(a + b*x)^14)/(7*b^6) + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^15)/(15*b^6)
+ (B*e^4*(a + b*x)^16)/(16*b^6)
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Rubi [A] time = 3.94455, antiderivative size = 204, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05
\[ \frac{e^3 (a+b x)^{15} (-5 a B e+A b e+4 b B d)}{15 b^6}+\frac{e^2 (a+b x)^{14} (b d-a e) (-5 a B e+2 A b e+3 b B d)}{7 b^6}+\frac{2 e (a+b x)^{13} (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{13 b^6}+\frac{(a+b x)^{12} (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{12 b^6}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^4}{11 b^6}+\frac{B e^4 (a+b x)^{16}}{16 b^6} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^10*(A + B*x)*(d + e*x)^4,x]
[Out]
((A*b - a*B)*(b*d - a*e)^4*(a + b*x)^11)/(11*b^6) + ((b*d - a*e)^3*(b*B*d + 4*A*
b*e - 5*a*B*e)*(a + b*x)^12)/(12*b^6) + (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e -
5*a*B*e)*(a + b*x)^13)/(13*b^6) + (e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)
*(a + b*x)^14)/(7*b^6) + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^15)/(15*b^6)
+ (B*e^4*(a + b*x)^16)/(16*b^6)
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**10*(B*x+A)*(e*x+d)**4,x)
[Out]
Timed out
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Mathematica [B] time = 2.26341, size = 1098, normalized size = 5.38 \[ \frac{x \left (8008 \left (6 A \left (5 d^4+10 e x d^3+10 e^2 x^2 d^2+5 e^3 x^3 d+e^4 x^4\right )+B x \left (15 d^4+40 e x d^3+45 e^2 x^2 d^2+24 e^3 x^3 d+5 e^4 x^4\right )\right ) a^{10}+11440 b x \left (7 A \left (15 d^4+40 e x d^3+45 e^2 x^2 d^2+24 e^3 x^3 d+5 e^4 x^4\right )+2 B x \left (35 d^4+105 e x d^3+126 e^2 x^2 d^2+70 e^3 x^3 d+15 e^4 x^4\right )\right ) a^9+12870 b^2 x^2 \left (8 A \left (35 d^4+105 e x d^3+126 e^2 x^2 d^2+70 e^3 x^3 d+15 e^4 x^4\right )+3 B x \left (70 d^4+224 e x d^3+280 e^2 x^2 d^2+160 e^3 x^3 d+35 e^4 x^4\right )\right ) a^8+11440 b^3 x^3 \left (9 A \left (70 d^4+224 e x d^3+280 e^2 x^2 d^2+160 e^3 x^3 d+35 e^4 x^4\right )+4 B x \left (126 d^4+420 e x d^3+540 e^2 x^2 d^2+315 e^3 x^3 d+70 e^4 x^4\right )\right ) a^7+40040 b^4 x^4 \left (2 A \left (126 d^4+420 e x d^3+540 e^2 x^2 d^2+315 e^3 x^3 d+70 e^4 x^4\right )+B x \left (210 d^4+720 e x d^3+945 e^2 x^2 d^2+560 e^3 x^3 d+126 e^4 x^4\right )\right ) a^6+4368 b^5 x^5 \left (11 A \left (210 d^4+720 e x d^3+945 e^2 x^2 d^2+560 e^3 x^3 d+126 e^4 x^4\right )+6 B x \left (330 d^4+1155 e x d^3+1540 e^2 x^2 d^2+924 e^3 x^3 d+210 e^4 x^4\right )\right ) a^5+1820 b^6 x^6 \left (12 A \left (330 d^4+1155 e x d^3+1540 e^2 x^2 d^2+924 e^3 x^3 d+210 e^4 x^4\right )+7 B x \left (495 d^4+1760 e x d^3+2376 e^2 x^2 d^2+1440 e^3 x^3 d+330 e^4 x^4\right )\right ) a^4+560 b^7 x^7 \left (13 A \left (495 d^4+1760 e x d^3+2376 e^2 x^2 d^2+1440 e^3 x^3 d+330 e^4 x^4\right )+8 B x \left (715 d^4+2574 e x d^3+3510 e^2 x^2 d^2+2145 e^3 x^3 d+495 e^4 x^4\right )\right ) a^3+120 b^8 x^8 \left (14 A \left (715 d^4+2574 e x d^3+3510 e^2 x^2 d^2+2145 e^3 x^3 d+495 e^4 x^4\right )+9 B x \left (1001 d^4+3640 e x d^3+5005 e^2 x^2 d^2+3080 e^3 x^3 d+715 e^4 x^4\right )\right ) a^2+80 b^9 x^9 \left (3 A \left (1001 d^4+3640 e x d^3+5005 e^2 x^2 d^2+3080 e^3 x^3 d+715 e^4 x^4\right )+2 B x \left (1365 d^4+5005 e x d^3+6930 e^2 x^2 d^2+4290 e^3 x^3 d+1001 e^4 x^4\right )\right ) a+b^{10} x^{10} \left (16 A \left (1365 d^4+5005 e x d^3+6930 e^2 x^2 d^2+4290 e^3 x^3 d+1001 e^4 x^4\right )+11 B x \left (1820 d^4+6720 e x d^3+9360 e^2 x^2 d^2+5824 e^3 x^3 d+1365 e^4 x^4\right )\right )\right )}{240240} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^4,x]
[Out]
(x*(8008*a^10*(6*A*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4)
+ B*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4)) + 1144
0*a^9*b*x*(7*A*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4)
+ 2*B*x*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4)) +
12870*a^8*b^2*x^2*(8*A*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 +
15*e^4*x^4) + 3*B*x*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 3
5*e^4*x^4)) + 11440*a^7*b^3*x^3*(9*A*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 1
60*d*e^3*x^3 + 35*e^4*x^4) + 4*B*x*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 31
5*d*e^3*x^3 + 70*e^4*x^4)) + 40040*a^6*b^4*x^4*(2*A*(126*d^4 + 420*d^3*e*x + 540
*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4) + B*x*(210*d^4 + 720*d^3*e*x + 945*d^
2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4)) + 4368*a^5*b^5*x^5*(11*A*(210*d^4 + 72
0*d^3*e*x + 945*d^2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4) + 6*B*x*(330*d^4 + 11
55*d^3*e*x + 1540*d^2*e^2*x^2 + 924*d*e^3*x^3 + 210*e^4*x^4)) + 1820*a^4*b^6*x^6
*(12*A*(330*d^4 + 1155*d^3*e*x + 1540*d^2*e^2*x^2 + 924*d*e^3*x^3 + 210*e^4*x^4)
+ 7*B*x*(495*d^4 + 1760*d^3*e*x + 2376*d^2*e^2*x^2 + 1440*d*e^3*x^3 + 330*e^4*x
^4)) + 560*a^3*b^7*x^7*(13*A*(495*d^4 + 1760*d^3*e*x + 2376*d^2*e^2*x^2 + 1440*d
*e^3*x^3 + 330*e^4*x^4) + 8*B*x*(715*d^4 + 2574*d^3*e*x + 3510*d^2*e^2*x^2 + 214
5*d*e^3*x^3 + 495*e^4*x^4)) + 120*a^2*b^8*x^8*(14*A*(715*d^4 + 2574*d^3*e*x + 35
10*d^2*e^2*x^2 + 2145*d*e^3*x^3 + 495*e^4*x^4) + 9*B*x*(1001*d^4 + 3640*d^3*e*x
+ 5005*d^2*e^2*x^2 + 3080*d*e^3*x^3 + 715*e^4*x^4)) + 80*a*b^9*x^9*(3*A*(1001*d^
4 + 3640*d^3*e*x + 5005*d^2*e^2*x^2 + 3080*d*e^3*x^3 + 715*e^4*x^4) + 2*B*x*(136
5*d^4 + 5005*d^3*e*x + 6930*d^2*e^2*x^2 + 4290*d*e^3*x^3 + 1001*e^4*x^4)) + b^10
*x^10*(16*A*(1365*d^4 + 5005*d^3*e*x + 6930*d^2*e^2*x^2 + 4290*d*e^3*x^3 + 1001*
e^4*x^4) + 11*B*x*(1820*d^4 + 6720*d^3*e*x + 9360*d^2*e^2*x^2 + 5824*d*e^3*x^3 +
1365*e^4*x^4))))/240240
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Maple [B] time = 0.003, size = 1337, normalized size = 6.6 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^10*(B*x+A)*(e*x+d)^4,x)
[Out]
1/16*b^10*B*e^4*x^16+1/15*((A*b^10+10*B*a*b^9)*e^4+4*b^10*B*d*e^3)*x^15+1/14*((1
0*A*a*b^9+45*B*a^2*b^8)*e^4+4*(A*b^10+10*B*a*b^9)*d*e^3+6*b^10*B*d^2*e^2)*x^14+1
/13*((45*A*a^2*b^8+120*B*a^3*b^7)*e^4+4*(10*A*a*b^9+45*B*a^2*b^8)*d*e^3+6*(A*b^1
0+10*B*a*b^9)*d^2*e^2+4*b^10*B*d^3*e)*x^13+1/12*((120*A*a^3*b^7+210*B*a^4*b^6)*e
^4+4*(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^3+6*(10*A*a*b^9+45*B*a^2*b^8)*d^2*e^2+4*(A
*b^10+10*B*a*b^9)*d^3*e+b^10*B*d^4)*x^12+1/11*((210*A*a^4*b^6+252*B*a^5*b^5)*e^4
+4*(120*A*a^3*b^7+210*B*a^4*b^6)*d*e^3+6*(45*A*a^2*b^8+120*B*a^3*b^7)*d^2*e^2+4*
(10*A*a*b^9+45*B*a^2*b^8)*d^3*e+(A*b^10+10*B*a*b^9)*d^4)*x^11+1/10*((252*A*a^5*b
^5+210*B*a^6*b^4)*e^4+4*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e^3+6*(120*A*a^3*b^7+210
*B*a^4*b^6)*d^2*e^2+4*(45*A*a^2*b^8+120*B*a^3*b^7)*d^3*e+(10*A*a*b^9+45*B*a^2*b^
8)*d^4)*x^10+1/9*((210*A*a^6*b^4+120*B*a^7*b^3)*e^4+4*(252*A*a^5*b^5+210*B*a^6*b
^4)*d*e^3+6*(210*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^2+4*(120*A*a^3*b^7+210*B*a^4*b^6
)*d^3*e+(45*A*a^2*b^8+120*B*a^3*b^7)*d^4)*x^9+1/8*((120*A*a^7*b^3+45*B*a^8*b^2)*
e^4+4*(210*A*a^6*b^4+120*B*a^7*b^3)*d*e^3+6*(252*A*a^5*b^5+210*B*a^6*b^4)*d^2*e^
2+4*(210*A*a^4*b^6+252*B*a^5*b^5)*d^3*e+(120*A*a^3*b^7+210*B*a^4*b^6)*d^4)*x^8+1
/7*((45*A*a^8*b^2+10*B*a^9*b)*e^4+4*(120*A*a^7*b^3+45*B*a^8*b^2)*d*e^3+6*(210*A*
a^6*b^4+120*B*a^7*b^3)*d^2*e^2+4*(252*A*a^5*b^5+210*B*a^6*b^4)*d^3*e+(210*A*a^4*
b^6+252*B*a^5*b^5)*d^4)*x^7+1/6*((10*A*a^9*b+B*a^10)*e^4+4*(45*A*a^8*b^2+10*B*a^
9*b)*d*e^3+6*(120*A*a^7*b^3+45*B*a^8*b^2)*d^2*e^2+4*(210*A*a^6*b^4+120*B*a^7*b^3
)*d^3*e+(252*A*a^5*b^5+210*B*a^6*b^4)*d^4)*x^6+1/5*(a^10*A*e^4+4*(10*A*a^9*b+B*a
^10)*d*e^3+6*(45*A*a^8*b^2+10*B*a^9*b)*d^2*e^2+4*(120*A*a^7*b^3+45*B*a^8*b^2)*d^
3*e+(210*A*a^6*b^4+120*B*a^7*b^3)*d^4)*x^5+1/4*(4*a^10*A*d*e^3+6*(10*A*a^9*b+B*a
^10)*d^2*e^2+4*(45*A*a^8*b^2+10*B*a^9*b)*d^3*e+(120*A*a^7*b^3+45*B*a^8*b^2)*d^4)
*x^4+1/3*(6*a^10*A*d^2*e^2+4*(10*A*a^9*b+B*a^10)*d^3*e+(45*A*a^8*b^2+10*B*a^9*b)
*d^4)*x^3+1/2*(4*a^10*A*d^3*e+(10*A*a^9*b+B*a^10)*d^4)*x^2+a^10*A*d^4*x
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Maxima [A] time = 1.3745, size = 1825, normalized size = 8.95 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*(e*x + d)^4,x, algorithm="maxima")
[Out]
1/16*B*b^10*e^4*x^16 + A*a^10*d^4*x + 1/15*(4*B*b^10*d*e^3 + (10*B*a*b^9 + A*b^1
0)*e^4)*x^15 + 1/14*(6*B*b^10*d^2*e^2 + 4*(10*B*a*b^9 + A*b^10)*d*e^3 + 5*(9*B*a
^2*b^8 + 2*A*a*b^9)*e^4)*x^14 + 1/13*(4*B*b^10*d^3*e + 6*(10*B*a*b^9 + A*b^10)*d
^2*e^2 + 20*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^3 + 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^4
)*x^13 + 1/12*(B*b^10*d^4 + 4*(10*B*a*b^9 + A*b^10)*d^3*e + 30*(9*B*a^2*b^8 + 2*
A*a*b^9)*d^2*e^2 + 60*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^3 + 30*(7*B*a^4*b^6 + 4*A*
a^3*b^7)*e^4)*x^12 + 1/11*((10*B*a*b^9 + A*b^10)*d^4 + 20*(9*B*a^2*b^8 + 2*A*a*b
^9)*d^3*e + 90*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^2 + 120*(7*B*a^4*b^6 + 4*A*a^3*
b^7)*d*e^3 + 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^4)*x^11 + 1/10*(5*(9*B*a^2*b^8 + 2
*A*a*b^9)*d^4 + 60*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e + 180*(7*B*a^4*b^6 + 4*A*a^
3*b^7)*d^2*e^2 + 168*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^3 + 42*(5*B*a^6*b^4 + 6*A*a
^5*b^5)*e^4)*x^10 + 1/3*(5*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4 + 40*(7*B*a^4*b^6 + 4
*A*a^3*b^7)*d^3*e + 84*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^2 + 56*(5*B*a^6*b^4 + 6
*A*a^5*b^5)*d*e^3 + 10*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^4)*x^9 + 3/8*(10*(7*B*a^4*b
^6 + 4*A*a^3*b^7)*d^4 + 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e + 84*(5*B*a^6*b^4 +
6*A*a^5*b^5)*d^2*e^2 + 40*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^3 + 5*(3*B*a^8*b^2 +
8*A*a^7*b^3)*e^4)*x^8 + 1/7*(42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4 + 168*(5*B*a^6*b
^4 + 6*A*a^5*b^5)*d^3*e + 180*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^2 + 60*(3*B*a^8*
b^2 + 8*A*a^7*b^3)*d*e^3 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^4)*x^7 + 1/6*(42*(5*B*a
^6*b^4 + 6*A*a^5*b^5)*d^4 + 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e + 90*(3*B*a^8*
b^2 + 8*A*a^7*b^3)*d^2*e^2 + 20*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^3 + (B*a^10 + 10*A
*a^9*b)*e^4)*x^6 + 1/5*(A*a^10*e^4 + 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4 + 60*(3*
B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e + 30*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^2 + 4*(B*a^1
0 + 10*A*a^9*b)*d*e^3)*x^5 + 1/4*(4*A*a^10*d*e^3 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3
)*d^4 + 20*(2*B*a^9*b + 9*A*a^8*b^2)*d^3*e + 6*(B*a^10 + 10*A*a^9*b)*d^2*e^2)*x^
4 + 1/3*(6*A*a^10*d^2*e^2 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^4 + 4*(B*a^10 + 10*A*a
^9*b)*d^3*e)*x^3 + 1/2*(4*A*a^10*d^3*e + (B*a^10 + 10*A*a^9*b)*d^4)*x^2
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Fricas [A] time = 0.198461, size = 1, normalized size = 0. \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*(e*x + d)^4,x, algorithm="fricas")
[Out]
1/16*x^16*e^4*b^10*B + 4/15*x^15*e^3*d*b^10*B + 2/3*x^15*e^4*b^9*a*B + 1/15*x^15
*e^4*b^10*A + 3/7*x^14*e^2*d^2*b^10*B + 20/7*x^14*e^3*d*b^9*a*B + 45/14*x^14*e^4
*b^8*a^2*B + 2/7*x^14*e^3*d*b^10*A + 5/7*x^14*e^4*b^9*a*A + 4/13*x^13*e*d^3*b^10
*B + 60/13*x^13*e^2*d^2*b^9*a*B + 180/13*x^13*e^3*d*b^8*a^2*B + 120/13*x^13*e^4*
b^7*a^3*B + 6/13*x^13*e^2*d^2*b^10*A + 40/13*x^13*e^3*d*b^9*a*A + 45/13*x^13*e^4
*b^8*a^2*A + 1/12*x^12*d^4*b^10*B + 10/3*x^12*e*d^3*b^9*a*B + 45/2*x^12*e^2*d^2*
b^8*a^2*B + 40*x^12*e^3*d*b^7*a^3*B + 35/2*x^12*e^4*b^6*a^4*B + 1/3*x^12*e*d^3*b
^10*A + 5*x^12*e^2*d^2*b^9*a*A + 15*x^12*e^3*d*b^8*a^2*A + 10*x^12*e^4*b^7*a^3*A
+ 10/11*x^11*d^4*b^9*a*B + 180/11*x^11*e*d^3*b^8*a^2*B + 720/11*x^11*e^2*d^2*b^
7*a^3*B + 840/11*x^11*e^3*d*b^6*a^4*B + 252/11*x^11*e^4*b^5*a^5*B + 1/11*x^11*d^
4*b^10*A + 40/11*x^11*e*d^3*b^9*a*A + 270/11*x^11*e^2*d^2*b^8*a^2*A + 480/11*x^1
1*e^3*d*b^7*a^3*A + 210/11*x^11*e^4*b^6*a^4*A + 9/2*x^10*d^4*b^8*a^2*B + 48*x^10
*e*d^3*b^7*a^3*B + 126*x^10*e^2*d^2*b^6*a^4*B + 504/5*x^10*e^3*d*b^5*a^5*B + 21*
x^10*e^4*b^4*a^6*B + x^10*d^4*b^9*a*A + 18*x^10*e*d^3*b^8*a^2*A + 72*x^10*e^2*d^
2*b^7*a^3*A + 84*x^10*e^3*d*b^6*a^4*A + 126/5*x^10*e^4*b^5*a^5*A + 40/3*x^9*d^4*
b^7*a^3*B + 280/3*x^9*e*d^3*b^6*a^4*B + 168*x^9*e^2*d^2*b^5*a^5*B + 280/3*x^9*e^
3*d*b^4*a^6*B + 40/3*x^9*e^4*b^3*a^7*B + 5*x^9*d^4*b^8*a^2*A + 160/3*x^9*e*d^3*b
^7*a^3*A + 140*x^9*e^2*d^2*b^6*a^4*A + 112*x^9*e^3*d*b^5*a^5*A + 70/3*x^9*e^4*b^
4*a^6*A + 105/4*x^8*d^4*b^6*a^4*B + 126*x^8*e*d^3*b^5*a^5*B + 315/2*x^8*e^2*d^2*
b^4*a^6*B + 60*x^8*e^3*d*b^3*a^7*B + 45/8*x^8*e^4*b^2*a^8*B + 15*x^8*d^4*b^7*a^3
*A + 105*x^8*e*d^3*b^6*a^4*A + 189*x^8*e^2*d^2*b^5*a^5*A + 105*x^8*e^3*d*b^4*a^6
*A + 15*x^8*e^4*b^3*a^7*A + 36*x^7*d^4*b^5*a^5*B + 120*x^7*e*d^3*b^4*a^6*B + 720
/7*x^7*e^2*d^2*b^3*a^7*B + 180/7*x^7*e^3*d*b^2*a^8*B + 10/7*x^7*e^4*b*a^9*B + 30
*x^7*d^4*b^6*a^4*A + 144*x^7*e*d^3*b^5*a^5*A + 180*x^7*e^2*d^2*b^4*a^6*A + 480/7
*x^7*e^3*d*b^3*a^7*A + 45/7*x^7*e^4*b^2*a^8*A + 35*x^6*d^4*b^4*a^6*B + 80*x^6*e*
d^3*b^3*a^7*B + 45*x^6*e^2*d^2*b^2*a^8*B + 20/3*x^6*e^3*d*b*a^9*B + 1/6*x^6*e^4*
a^10*B + 42*x^6*d^4*b^5*a^5*A + 140*x^6*e*d^3*b^4*a^6*A + 120*x^6*e^2*d^2*b^3*a^
7*A + 30*x^6*e^3*d*b^2*a^8*A + 5/3*x^6*e^4*b*a^9*A + 24*x^5*d^4*b^3*a^7*B + 36*x
^5*e*d^3*b^2*a^8*B + 12*x^5*e^2*d^2*b*a^9*B + 4/5*x^5*e^3*d*a^10*B + 42*x^5*d^4*
b^4*a^6*A + 96*x^5*e*d^3*b^3*a^7*A + 54*x^5*e^2*d^2*b^2*a^8*A + 8*x^5*e^3*d*b*a^
9*A + 1/5*x^5*e^4*a^10*A + 45/4*x^4*d^4*b^2*a^8*B + 10*x^4*e*d^3*b*a^9*B + 3/2*x
^4*e^2*d^2*a^10*B + 30*x^4*d^4*b^3*a^7*A + 45*x^4*e*d^3*b^2*a^8*A + 15*x^4*e^2*d
^2*b*a^9*A + x^4*e^3*d*a^10*A + 10/3*x^3*d^4*b*a^9*B + 4/3*x^3*e*d^3*a^10*B + 15
*x^3*d^4*b^2*a^8*A + 40/3*x^3*e*d^3*b*a^9*A + 2*x^3*e^2*d^2*a^10*A + 1/2*x^2*d^4
*a^10*B + 5*x^2*d^4*b*a^9*A + 2*x^2*e*d^3*a^10*A + x*d^4*a^10*A
_______________________________________________________________________________________
Sympy [A] time = 0.77546, size = 1676, normalized size = 8.22 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**10*(B*x+A)*(e*x+d)**4,x)
[Out]
A*a**10*d**4*x + B*b**10*e**4*x**16/16 + x**15*(A*b**10*e**4/15 + 2*B*a*b**9*e**
4/3 + 4*B*b**10*d*e**3/15) + x**14*(5*A*a*b**9*e**4/7 + 2*A*b**10*d*e**3/7 + 45*
B*a**2*b**8*e**4/14 + 20*B*a*b**9*d*e**3/7 + 3*B*b**10*d**2*e**2/7) + x**13*(45*
A*a**2*b**8*e**4/13 + 40*A*a*b**9*d*e**3/13 + 6*A*b**10*d**2*e**2/13 + 120*B*a**
3*b**7*e**4/13 + 180*B*a**2*b**8*d*e**3/13 + 60*B*a*b**9*d**2*e**2/13 + 4*B*b**1
0*d**3*e/13) + x**12*(10*A*a**3*b**7*e**4 + 15*A*a**2*b**8*d*e**3 + 5*A*a*b**9*d
**2*e**2 + A*b**10*d**3*e/3 + 35*B*a**4*b**6*e**4/2 + 40*B*a**3*b**7*d*e**3 + 45
*B*a**2*b**8*d**2*e**2/2 + 10*B*a*b**9*d**3*e/3 + B*b**10*d**4/12) + x**11*(210*
A*a**4*b**6*e**4/11 + 480*A*a**3*b**7*d*e**3/11 + 270*A*a**2*b**8*d**2*e**2/11 +
40*A*a*b**9*d**3*e/11 + A*b**10*d**4/11 + 252*B*a**5*b**5*e**4/11 + 840*B*a**4*
b**6*d*e**3/11 + 720*B*a**3*b**7*d**2*e**2/11 + 180*B*a**2*b**8*d**3*e/11 + 10*B
*a*b**9*d**4/11) + x**10*(126*A*a**5*b**5*e**4/5 + 84*A*a**4*b**6*d*e**3 + 72*A*
a**3*b**7*d**2*e**2 + 18*A*a**2*b**8*d**3*e + A*a*b**9*d**4 + 21*B*a**6*b**4*e**
4 + 504*B*a**5*b**5*d*e**3/5 + 126*B*a**4*b**6*d**2*e**2 + 48*B*a**3*b**7*d**3*e
+ 9*B*a**2*b**8*d**4/2) + x**9*(70*A*a**6*b**4*e**4/3 + 112*A*a**5*b**5*d*e**3
+ 140*A*a**4*b**6*d**2*e**2 + 160*A*a**3*b**7*d**3*e/3 + 5*A*a**2*b**8*d**4 + 40
*B*a**7*b**3*e**4/3 + 280*B*a**6*b**4*d*e**3/3 + 168*B*a**5*b**5*d**2*e**2 + 280
*B*a**4*b**6*d**3*e/3 + 40*B*a**3*b**7*d**4/3) + x**8*(15*A*a**7*b**3*e**4 + 105
*A*a**6*b**4*d*e**3 + 189*A*a**5*b**5*d**2*e**2 + 105*A*a**4*b**6*d**3*e + 15*A*
a**3*b**7*d**4 + 45*B*a**8*b**2*e**4/8 + 60*B*a**7*b**3*d*e**3 + 315*B*a**6*b**4
*d**2*e**2/2 + 126*B*a**5*b**5*d**3*e + 105*B*a**4*b**6*d**4/4) + x**7*(45*A*a**
8*b**2*e**4/7 + 480*A*a**7*b**3*d*e**3/7 + 180*A*a**6*b**4*d**2*e**2 + 144*A*a**
5*b**5*d**3*e + 30*A*a**4*b**6*d**4 + 10*B*a**9*b*e**4/7 + 180*B*a**8*b**2*d*e**
3/7 + 720*B*a**7*b**3*d**2*e**2/7 + 120*B*a**6*b**4*d**3*e + 36*B*a**5*b**5*d**4
) + x**6*(5*A*a**9*b*e**4/3 + 30*A*a**8*b**2*d*e**3 + 120*A*a**7*b**3*d**2*e**2
+ 140*A*a**6*b**4*d**3*e + 42*A*a**5*b**5*d**4 + B*a**10*e**4/6 + 20*B*a**9*b*d*
e**3/3 + 45*B*a**8*b**2*d**2*e**2 + 80*B*a**7*b**3*d**3*e + 35*B*a**6*b**4*d**4)
+ x**5*(A*a**10*e**4/5 + 8*A*a**9*b*d*e**3 + 54*A*a**8*b**2*d**2*e**2 + 96*A*a*
*7*b**3*d**3*e + 42*A*a**6*b**4*d**4 + 4*B*a**10*d*e**3/5 + 12*B*a**9*b*d**2*e**
2 + 36*B*a**8*b**2*d**3*e + 24*B*a**7*b**3*d**4) + x**4*(A*a**10*d*e**3 + 15*A*a
**9*b*d**2*e**2 + 45*A*a**8*b**2*d**3*e + 30*A*a**7*b**3*d**4 + 3*B*a**10*d**2*e
**2/2 + 10*B*a**9*b*d**3*e + 45*B*a**8*b**2*d**4/4) + x**3*(2*A*a**10*d**2*e**2
+ 40*A*a**9*b*d**3*e/3 + 15*A*a**8*b**2*d**4 + 4*B*a**10*d**3*e/3 + 10*B*a**9*b*
d**4/3) + x**2*(2*A*a**10*d**3*e + 5*A*a**9*b*d**4 + B*a**10*d**4/2)
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21632, size = 1, normalized size = 0. \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*(e*x + d)^4,x, algorithm="giac")
[Out]
Done