3.1301 \(\int (a+b x)^{10} (c+d x)^{10} \, dx\)
Optimal. Leaf size=279 \[ \frac{d^9 (a+b x)^{20} (b c-a d)}{2 b^{11}}+\frac{45 d^8 (a+b x)^{19} (b c-a d)^2}{19 b^{11}}+\frac{20 d^7 (a+b x)^{18} (b c-a d)^3}{3 b^{11}}+\frac{210 d^6 (a+b x)^{17} (b c-a d)^4}{17 b^{11}}+\frac{63 d^5 (a+b x)^{16} (b c-a d)^5}{4 b^{11}}+\frac{14 d^4 (a+b x)^{15} (b c-a d)^6}{b^{11}}+\frac{60 d^3 (a+b x)^{14} (b c-a d)^7}{7 b^{11}}+\frac{45 d^2 (a+b x)^{13} (b c-a d)^8}{13 b^{11}}+\frac{5 d (a+b x)^{12} (b c-a d)^9}{6 b^{11}}+\frac{(a+b x)^{11} (b c-a d)^{10}}{11 b^{11}}+\frac{d^{10} (a+b x)^{21}}{21 b^{11}} \]
[Out]
((b*c - a*d)^10*(a + b*x)^11)/(11*b^11) + (5*d*(b*c - a*d)^9*(a + b*x)^12)/(6*b^11) + (45*d^2*(b*c - a*d)^8*(a
+ b*x)^13)/(13*b^11) + (60*d^3*(b*c - a*d)^7*(a + b*x)^14)/(7*b^11) + (14*d^4*(b*c - a*d)^6*(a + b*x)^15)/b^1
1 + (63*d^5*(b*c - a*d)^5*(a + b*x)^16)/(4*b^11) + (210*d^6*(b*c - a*d)^4*(a + b*x)^17)/(17*b^11) + (20*d^7*(b
*c - a*d)^3*(a + b*x)^18)/(3*b^11) + (45*d^8*(b*c - a*d)^2*(a + b*x)^19)/(19*b^11) + (d^9*(b*c - a*d)*(a + b*x
)^20)/(2*b^11) + (d^10*(a + b*x)^21)/(21*b^11)
________________________________________________________________________________________
Rubi [A] time = 1.11221, antiderivative size = 279, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used =
{43} \[ \frac{d^9 (a+b x)^{20} (b c-a d)}{2 b^{11}}+\frac{45 d^8 (a+b x)^{19} (b c-a d)^2}{19 b^{11}}+\frac{20 d^7 (a+b x)^{18} (b c-a d)^3}{3 b^{11}}+\frac{210 d^6 (a+b x)^{17} (b c-a d)^4}{17 b^{11}}+\frac{63 d^5 (a+b x)^{16} (b c-a d)^5}{4 b^{11}}+\frac{14 d^4 (a+b x)^{15} (b c-a d)^6}{b^{11}}+\frac{60 d^3 (a+b x)^{14} (b c-a d)^7}{7 b^{11}}+\frac{45 d^2 (a+b x)^{13} (b c-a d)^8}{13 b^{11}}+\frac{5 d (a+b x)^{12} (b c-a d)^9}{6 b^{11}}+\frac{(a+b x)^{11} (b c-a d)^{10}}{11 b^{11}}+\frac{d^{10} (a+b x)^{21}}{21 b^{11}} \]
Antiderivative was successfully verified.
[In]
Int[(a + b*x)^10*(c + d*x)^10,x]
[Out]
((b*c - a*d)^10*(a + b*x)^11)/(11*b^11) + (5*d*(b*c - a*d)^9*(a + b*x)^12)/(6*b^11) + (45*d^2*(b*c - a*d)^8*(a
+ b*x)^13)/(13*b^11) + (60*d^3*(b*c - a*d)^7*(a + b*x)^14)/(7*b^11) + (14*d^4*(b*c - a*d)^6*(a + b*x)^15)/b^1
1 + (63*d^5*(b*c - a*d)^5*(a + b*x)^16)/(4*b^11) + (210*d^6*(b*c - a*d)^4*(a + b*x)^17)/(17*b^11) + (20*d^7*(b
*c - a*d)^3*(a + b*x)^18)/(3*b^11) + (45*d^8*(b*c - a*d)^2*(a + b*x)^19)/(19*b^11) + (d^9*(b*c - a*d)*(a + b*x
)^20)/(2*b^11) + (d^10*(a + b*x)^21)/(21*b^11)
Rule 43
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])
Rubi steps
\begin{align*} \int (a+b x)^{10} (c+d x)^{10} \, dx &=\int \left (\frac{(b c-a d)^{10} (a+b x)^{10}}{b^{10}}+\frac{10 d (b c-a d)^9 (a+b x)^{11}}{b^{10}}+\frac{45 d^2 (b c-a d)^8 (a+b x)^{12}}{b^{10}}+\frac{120 d^3 (b c-a d)^7 (a+b x)^{13}}{b^{10}}+\frac{210 d^4 (b c-a d)^6 (a+b x)^{14}}{b^{10}}+\frac{252 d^5 (b c-a d)^5 (a+b x)^{15}}{b^{10}}+\frac{210 d^6 (b c-a d)^4 (a+b x)^{16}}{b^{10}}+\frac{120 d^7 (b c-a d)^3 (a+b x)^{17}}{b^{10}}+\frac{45 d^8 (b c-a d)^2 (a+b x)^{18}}{b^{10}}+\frac{10 d^9 (b c-a d) (a+b x)^{19}}{b^{10}}+\frac{d^{10} (a+b x)^{20}}{b^{10}}\right ) \, dx\\ &=\frac{(b c-a d)^{10} (a+b x)^{11}}{11 b^{11}}+\frac{5 d (b c-a d)^9 (a+b x)^{12}}{6 b^{11}}+\frac{45 d^2 (b c-a d)^8 (a+b x)^{13}}{13 b^{11}}+\frac{60 d^3 (b c-a d)^7 (a+b x)^{14}}{7 b^{11}}+\frac{14 d^4 (b c-a d)^6 (a+b x)^{15}}{b^{11}}+\frac{63 d^5 (b c-a d)^5 (a+b x)^{16}}{4 b^{11}}+\frac{210 d^6 (b c-a d)^4 (a+b x)^{17}}{17 b^{11}}+\frac{20 d^7 (b c-a d)^3 (a+b x)^{18}}{3 b^{11}}+\frac{45 d^8 (b c-a d)^2 (a+b x)^{19}}{19 b^{11}}+\frac{d^9 (b c-a d) (a+b x)^{20}}{2 b^{11}}+\frac{d^{10} (a+b x)^{21}}{21 b^{11}}\\ \end{align*}
Mathematica [B] time = 0.171711, size = 1539, normalized size = 5.52 \[ \frac{1}{21} b^{10} d^{10} x^{21}+\frac{1}{2} b^9 d^9 (b c+a d) x^{20}+\frac{5}{19} b^8 d^8 \left (9 b^2 c^2+20 a b d c+9 a^2 d^2\right ) x^{19}+\frac{5}{3} b^7 d^7 \left (4 b^3 c^3+15 a b^2 d c^2+15 a^2 b d^2 c+4 a^3 d^3\right ) x^{18}+\frac{15}{17} b^6 d^6 \left (14 b^4 c^4+80 a b^3 d c^3+135 a^2 b^2 d^2 c^2+80 a^3 b d^3 c+14 a^4 d^4\right ) x^{17}+\frac{3}{4} b^5 d^5 \left (21 b^5 c^5+175 a b^4 d c^4+450 a^2 b^3 d^2 c^3+450 a^3 b^2 d^3 c^2+175 a^4 b d^4 c+21 a^5 d^5\right ) x^{16}+2 b^4 d^4 \left (7 b^6 c^6+84 a b^5 d c^5+315 a^2 b^4 d^2 c^4+480 a^3 b^3 d^3 c^3+315 a^4 b^2 d^4 c^2+84 a^5 b d^5 c+7 a^6 d^6\right ) x^{15}+\frac{30}{7} b^3 d^3 \left (2 b^7 c^7+35 a b^6 d c^6+189 a^2 b^5 d^2 c^5+420 a^3 b^4 d^3 c^4+420 a^4 b^3 d^4 c^3+189 a^5 b^2 d^5 c^2+35 a^6 b d^6 c+2 a^7 d^7\right ) x^{14}+\frac{15}{13} b^2 d^2 \left (3 b^8 c^8+80 a b^7 d c^7+630 a^2 b^6 d^2 c^6+2016 a^3 b^5 d^3 c^5+2940 a^4 b^4 d^4 c^4+2016 a^5 b^3 d^5 c^3+630 a^6 b^2 d^6 c^2+80 a^7 b d^7 c+3 a^8 d^8\right ) x^{13}+\frac{5}{6} b d \left (b^9 c^9+45 a b^8 d c^8+540 a^2 b^7 d^2 c^7+2520 a^3 b^6 d^3 c^6+5292 a^4 b^5 d^4 c^5+5292 a^5 b^4 d^5 c^4+2520 a^6 b^3 d^6 c^3+540 a^7 b^2 d^7 c^2+45 a^8 b d^8 c+a^9 d^9\right ) x^{12}+\frac{1}{11} \left (b^{10} c^{10}+100 a b^9 d c^9+2025 a^2 b^8 d^2 c^8+14400 a^3 b^7 d^3 c^7+44100 a^4 b^6 d^4 c^6+63504 a^5 b^5 d^5 c^5+44100 a^6 b^4 d^6 c^4+14400 a^7 b^3 d^7 c^3+2025 a^8 b^2 d^8 c^2+100 a^9 b d^9 c+a^{10} d^{10}\right ) x^{11}+a c \left (b^9 c^9+45 a b^8 d c^8+540 a^2 b^7 d^2 c^7+2520 a^3 b^6 d^3 c^6+5292 a^4 b^5 d^4 c^5+5292 a^5 b^4 d^5 c^4+2520 a^6 b^3 d^6 c^3+540 a^7 b^2 d^7 c^2+45 a^8 b d^8 c+a^9 d^9\right ) x^{10}+\frac{5}{3} a^2 c^2 \left (3 b^8 c^8+80 a b^7 d c^7+630 a^2 b^6 d^2 c^6+2016 a^3 b^5 d^3 c^5+2940 a^4 b^4 d^4 c^4+2016 a^5 b^3 d^5 c^3+630 a^6 b^2 d^6 c^2+80 a^7 b d^7 c+3 a^8 d^8\right ) x^9+\frac{15}{2} a^3 c^3 \left (2 b^7 c^7+35 a b^6 d c^6+189 a^2 b^5 d^2 c^5+420 a^3 b^4 d^3 c^4+420 a^4 b^3 d^4 c^3+189 a^5 b^2 d^5 c^2+35 a^6 b d^6 c+2 a^7 d^7\right ) x^8+\frac{30}{7} a^4 c^4 \left (7 b^6 c^6+84 a b^5 d c^5+315 a^2 b^4 d^2 c^4+480 a^3 b^3 d^3 c^3+315 a^4 b^2 d^4 c^2+84 a^5 b d^5 c+7 a^6 d^6\right ) x^7+2 a^5 c^5 \left (21 b^5 c^5+175 a b^4 d c^4+450 a^2 b^3 d^2 c^3+450 a^3 b^2 d^3 c^2+175 a^4 b d^4 c+21 a^5 d^5\right ) x^6+3 a^6 c^6 \left (14 b^4 c^4+80 a b^3 d c^3+135 a^2 b^2 d^2 c^2+80 a^3 b d^3 c+14 a^4 d^4\right ) x^5+\frac{15}{2} a^7 c^7 \left (4 b^3 c^3+15 a b^2 d c^2+15 a^2 b d^2 c+4 a^3 d^3\right ) x^4+\frac{5}{3} a^8 c^8 \left (9 b^2 c^2+20 a b d c+9 a^2 d^2\right ) x^3+5 a^9 c^9 (b c+a d) x^2+a^{10} c^{10} x \]
Antiderivative was successfully verified.
[In]
Integrate[(a + b*x)^10*(c + d*x)^10,x]
[Out]
a^10*c^10*x + 5*a^9*c^9*(b*c + a*d)*x^2 + (5*a^8*c^8*(9*b^2*c^2 + 20*a*b*c*d + 9*a^2*d^2)*x^3)/3 + (15*a^7*c^7
*(4*b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 4*a^3*d^3)*x^4)/2 + 3*a^6*c^6*(14*b^4*c^4 + 80*a*b^3*c^3*d + 1
35*a^2*b^2*c^2*d^2 + 80*a^3*b*c*d^3 + 14*a^4*d^4)*x^5 + 2*a^5*c^5*(21*b^5*c^5 + 175*a*b^4*c^4*d + 450*a^2*b^3*
c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 + 21*a^5*d^5)*x^6 + (30*a^4*c^4*(7*b^6*c^6 + 84*a*b^5*c^5*d +
315*a^2*b^4*c^4*d^2 + 480*a^3*b^3*c^3*d^3 + 315*a^4*b^2*c^2*d^4 + 84*a^5*b*c*d^5 + 7*a^6*d^6)*x^7)/7 + (15*a^3
*c^3*(2*b^7*c^7 + 35*a*b^6*c^6*d + 189*a^2*b^5*c^5*d^2 + 420*a^3*b^4*c^4*d^3 + 420*a^4*b^3*c^3*d^4 + 189*a^5*b
^2*c^2*d^5 + 35*a^6*b*c*d^6 + 2*a^7*d^7)*x^8)/2 + (5*a^2*c^2*(3*b^8*c^8 + 80*a*b^7*c^7*d + 630*a^2*b^6*c^6*d^2
+ 2016*a^3*b^5*c^5*d^3 + 2940*a^4*b^4*c^4*d^4 + 2016*a^5*b^3*c^3*d^5 + 630*a^6*b^2*c^2*d^6 + 80*a^7*b*c*d^7 +
3*a^8*d^8)*x^9)/3 + a*c*(b^9*c^9 + 45*a*b^8*c^8*d + 540*a^2*b^7*c^7*d^2 + 2520*a^3*b^6*c^6*d^3 + 5292*a^4*b^5
*c^5*d^4 + 5292*a^5*b^4*c^4*d^5 + 2520*a^6*b^3*c^3*d^6 + 540*a^7*b^2*c^2*d^7 + 45*a^8*b*c*d^8 + a^9*d^9)*x^10
+ ((b^10*c^10 + 100*a*b^9*c^9*d + 2025*a^2*b^8*c^8*d^2 + 14400*a^3*b^7*c^7*d^3 + 44100*a^4*b^6*c^6*d^4 + 63504
*a^5*b^5*c^5*d^5 + 44100*a^6*b^4*c^4*d^6 + 14400*a^7*b^3*c^3*d^7 + 2025*a^8*b^2*c^2*d^8 + 100*a^9*b*c*d^9 + a^
10*d^10)*x^11)/11 + (5*b*d*(b^9*c^9 + 45*a*b^8*c^8*d + 540*a^2*b^7*c^7*d^2 + 2520*a^3*b^6*c^6*d^3 + 5292*a^4*b
^5*c^5*d^4 + 5292*a^5*b^4*c^4*d^5 + 2520*a^6*b^3*c^3*d^6 + 540*a^7*b^2*c^2*d^7 + 45*a^8*b*c*d^8 + a^9*d^9)*x^1
2)/6 + (15*b^2*d^2*(3*b^8*c^8 + 80*a*b^7*c^7*d + 630*a^2*b^6*c^6*d^2 + 2016*a^3*b^5*c^5*d^3 + 2940*a^4*b^4*c^4
*d^4 + 2016*a^5*b^3*c^3*d^5 + 630*a^6*b^2*c^2*d^6 + 80*a^7*b*c*d^7 + 3*a^8*d^8)*x^13)/13 + (30*b^3*d^3*(2*b^7*
c^7 + 35*a*b^6*c^6*d + 189*a^2*b^5*c^5*d^2 + 420*a^3*b^4*c^4*d^3 + 420*a^4*b^3*c^3*d^4 + 189*a^5*b^2*c^2*d^5 +
35*a^6*b*c*d^6 + 2*a^7*d^7)*x^14)/7 + 2*b^4*d^4*(7*b^6*c^6 + 84*a*b^5*c^5*d + 315*a^2*b^4*c^4*d^2 + 480*a^3*b
^3*c^3*d^3 + 315*a^4*b^2*c^2*d^4 + 84*a^5*b*c*d^5 + 7*a^6*d^6)*x^15 + (3*b^5*d^5*(21*b^5*c^5 + 175*a*b^4*c^4*d
+ 450*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 + 21*a^5*d^5)*x^16)/4 + (15*b^6*d^6*(14*b^4*c^4
+ 80*a*b^3*c^3*d + 135*a^2*b^2*c^2*d^2 + 80*a^3*b*c*d^3 + 14*a^4*d^4)*x^17)/17 + (5*b^7*d^7*(4*b^3*c^3 + 15*a
*b^2*c^2*d + 15*a^2*b*c*d^2 + 4*a^3*d^3)*x^18)/3 + (5*b^8*d^8*(9*b^2*c^2 + 20*a*b*c*d + 9*a^2*d^2)*x^19)/19 +
(b^9*d^9*(b*c + a*d)*x^20)/2 + (b^10*d^10*x^21)/21
________________________________________________________________________________________
Maple [B] time = 0.001, size = 1591, normalized size = 5.7 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((b*x+a)^10*(d*x+c)^10,x)
[Out]
1/21*b^10*d^10*x^21+1/20*(10*a*b^9*d^10+10*b^10*c*d^9)*x^20+1/19*(45*a^2*b^8*d^10+100*a*b^9*c*d^9+45*b^10*c^2*
d^8)*x^19+1/18*(120*a^3*b^7*d^10+450*a^2*b^8*c*d^9+450*a*b^9*c^2*d^8+120*b^10*c^3*d^7)*x^18+1/17*(210*a^4*b^6*
d^10+1200*a^3*b^7*c*d^9+2025*a^2*b^8*c^2*d^8+1200*a*b^9*c^3*d^7+210*b^10*c^4*d^6)*x^17+1/16*(252*a^5*b^5*d^10+
2100*a^4*b^6*c*d^9+5400*a^3*b^7*c^2*d^8+5400*a^2*b^8*c^3*d^7+2100*a*b^9*c^4*d^6+252*b^10*c^5*d^5)*x^16+1/15*(2
10*a^6*b^4*d^10+2520*a^5*b^5*c*d^9+9450*a^4*b^6*c^2*d^8+14400*a^3*b^7*c^3*d^7+9450*a^2*b^8*c^4*d^6+2520*a*b^9*
c^5*d^5+210*b^10*c^6*d^4)*x^15+1/14*(120*a^7*b^3*d^10+2100*a^6*b^4*c*d^9+11340*a^5*b^5*c^2*d^8+25200*a^4*b^6*c
^3*d^7+25200*a^3*b^7*c^4*d^6+11340*a^2*b^8*c^5*d^5+2100*a*b^9*c^6*d^4+120*b^10*c^7*d^3)*x^14+1/13*(45*a^8*b^2*
d^10+1200*a^7*b^3*c*d^9+9450*a^6*b^4*c^2*d^8+30240*a^5*b^5*c^3*d^7+44100*a^4*b^6*c^4*d^6+30240*a^3*b^7*c^5*d^5
+9450*a^2*b^8*c^6*d^4+1200*a*b^9*c^7*d^3+45*b^10*c^8*d^2)*x^13+1/12*(10*a^9*b*d^10+450*a^8*b^2*c*d^9+5400*a^7*
b^3*c^2*d^8+25200*a^6*b^4*c^3*d^7+52920*a^5*b^5*c^4*d^6+52920*a^4*b^6*c^5*d^5+25200*a^3*b^7*c^6*d^4+5400*a^2*b
^8*c^7*d^3+450*a*b^9*c^8*d^2+10*b^10*c^9*d)*x^12+1/11*(a^10*d^10+100*a^9*b*c*d^9+2025*a^8*b^2*c^2*d^8+14400*a^
7*b^3*c^3*d^7+44100*a^6*b^4*c^4*d^6+63504*a^5*b^5*c^5*d^5+44100*a^4*b^6*c^6*d^4+14400*a^3*b^7*c^7*d^3+2025*a^2
*b^8*c^8*d^2+100*a*b^9*c^9*d+b^10*c^10)*x^11+1/10*(10*a^10*c*d^9+450*a^9*b*c^2*d^8+5400*a^8*b^2*c^3*d^7+25200*
a^7*b^3*c^4*d^6+52920*a^6*b^4*c^5*d^5+52920*a^5*b^5*c^6*d^4+25200*a^4*b^6*c^7*d^3+5400*a^3*b^7*c^8*d^2+450*a^2
*b^8*c^9*d+10*a*b^9*c^10)*x^10+1/9*(45*a^10*c^2*d^8+1200*a^9*b*c^3*d^7+9450*a^8*b^2*c^4*d^6+30240*a^7*b^3*c^5*
d^5+44100*a^6*b^4*c^6*d^4+30240*a^5*b^5*c^7*d^3+9450*a^4*b^6*c^8*d^2+1200*a^3*b^7*c^9*d+45*a^2*b^8*c^10)*x^9+1
/8*(120*a^10*c^3*d^7+2100*a^9*b*c^4*d^6+11340*a^8*b^2*c^5*d^5+25200*a^7*b^3*c^6*d^4+25200*a^6*b^4*c^7*d^3+1134
0*a^5*b^5*c^8*d^2+2100*a^4*b^6*c^9*d+120*a^3*b^7*c^10)*x^8+1/7*(210*a^10*c^4*d^6+2520*a^9*b*c^5*d^5+9450*a^8*b
^2*c^6*d^4+14400*a^7*b^3*c^7*d^3+9450*a^6*b^4*c^8*d^2+2520*a^5*b^5*c^9*d+210*a^4*b^6*c^10)*x^7+1/6*(252*a^10*c
^5*d^5+2100*a^9*b*c^6*d^4+5400*a^8*b^2*c^7*d^3+5400*a^7*b^3*c^8*d^2+2100*a^6*b^4*c^9*d+252*a^5*b^5*c^10)*x^6+1
/5*(210*a^10*c^6*d^4+1200*a^9*b*c^7*d^3+2025*a^8*b^2*c^8*d^2+1200*a^7*b^3*c^9*d+210*a^6*b^4*c^10)*x^5+1/4*(120
*a^10*c^7*d^3+450*a^9*b*c^8*d^2+450*a^8*b^2*c^9*d+120*a^7*b^3*c^10)*x^4+1/3*(45*a^10*c^8*d^2+100*a^9*b*c^9*d+4
5*a^8*b^2*c^10)*x^3+1/2*(10*a^10*c^9*d+10*a^9*b*c^10)*x^2+a^10*c^10*x
________________________________________________________________________________________
Maxima [B] time = 1.01421, size = 2134, normalized size = 7.65 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^10*(d*x+c)^10,x, algorithm="maxima")
[Out]
1/21*b^10*d^10*x^21 + a^10*c^10*x + 1/2*(b^10*c*d^9 + a*b^9*d^10)*x^20 + 5/19*(9*b^10*c^2*d^8 + 20*a*b^9*c*d^9
+ 9*a^2*b^8*d^10)*x^19 + 5/3*(4*b^10*c^3*d^7 + 15*a*b^9*c^2*d^8 + 15*a^2*b^8*c*d^9 + 4*a^3*b^7*d^10)*x^18 + 1
5/17*(14*b^10*c^4*d^6 + 80*a*b^9*c^3*d^7 + 135*a^2*b^8*c^2*d^8 + 80*a^3*b^7*c*d^9 + 14*a^4*b^6*d^10)*x^17 + 3/
4*(21*b^10*c^5*d^5 + 175*a*b^9*c^4*d^6 + 450*a^2*b^8*c^3*d^7 + 450*a^3*b^7*c^2*d^8 + 175*a^4*b^6*c*d^9 + 21*a^
5*b^5*d^10)*x^16 + 2*(7*b^10*c^6*d^4 + 84*a*b^9*c^5*d^5 + 315*a^2*b^8*c^4*d^6 + 480*a^3*b^7*c^3*d^7 + 315*a^4*
b^6*c^2*d^8 + 84*a^5*b^5*c*d^9 + 7*a^6*b^4*d^10)*x^15 + 30/7*(2*b^10*c^7*d^3 + 35*a*b^9*c^6*d^4 + 189*a^2*b^8*
c^5*d^5 + 420*a^3*b^7*c^4*d^6 + 420*a^4*b^6*c^3*d^7 + 189*a^5*b^5*c^2*d^8 + 35*a^6*b^4*c*d^9 + 2*a^7*b^3*d^10)
*x^14 + 15/13*(3*b^10*c^8*d^2 + 80*a*b^9*c^7*d^3 + 630*a^2*b^8*c^6*d^4 + 2016*a^3*b^7*c^5*d^5 + 2940*a^4*b^6*c
^4*d^6 + 2016*a^5*b^5*c^3*d^7 + 630*a^6*b^4*c^2*d^8 + 80*a^7*b^3*c*d^9 + 3*a^8*b^2*d^10)*x^13 + 5/6*(b^10*c^9*
d + 45*a*b^9*c^8*d^2 + 540*a^2*b^8*c^7*d^3 + 2520*a^3*b^7*c^6*d^4 + 5292*a^4*b^6*c^5*d^5 + 5292*a^5*b^5*c^4*d^
6 + 2520*a^6*b^4*c^3*d^7 + 540*a^7*b^3*c^2*d^8 + 45*a^8*b^2*c*d^9 + a^9*b*d^10)*x^12 + 1/11*(b^10*c^10 + 100*a
*b^9*c^9*d + 2025*a^2*b^8*c^8*d^2 + 14400*a^3*b^7*c^7*d^3 + 44100*a^4*b^6*c^6*d^4 + 63504*a^5*b^5*c^5*d^5 + 44
100*a^6*b^4*c^4*d^6 + 14400*a^7*b^3*c^3*d^7 + 2025*a^8*b^2*c^2*d^8 + 100*a^9*b*c*d^9 + a^10*d^10)*x^11 + (a*b^
9*c^10 + 45*a^2*b^8*c^9*d + 540*a^3*b^7*c^8*d^2 + 2520*a^4*b^6*c^7*d^3 + 5292*a^5*b^5*c^6*d^4 + 5292*a^6*b^4*c
^5*d^5 + 2520*a^7*b^3*c^4*d^6 + 540*a^8*b^2*c^3*d^7 + 45*a^9*b*c^2*d^8 + a^10*c*d^9)*x^10 + 5/3*(3*a^2*b^8*c^1
0 + 80*a^3*b^7*c^9*d + 630*a^4*b^6*c^8*d^2 + 2016*a^5*b^5*c^7*d^3 + 2940*a^6*b^4*c^6*d^4 + 2016*a^7*b^3*c^5*d^
5 + 630*a^8*b^2*c^4*d^6 + 80*a^9*b*c^3*d^7 + 3*a^10*c^2*d^8)*x^9 + 15/2*(2*a^3*b^7*c^10 + 35*a^4*b^6*c^9*d + 1
89*a^5*b^5*c^8*d^2 + 420*a^6*b^4*c^7*d^3 + 420*a^7*b^3*c^6*d^4 + 189*a^8*b^2*c^5*d^5 + 35*a^9*b*c^4*d^6 + 2*a^
10*c^3*d^7)*x^8 + 30/7*(7*a^4*b^6*c^10 + 84*a^5*b^5*c^9*d + 315*a^6*b^4*c^8*d^2 + 480*a^7*b^3*c^7*d^3 + 315*a^
8*b^2*c^6*d^4 + 84*a^9*b*c^5*d^5 + 7*a^10*c^4*d^6)*x^7 + 2*(21*a^5*b^5*c^10 + 175*a^6*b^4*c^9*d + 450*a^7*b^3*
c^8*d^2 + 450*a^8*b^2*c^7*d^3 + 175*a^9*b*c^6*d^4 + 21*a^10*c^5*d^5)*x^6 + 3*(14*a^6*b^4*c^10 + 80*a^7*b^3*c^9
*d + 135*a^8*b^2*c^8*d^2 + 80*a^9*b*c^7*d^3 + 14*a^10*c^6*d^4)*x^5 + 15/2*(4*a^7*b^3*c^10 + 15*a^8*b^2*c^9*d +
15*a^9*b*c^8*d^2 + 4*a^10*c^7*d^3)*x^4 + 5/3*(9*a^8*b^2*c^10 + 20*a^9*b*c^9*d + 9*a^10*c^8*d^2)*x^3 + 5*(a^9*
b*c^10 + a^10*c^9*d)*x^2
________________________________________________________________________________________
Fricas [B] time = 1.57117, size = 4215, normalized size = 15.11 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^10*(d*x+c)^10,x, algorithm="fricas")
[Out]
1/21*x^21*d^10*b^10 + 1/2*x^20*d^9*c*b^10 + 1/2*x^20*d^10*b^9*a + 45/19*x^19*d^8*c^2*b^10 + 100/19*x^19*d^9*c*
b^9*a + 45/19*x^19*d^10*b^8*a^2 + 20/3*x^18*d^7*c^3*b^10 + 25*x^18*d^8*c^2*b^9*a + 25*x^18*d^9*c*b^8*a^2 + 20/
3*x^18*d^10*b^7*a^3 + 210/17*x^17*d^6*c^4*b^10 + 1200/17*x^17*d^7*c^3*b^9*a + 2025/17*x^17*d^8*c^2*b^8*a^2 + 1
200/17*x^17*d^9*c*b^7*a^3 + 210/17*x^17*d^10*b^6*a^4 + 63/4*x^16*d^5*c^5*b^10 + 525/4*x^16*d^6*c^4*b^9*a + 675
/2*x^16*d^7*c^3*b^8*a^2 + 675/2*x^16*d^8*c^2*b^7*a^3 + 525/4*x^16*d^9*c*b^6*a^4 + 63/4*x^16*d^10*b^5*a^5 + 14*
x^15*d^4*c^6*b^10 + 168*x^15*d^5*c^5*b^9*a + 630*x^15*d^6*c^4*b^8*a^2 + 960*x^15*d^7*c^3*b^7*a^3 + 630*x^15*d^
8*c^2*b^6*a^4 + 168*x^15*d^9*c*b^5*a^5 + 14*x^15*d^10*b^4*a^6 + 60/7*x^14*d^3*c^7*b^10 + 150*x^14*d^4*c^6*b^9*
a + 810*x^14*d^5*c^5*b^8*a^2 + 1800*x^14*d^6*c^4*b^7*a^3 + 1800*x^14*d^7*c^3*b^6*a^4 + 810*x^14*d^8*c^2*b^5*a^
5 + 150*x^14*d^9*c*b^4*a^6 + 60/7*x^14*d^10*b^3*a^7 + 45/13*x^13*d^2*c^8*b^10 + 1200/13*x^13*d^3*c^7*b^9*a + 9
450/13*x^13*d^4*c^6*b^8*a^2 + 30240/13*x^13*d^5*c^5*b^7*a^3 + 44100/13*x^13*d^6*c^4*b^6*a^4 + 30240/13*x^13*d^
7*c^3*b^5*a^5 + 9450/13*x^13*d^8*c^2*b^4*a^6 + 1200/13*x^13*d^9*c*b^3*a^7 + 45/13*x^13*d^10*b^2*a^8 + 5/6*x^12
*d*c^9*b^10 + 75/2*x^12*d^2*c^8*b^9*a + 450*x^12*d^3*c^7*b^8*a^2 + 2100*x^12*d^4*c^6*b^7*a^3 + 4410*x^12*d^5*c
^5*b^6*a^4 + 4410*x^12*d^6*c^4*b^5*a^5 + 2100*x^12*d^7*c^3*b^4*a^6 + 450*x^12*d^8*c^2*b^3*a^7 + 75/2*x^12*d^9*
c*b^2*a^8 + 5/6*x^12*d^10*b*a^9 + 1/11*x^11*c^10*b^10 + 100/11*x^11*d*c^9*b^9*a + 2025/11*x^11*d^2*c^8*b^8*a^2
+ 14400/11*x^11*d^3*c^7*b^7*a^3 + 44100/11*x^11*d^4*c^6*b^6*a^4 + 63504/11*x^11*d^5*c^5*b^5*a^5 + 44100/11*x^
11*d^6*c^4*b^4*a^6 + 14400/11*x^11*d^7*c^3*b^3*a^7 + 2025/11*x^11*d^8*c^2*b^2*a^8 + 100/11*x^11*d^9*c*b*a^9 +
1/11*x^11*d^10*a^10 + x^10*c^10*b^9*a + 45*x^10*d*c^9*b^8*a^2 + 540*x^10*d^2*c^8*b^7*a^3 + 2520*x^10*d^3*c^7*b
^6*a^4 + 5292*x^10*d^4*c^6*b^5*a^5 + 5292*x^10*d^5*c^5*b^4*a^6 + 2520*x^10*d^6*c^4*b^3*a^7 + 540*x^10*d^7*c^3*
b^2*a^8 + 45*x^10*d^8*c^2*b*a^9 + x^10*d^9*c*a^10 + 5*x^9*c^10*b^8*a^2 + 400/3*x^9*d*c^9*b^7*a^3 + 1050*x^9*d^
2*c^8*b^6*a^4 + 3360*x^9*d^3*c^7*b^5*a^5 + 4900*x^9*d^4*c^6*b^4*a^6 + 3360*x^9*d^5*c^5*b^3*a^7 + 1050*x^9*d^6*
c^4*b^2*a^8 + 400/3*x^9*d^7*c^3*b*a^9 + 5*x^9*d^8*c^2*a^10 + 15*x^8*c^10*b^7*a^3 + 525/2*x^8*d*c^9*b^6*a^4 + 2
835/2*x^8*d^2*c^8*b^5*a^5 + 3150*x^8*d^3*c^7*b^4*a^6 + 3150*x^8*d^4*c^6*b^3*a^7 + 2835/2*x^8*d^5*c^5*b^2*a^8 +
525/2*x^8*d^6*c^4*b*a^9 + 15*x^8*d^7*c^3*a^10 + 30*x^7*c^10*b^6*a^4 + 360*x^7*d*c^9*b^5*a^5 + 1350*x^7*d^2*c^
8*b^4*a^6 + 14400/7*x^7*d^3*c^7*b^3*a^7 + 1350*x^7*d^4*c^6*b^2*a^8 + 360*x^7*d^5*c^5*b*a^9 + 30*x^7*d^6*c^4*a^
10 + 42*x^6*c^10*b^5*a^5 + 350*x^6*d*c^9*b^4*a^6 + 900*x^6*d^2*c^8*b^3*a^7 + 900*x^6*d^3*c^7*b^2*a^8 + 350*x^6
*d^4*c^6*b*a^9 + 42*x^6*d^5*c^5*a^10 + 42*x^5*c^10*b^4*a^6 + 240*x^5*d*c^9*b^3*a^7 + 405*x^5*d^2*c^8*b^2*a^8 +
240*x^5*d^3*c^7*b*a^9 + 42*x^5*d^4*c^6*a^10 + 30*x^4*c^10*b^3*a^7 + 225/2*x^4*d*c^9*b^2*a^8 + 225/2*x^4*d^2*c
^8*b*a^9 + 30*x^4*d^3*c^7*a^10 + 15*x^3*c^10*b^2*a^8 + 100/3*x^3*d*c^9*b*a^9 + 15*x^3*d^2*c^8*a^10 + 5*x^2*c^1
0*b*a^9 + 5*x^2*d*c^9*a^10 + x*c^10*a^10
________________________________________________________________________________________
Sympy [B] time = 0.256867, size = 1775, normalized size = 6.36 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)**10*(d*x+c)**10,x)
[Out]
a**10*c**10*x + b**10*d**10*x**21/21 + x**20*(a*b**9*d**10/2 + b**10*c*d**9/2) + x**19*(45*a**2*b**8*d**10/19
+ 100*a*b**9*c*d**9/19 + 45*b**10*c**2*d**8/19) + x**18*(20*a**3*b**7*d**10/3 + 25*a**2*b**8*c*d**9 + 25*a*b**
9*c**2*d**8 + 20*b**10*c**3*d**7/3) + x**17*(210*a**4*b**6*d**10/17 + 1200*a**3*b**7*c*d**9/17 + 2025*a**2*b**
8*c**2*d**8/17 + 1200*a*b**9*c**3*d**7/17 + 210*b**10*c**4*d**6/17) + x**16*(63*a**5*b**5*d**10/4 + 525*a**4*b
**6*c*d**9/4 + 675*a**3*b**7*c**2*d**8/2 + 675*a**2*b**8*c**3*d**7/2 + 525*a*b**9*c**4*d**6/4 + 63*b**10*c**5*
d**5/4) + x**15*(14*a**6*b**4*d**10 + 168*a**5*b**5*c*d**9 + 630*a**4*b**6*c**2*d**8 + 960*a**3*b**7*c**3*d**7
+ 630*a**2*b**8*c**4*d**6 + 168*a*b**9*c**5*d**5 + 14*b**10*c**6*d**4) + x**14*(60*a**7*b**3*d**10/7 + 150*a*
*6*b**4*c*d**9 + 810*a**5*b**5*c**2*d**8 + 1800*a**4*b**6*c**3*d**7 + 1800*a**3*b**7*c**4*d**6 + 810*a**2*b**8
*c**5*d**5 + 150*a*b**9*c**6*d**4 + 60*b**10*c**7*d**3/7) + x**13*(45*a**8*b**2*d**10/13 + 1200*a**7*b**3*c*d*
*9/13 + 9450*a**6*b**4*c**2*d**8/13 + 30240*a**5*b**5*c**3*d**7/13 + 44100*a**4*b**6*c**4*d**6/13 + 30240*a**3
*b**7*c**5*d**5/13 + 9450*a**2*b**8*c**6*d**4/13 + 1200*a*b**9*c**7*d**3/13 + 45*b**10*c**8*d**2/13) + x**12*(
5*a**9*b*d**10/6 + 75*a**8*b**2*c*d**9/2 + 450*a**7*b**3*c**2*d**8 + 2100*a**6*b**4*c**3*d**7 + 4410*a**5*b**5
*c**4*d**6 + 4410*a**4*b**6*c**5*d**5 + 2100*a**3*b**7*c**6*d**4 + 450*a**2*b**8*c**7*d**3 + 75*a*b**9*c**8*d*
*2/2 + 5*b**10*c**9*d/6) + x**11*(a**10*d**10/11 + 100*a**9*b*c*d**9/11 + 2025*a**8*b**2*c**2*d**8/11 + 14400*
a**7*b**3*c**3*d**7/11 + 44100*a**6*b**4*c**4*d**6/11 + 63504*a**5*b**5*c**5*d**5/11 + 44100*a**4*b**6*c**6*d*
*4/11 + 14400*a**3*b**7*c**7*d**3/11 + 2025*a**2*b**8*c**8*d**2/11 + 100*a*b**9*c**9*d/11 + b**10*c**10/11) +
x**10*(a**10*c*d**9 + 45*a**9*b*c**2*d**8 + 540*a**8*b**2*c**3*d**7 + 2520*a**7*b**3*c**4*d**6 + 5292*a**6*b**
4*c**5*d**5 + 5292*a**5*b**5*c**6*d**4 + 2520*a**4*b**6*c**7*d**3 + 540*a**3*b**7*c**8*d**2 + 45*a**2*b**8*c**
9*d + a*b**9*c**10) + x**9*(5*a**10*c**2*d**8 + 400*a**9*b*c**3*d**7/3 + 1050*a**8*b**2*c**4*d**6 + 3360*a**7*
b**3*c**5*d**5 + 4900*a**6*b**4*c**6*d**4 + 3360*a**5*b**5*c**7*d**3 + 1050*a**4*b**6*c**8*d**2 + 400*a**3*b**
7*c**9*d/3 + 5*a**2*b**8*c**10) + x**8*(15*a**10*c**3*d**7 + 525*a**9*b*c**4*d**6/2 + 2835*a**8*b**2*c**5*d**5
/2 + 3150*a**7*b**3*c**6*d**4 + 3150*a**6*b**4*c**7*d**3 + 2835*a**5*b**5*c**8*d**2/2 + 525*a**4*b**6*c**9*d/2
+ 15*a**3*b**7*c**10) + x**7*(30*a**10*c**4*d**6 + 360*a**9*b*c**5*d**5 + 1350*a**8*b**2*c**6*d**4 + 14400*a*
*7*b**3*c**7*d**3/7 + 1350*a**6*b**4*c**8*d**2 + 360*a**5*b**5*c**9*d + 30*a**4*b**6*c**10) + x**6*(42*a**10*c
**5*d**5 + 350*a**9*b*c**6*d**4 + 900*a**8*b**2*c**7*d**3 + 900*a**7*b**3*c**8*d**2 + 350*a**6*b**4*c**9*d + 4
2*a**5*b**5*c**10) + x**5*(42*a**10*c**6*d**4 + 240*a**9*b*c**7*d**3 + 405*a**8*b**2*c**8*d**2 + 240*a**7*b**3
*c**9*d + 42*a**6*b**4*c**10) + x**4*(30*a**10*c**7*d**3 + 225*a**9*b*c**8*d**2/2 + 225*a**8*b**2*c**9*d/2 + 3
0*a**7*b**3*c**10) + x**3*(15*a**10*c**8*d**2 + 100*a**9*b*c**9*d/3 + 15*a**8*b**2*c**10) + x**2*(5*a**10*c**9
*d + 5*a**9*b*c**10)
________________________________________________________________________________________
Giac [B] time = 1.06944, size = 2475, normalized size = 8.87 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^10*(d*x+c)^10,x, algorithm="giac")
[Out]
1/21*b^10*d^10*x^21 + 1/2*b^10*c*d^9*x^20 + 1/2*a*b^9*d^10*x^20 + 45/19*b^10*c^2*d^8*x^19 + 100/19*a*b^9*c*d^9
*x^19 + 45/19*a^2*b^8*d^10*x^19 + 20/3*b^10*c^3*d^7*x^18 + 25*a*b^9*c^2*d^8*x^18 + 25*a^2*b^8*c*d^9*x^18 + 20/
3*a^3*b^7*d^10*x^18 + 210/17*b^10*c^4*d^6*x^17 + 1200/17*a*b^9*c^3*d^7*x^17 + 2025/17*a^2*b^8*c^2*d^8*x^17 + 1
200/17*a^3*b^7*c*d^9*x^17 + 210/17*a^4*b^6*d^10*x^17 + 63/4*b^10*c^5*d^5*x^16 + 525/4*a*b^9*c^4*d^6*x^16 + 675
/2*a^2*b^8*c^3*d^7*x^16 + 675/2*a^3*b^7*c^2*d^8*x^16 + 525/4*a^4*b^6*c*d^9*x^16 + 63/4*a^5*b^5*d^10*x^16 + 14*
b^10*c^6*d^4*x^15 + 168*a*b^9*c^5*d^5*x^15 + 630*a^2*b^8*c^4*d^6*x^15 + 960*a^3*b^7*c^3*d^7*x^15 + 630*a^4*b^6
*c^2*d^8*x^15 + 168*a^5*b^5*c*d^9*x^15 + 14*a^6*b^4*d^10*x^15 + 60/7*b^10*c^7*d^3*x^14 + 150*a*b^9*c^6*d^4*x^1
4 + 810*a^2*b^8*c^5*d^5*x^14 + 1800*a^3*b^7*c^4*d^6*x^14 + 1800*a^4*b^6*c^3*d^7*x^14 + 810*a^5*b^5*c^2*d^8*x^1
4 + 150*a^6*b^4*c*d^9*x^14 + 60/7*a^7*b^3*d^10*x^14 + 45/13*b^10*c^8*d^2*x^13 + 1200/13*a*b^9*c^7*d^3*x^13 + 9
450/13*a^2*b^8*c^6*d^4*x^13 + 30240/13*a^3*b^7*c^5*d^5*x^13 + 44100/13*a^4*b^6*c^4*d^6*x^13 + 30240/13*a^5*b^5
*c^3*d^7*x^13 + 9450/13*a^6*b^4*c^2*d^8*x^13 + 1200/13*a^7*b^3*c*d^9*x^13 + 45/13*a^8*b^2*d^10*x^13 + 5/6*b^10
*c^9*d*x^12 + 75/2*a*b^9*c^8*d^2*x^12 + 450*a^2*b^8*c^7*d^3*x^12 + 2100*a^3*b^7*c^6*d^4*x^12 + 4410*a^4*b^6*c^
5*d^5*x^12 + 4410*a^5*b^5*c^4*d^6*x^12 + 2100*a^6*b^4*c^3*d^7*x^12 + 450*a^7*b^3*c^2*d^8*x^12 + 75/2*a^8*b^2*c
*d^9*x^12 + 5/6*a^9*b*d^10*x^12 + 1/11*b^10*c^10*x^11 + 100/11*a*b^9*c^9*d*x^11 + 2025/11*a^2*b^8*c^8*d^2*x^11
+ 14400/11*a^3*b^7*c^7*d^3*x^11 + 44100/11*a^4*b^6*c^6*d^4*x^11 + 63504/11*a^5*b^5*c^5*d^5*x^11 + 44100/11*a^
6*b^4*c^4*d^6*x^11 + 14400/11*a^7*b^3*c^3*d^7*x^11 + 2025/11*a^8*b^2*c^2*d^8*x^11 + 100/11*a^9*b*c*d^9*x^11 +
1/11*a^10*d^10*x^11 + a*b^9*c^10*x^10 + 45*a^2*b^8*c^9*d*x^10 + 540*a^3*b^7*c^8*d^2*x^10 + 2520*a^4*b^6*c^7*d^
3*x^10 + 5292*a^5*b^5*c^6*d^4*x^10 + 5292*a^6*b^4*c^5*d^5*x^10 + 2520*a^7*b^3*c^4*d^6*x^10 + 540*a^8*b^2*c^3*d
^7*x^10 + 45*a^9*b*c^2*d^8*x^10 + a^10*c*d^9*x^10 + 5*a^2*b^8*c^10*x^9 + 400/3*a^3*b^7*c^9*d*x^9 + 1050*a^4*b^
6*c^8*d^2*x^9 + 3360*a^5*b^5*c^7*d^3*x^9 + 4900*a^6*b^4*c^6*d^4*x^9 + 3360*a^7*b^3*c^5*d^5*x^9 + 1050*a^8*b^2*
c^4*d^6*x^9 + 400/3*a^9*b*c^3*d^7*x^9 + 5*a^10*c^2*d^8*x^9 + 15*a^3*b^7*c^10*x^8 + 525/2*a^4*b^6*c^9*d*x^8 + 2
835/2*a^5*b^5*c^8*d^2*x^8 + 3150*a^6*b^4*c^7*d^3*x^8 + 3150*a^7*b^3*c^6*d^4*x^8 + 2835/2*a^8*b^2*c^5*d^5*x^8 +
525/2*a^9*b*c^4*d^6*x^8 + 15*a^10*c^3*d^7*x^8 + 30*a^4*b^6*c^10*x^7 + 360*a^5*b^5*c^9*d*x^7 + 1350*a^6*b^4*c^
8*d^2*x^7 + 14400/7*a^7*b^3*c^7*d^3*x^7 + 1350*a^8*b^2*c^6*d^4*x^7 + 360*a^9*b*c^5*d^5*x^7 + 30*a^10*c^4*d^6*x
^7 + 42*a^5*b^5*c^10*x^6 + 350*a^6*b^4*c^9*d*x^6 + 900*a^7*b^3*c^8*d^2*x^6 + 900*a^8*b^2*c^7*d^3*x^6 + 350*a^9
*b*c^6*d^4*x^6 + 42*a^10*c^5*d^5*x^6 + 42*a^6*b^4*c^10*x^5 + 240*a^7*b^3*c^9*d*x^5 + 405*a^8*b^2*c^8*d^2*x^5 +
240*a^9*b*c^7*d^3*x^5 + 42*a^10*c^6*d^4*x^5 + 30*a^7*b^3*c^10*x^4 + 225/2*a^8*b^2*c^9*d*x^4 + 225/2*a^9*b*c^8
*d^2*x^4 + 30*a^10*c^7*d^3*x^4 + 15*a^8*b^2*c^10*x^3 + 100/3*a^9*b*c^9*d*x^3 + 15*a^10*c^8*d^2*x^3 + 5*a^9*b*c
^10*x^2 + 5*a^10*c^9*d*x^2 + a^10*c^10*x