3.13.19 \(\int \frac {(c+d x)^{10}}{(a+b x)^{14}} \, dx\)

Optimal. Leaf size=89 \[ -\frac {d^2 (c+d x)^{11}}{858 (a+b x)^{11} (b c-a d)^3}+\frac {d (c+d x)^{11}}{78 (a+b x)^{12} (b c-a d)^2}-\frac {(c+d x)^{11}}{13 (a+b x)^{13} (b c-a d)} \]

________________________________________________________________________________________

Rubi [A]  time = 0.02, antiderivative size = 89, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {45, 37} \begin {gather*} -\frac {d^2 (c+d x)^{11}}{858 (a+b x)^{11} (b c-a d)^3}+\frac {d (c+d x)^{11}}{78 (a+b x)^{12} (b c-a d)^2}-\frac {(c+d x)^{11}}{13 (a+b x)^{13} (b c-a d)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(c + d*x)^10/(a + b*x)^14,x]

[Out]

-(c + d*x)^11/(13*(b*c - a*d)*(a + b*x)^13) + (d*(c + d*x)^11)/(78*(b*c - a*d)^2*(a + b*x)^12) - (d^2*(c + d*x
)^11)/(858*(b*c - a*d)^3*(a + b*x)^11)

Rule 37

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n +
1))/((b*c - a*d)*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[m + n + 2, 0] && NeQ
[m, -1]

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n + 1
))/((b*c - a*d)*(m + 1)), x] - Dist[(d*Simplify[m + n + 2])/((b*c - a*d)*(m + 1)), Int[(a + b*x)^Simplify[m +
1]*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && ILtQ[Simplify[m + n + 2], 0] &&
NeQ[m, -1] &&  !(LtQ[m, -1] && LtQ[n, -1] && (EqQ[a, 0] || (NeQ[c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && (
SumSimplerQ[m, 1] ||  !SumSimplerQ[n, 1])

Rubi steps

\begin {align*} \int \frac {(c+d x)^{10}}{(a+b x)^{14}} \, dx &=-\frac {(c+d x)^{11}}{13 (b c-a d) (a+b x)^{13}}-\frac {(2 d) \int \frac {(c+d x)^{10}}{(a+b x)^{13}} \, dx}{13 (b c-a d)}\\ &=-\frac {(c+d x)^{11}}{13 (b c-a d) (a+b x)^{13}}+\frac {d (c+d x)^{11}}{78 (b c-a d)^2 (a+b x)^{12}}+\frac {d^2 \int \frac {(c+d x)^{10}}{(a+b x)^{12}} \, dx}{78 (b c-a d)^2}\\ &=-\frac {(c+d x)^{11}}{13 (b c-a d) (a+b x)^{13}}+\frac {d (c+d x)^{11}}{78 (b c-a d)^2 (a+b x)^{12}}-\frac {d^2 (c+d x)^{11}}{858 (b c-a d)^3 (a+b x)^{11}}\\ \end {align*}

________________________________________________________________________________________

Mathematica [B]  time = 0.29, size = 690, normalized size = 7.75 \begin {gather*} -\frac {a^{10} d^{10}+a^9 b d^9 (3 c+13 d x)+3 a^8 b^2 d^8 \left (2 c^2+13 c d x+26 d^2 x^2\right )+2 a^7 b^3 d^7 \left (5 c^3+39 c^2 d x+117 c d^2 x^2+143 d^3 x^3\right )+a^6 b^4 d^6 \left (15 c^4+130 c^3 d x+468 c^2 d^2 x^2+858 c d^3 x^3+715 d^4 x^4\right )+3 a^5 b^5 d^5 \left (7 c^5+65 c^4 d x+260 c^3 d^2 x^2+572 c^2 d^3 x^3+715 c d^4 x^4+429 d^5 x^5\right )+a^4 b^6 d^4 \left (28 c^6+273 c^5 d x+1170 c^4 d^2 x^2+2860 c^3 d^3 x^3+4290 c^2 d^4 x^4+3861 c d^5 x^5+1716 d^6 x^6\right )+2 a^3 b^7 d^3 \left (18 c^7+182 c^6 d x+819 c^5 d^2 x^2+2145 c^4 d^3 x^3+3575 c^3 d^4 x^4+3861 c^2 d^5 x^5+2574 c d^6 x^6+858 d^7 x^7\right )+3 a^2 b^8 d^2 \left (15 c^8+156 c^7 d x+728 c^6 d^2 x^2+2002 c^5 d^3 x^3+3575 c^4 d^4 x^4+4290 c^3 d^5 x^5+3432 c^2 d^6 x^6+1716 c d^7 x^7+429 d^8 x^8\right )+a b^9 d \left (55 c^9+585 c^8 d x+2808 c^7 d^2 x^2+8008 c^6 d^3 x^3+15015 c^5 d^4 x^4+19305 c^4 d^5 x^5+17160 c^3 d^6 x^6+10296 c^2 d^7 x^7+3861 c d^8 x^8+715 d^9 x^9\right )+b^{10} \left (66 c^{10}+715 c^9 d x+3510 c^8 d^2 x^2+10296 c^7 d^3 x^3+20020 c^6 d^4 x^4+27027 c^5 d^5 x^5+25740 c^4 d^6 x^6+17160 c^3 d^7 x^7+7722 c^2 d^8 x^8+2145 c d^9 x^9+286 d^{10} x^{10}\right )}{858 b^{11} (a+b x)^{13}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(c + d*x)^10/(a + b*x)^14,x]

[Out]

-1/858*(a^10*d^10 + a^9*b*d^9*(3*c + 13*d*x) + 3*a^8*b^2*d^8*(2*c^2 + 13*c*d*x + 26*d^2*x^2) + 2*a^7*b^3*d^7*(
5*c^3 + 39*c^2*d*x + 117*c*d^2*x^2 + 143*d^3*x^3) + a^6*b^4*d^6*(15*c^4 + 130*c^3*d*x + 468*c^2*d^2*x^2 + 858*
c*d^3*x^3 + 715*d^4*x^4) + 3*a^5*b^5*d^5*(7*c^5 + 65*c^4*d*x + 260*c^3*d^2*x^2 + 572*c^2*d^3*x^3 + 715*c*d^4*x
^4 + 429*d^5*x^5) + a^4*b^6*d^4*(28*c^6 + 273*c^5*d*x + 1170*c^4*d^2*x^2 + 2860*c^3*d^3*x^3 + 4290*c^2*d^4*x^4
+ 3861*c*d^5*x^5 + 1716*d^6*x^6) + 2*a^3*b^7*d^3*(18*c^7 + 182*c^6*d*x + 819*c^5*d^2*x^2 + 2145*c^4*d^3*x^3 +
3575*c^3*d^4*x^4 + 3861*c^2*d^5*x^5 + 2574*c*d^6*x^6 + 858*d^7*x^7) + 3*a^2*b^8*d^2*(15*c^8 + 156*c^7*d*x + 7
28*c^6*d^2*x^2 + 2002*c^5*d^3*x^3 + 3575*c^4*d^4*x^4 + 4290*c^3*d^5*x^5 + 3432*c^2*d^6*x^6 + 1716*c*d^7*x^7 +
429*d^8*x^8) + a*b^9*d*(55*c^9 + 585*c^8*d*x + 2808*c^7*d^2*x^2 + 8008*c^6*d^3*x^3 + 15015*c^5*d^4*x^4 + 19305
*c^4*d^5*x^5 + 17160*c^3*d^6*x^6 + 10296*c^2*d^7*x^7 + 3861*c*d^8*x^8 + 715*d^9*x^9) + b^10*(66*c^10 + 715*c^9
*d*x + 3510*c^8*d^2*x^2 + 10296*c^7*d^3*x^3 + 20020*c^6*d^4*x^4 + 27027*c^5*d^5*x^5 + 25740*c^4*d^6*x^6 + 1716
0*c^3*d^7*x^7 + 7722*c^2*d^8*x^8 + 2145*c*d^9*x^9 + 286*d^10*x^10))/(b^11*(a + b*x)^13)

________________________________________________________________________________________

IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(c+d x)^{10}}{(a+b x)^{14}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^14,x]

[Out]

IntegrateAlgebraic[(c + d*x)^10/(a + b*x)^14, x]

________________________________________________________________________________________

fricas [B]  time = 1.26, size = 997, normalized size = 11.20 \begin {gather*} -\frac {286 \, b^{10} d^{10} x^{10} + 66 \, b^{10} c^{10} + 55 \, a b^{9} c^{9} d + 45 \, a^{2} b^{8} c^{8} d^{2} + 36 \, a^{3} b^{7} c^{7} d^{3} + 28 \, a^{4} b^{6} c^{6} d^{4} + 21 \, a^{5} b^{5} c^{5} d^{5} + 15 \, a^{6} b^{4} c^{4} d^{6} + 10 \, a^{7} b^{3} c^{3} d^{7} + 6 \, a^{8} b^{2} c^{2} d^{8} + 3 \, a^{9} b c d^{9} + a^{10} d^{10} + 715 \, {\left (3 \, b^{10} c d^{9} + a b^{9} d^{10}\right )} x^{9} + 1287 \, {\left (6 \, b^{10} c^{2} d^{8} + 3 \, a b^{9} c d^{9} + a^{2} b^{8} d^{10}\right )} x^{8} + 1716 \, {\left (10 \, b^{10} c^{3} d^{7} + 6 \, a b^{9} c^{2} d^{8} + 3 \, a^{2} b^{8} c d^{9} + a^{3} b^{7} d^{10}\right )} x^{7} + 1716 \, {\left (15 \, b^{10} c^{4} d^{6} + 10 \, a b^{9} c^{3} d^{7} + 6 \, a^{2} b^{8} c^{2} d^{8} + 3 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right )} x^{6} + 1287 \, {\left (21 \, b^{10} c^{5} d^{5} + 15 \, a b^{9} c^{4} d^{6} + 10 \, a^{2} b^{8} c^{3} d^{7} + 6 \, a^{3} b^{7} c^{2} d^{8} + 3 \, a^{4} b^{6} c d^{9} + a^{5} b^{5} d^{10}\right )} x^{5} + 715 \, {\left (28 \, b^{10} c^{6} d^{4} + 21 \, a b^{9} c^{5} d^{5} + 15 \, a^{2} b^{8} c^{4} d^{6} + 10 \, a^{3} b^{7} c^{3} d^{7} + 6 \, a^{4} b^{6} c^{2} d^{8} + 3 \, a^{5} b^{5} c d^{9} + a^{6} b^{4} d^{10}\right )} x^{4} + 286 \, {\left (36 \, b^{10} c^{7} d^{3} + 28 \, a b^{9} c^{6} d^{4} + 21 \, a^{2} b^{8} c^{5} d^{5} + 15 \, a^{3} b^{7} c^{4} d^{6} + 10 \, a^{4} b^{6} c^{3} d^{7} + 6 \, a^{5} b^{5} c^{2} d^{8} + 3 \, a^{6} b^{4} c d^{9} + a^{7} b^{3} d^{10}\right )} x^{3} + 78 \, {\left (45 \, b^{10} c^{8} d^{2} + 36 \, a b^{9} c^{7} d^{3} + 28 \, a^{2} b^{8} c^{6} d^{4} + 21 \, a^{3} b^{7} c^{5} d^{5} + 15 \, a^{4} b^{6} c^{4} d^{6} + 10 \, a^{5} b^{5} c^{3} d^{7} + 6 \, a^{6} b^{4} c^{2} d^{8} + 3 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 13 \, {\left (55 \, b^{10} c^{9} d + 45 \, a b^{9} c^{8} d^{2} + 36 \, a^{2} b^{8} c^{7} d^{3} + 28 \, a^{3} b^{7} c^{6} d^{4} + 21 \, a^{4} b^{6} c^{5} d^{5} + 15 \, a^{5} b^{5} c^{4} d^{6} + 10 \, a^{6} b^{4} c^{3} d^{7} + 6 \, a^{7} b^{3} c^{2} d^{8} + 3 \, a^{8} b^{2} c d^{9} + a^{9} b d^{10}\right )} x}{858 \, {\left (b^{24} x^{13} + 13 \, a b^{23} x^{12} + 78 \, a^{2} b^{22} x^{11} + 286 \, a^{3} b^{21} x^{10} + 715 \, a^{4} b^{20} x^{9} + 1287 \, a^{5} b^{19} x^{8} + 1716 \, a^{6} b^{18} x^{7} + 1716 \, a^{7} b^{17} x^{6} + 1287 \, a^{8} b^{16} x^{5} + 715 \, a^{9} b^{15} x^{4} + 286 \, a^{10} b^{14} x^{3} + 78 \, a^{11} b^{13} x^{2} + 13 \, a^{12} b^{12} x + a^{13} b^{11}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^10/(b*x+a)^14,x, algorithm="fricas")

[Out]

-1/858*(286*b^10*d^10*x^10 + 66*b^10*c^10 + 55*a*b^9*c^9*d + 45*a^2*b^8*c^8*d^2 + 36*a^3*b^7*c^7*d^3 + 28*a^4*
b^6*c^6*d^4 + 21*a^5*b^5*c^5*d^5 + 15*a^6*b^4*c^4*d^6 + 10*a^7*b^3*c^3*d^7 + 6*a^8*b^2*c^2*d^8 + 3*a^9*b*c*d^9
+ a^10*d^10 + 715*(3*b^10*c*d^9 + a*b^9*d^10)*x^9 + 1287*(6*b^10*c^2*d^8 + 3*a*b^9*c*d^9 + a^2*b^8*d^10)*x^8
+ 1716*(10*b^10*c^3*d^7 + 6*a*b^9*c^2*d^8 + 3*a^2*b^8*c*d^9 + a^3*b^7*d^10)*x^7 + 1716*(15*b^10*c^4*d^6 + 10*a
*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 + 3*a^3*b^7*c*d^9 + a^4*b^6*d^10)*x^6 + 1287*(21*b^10*c^5*d^5 + 15*a*b^9*c^4*
d^6 + 10*a^2*b^8*c^3*d^7 + 6*a^3*b^7*c^2*d^8 + 3*a^4*b^6*c*d^9 + a^5*b^5*d^10)*x^5 + 715*(28*b^10*c^6*d^4 + 21
*a*b^9*c^5*d^5 + 15*a^2*b^8*c^4*d^6 + 10*a^3*b^7*c^3*d^7 + 6*a^4*b^6*c^2*d^8 + 3*a^5*b^5*c*d^9 + a^6*b^4*d^10)
*x^4 + 286*(36*b^10*c^7*d^3 + 28*a*b^9*c^6*d^4 + 21*a^2*b^8*c^5*d^5 + 15*a^3*b^7*c^4*d^6 + 10*a^4*b^6*c^3*d^7
+ 6*a^5*b^5*c^2*d^8 + 3*a^6*b^4*c*d^9 + a^7*b^3*d^10)*x^3 + 78*(45*b^10*c^8*d^2 + 36*a*b^9*c^7*d^3 + 28*a^2*b^
8*c^6*d^4 + 21*a^3*b^7*c^5*d^5 + 15*a^4*b^6*c^4*d^6 + 10*a^5*b^5*c^3*d^7 + 6*a^6*b^4*c^2*d^8 + 3*a^7*b^3*c*d^9
+ a^8*b^2*d^10)*x^2 + 13*(55*b^10*c^9*d + 45*a*b^9*c^8*d^2 + 36*a^2*b^8*c^7*d^3 + 28*a^3*b^7*c^6*d^4 + 21*a^4
*b^6*c^5*d^5 + 15*a^5*b^5*c^4*d^6 + 10*a^6*b^4*c^3*d^7 + 6*a^7*b^3*c^2*d^8 + 3*a^8*b^2*c*d^9 + a^9*b*d^10)*x)/
(b^24*x^13 + 13*a*b^23*x^12 + 78*a^2*b^22*x^11 + 286*a^3*b^21*x^10 + 715*a^4*b^20*x^9 + 1287*a^5*b^19*x^8 + 17
16*a^6*b^18*x^7 + 1716*a^7*b^17*x^6 + 1287*a^8*b^16*x^5 + 715*a^9*b^15*x^4 + 286*a^10*b^14*x^3 + 78*a^11*b^13*
x^2 + 13*a^12*b^12*x + a^13*b^11)

________________________________________________________________________________________

giac [B]  time = 1.28, size = 961, normalized size = 10.80 \begin {gather*} -\frac {286 \, b^{10} d^{10} x^{10} + 2145 \, b^{10} c d^{9} x^{9} + 715 \, a b^{9} d^{10} x^{9} + 7722 \, b^{10} c^{2} d^{8} x^{8} + 3861 \, a b^{9} c d^{9} x^{8} + 1287 \, a^{2} b^{8} d^{10} x^{8} + 17160 \, b^{10} c^{3} d^{7} x^{7} + 10296 \, a b^{9} c^{2} d^{8} x^{7} + 5148 \, a^{2} b^{8} c d^{9} x^{7} + 1716 \, a^{3} b^{7} d^{10} x^{7} + 25740 \, b^{10} c^{4} d^{6} x^{6} + 17160 \, a b^{9} c^{3} d^{7} x^{6} + 10296 \, a^{2} b^{8} c^{2} d^{8} x^{6} + 5148 \, a^{3} b^{7} c d^{9} x^{6} + 1716 \, a^{4} b^{6} d^{10} x^{6} + 27027 \, b^{10} c^{5} d^{5} x^{5} + 19305 \, a b^{9} c^{4} d^{6} x^{5} + 12870 \, a^{2} b^{8} c^{3} d^{7} x^{5} + 7722 \, a^{3} b^{7} c^{2} d^{8} x^{5} + 3861 \, a^{4} b^{6} c d^{9} x^{5} + 1287 \, a^{5} b^{5} d^{10} x^{5} + 20020 \, b^{10} c^{6} d^{4} x^{4} + 15015 \, a b^{9} c^{5} d^{5} x^{4} + 10725 \, a^{2} b^{8} c^{4} d^{6} x^{4} + 7150 \, a^{3} b^{7} c^{3} d^{7} x^{4} + 4290 \, a^{4} b^{6} c^{2} d^{8} x^{4} + 2145 \, a^{5} b^{5} c d^{9} x^{4} + 715 \, a^{6} b^{4} d^{10} x^{4} + 10296 \, b^{10} c^{7} d^{3} x^{3} + 8008 \, a b^{9} c^{6} d^{4} x^{3} + 6006 \, a^{2} b^{8} c^{5} d^{5} x^{3} + 4290 \, a^{3} b^{7} c^{4} d^{6} x^{3} + 2860 \, a^{4} b^{6} c^{3} d^{7} x^{3} + 1716 \, a^{5} b^{5} c^{2} d^{8} x^{3} + 858 \, a^{6} b^{4} c d^{9} x^{3} + 286 \, a^{7} b^{3} d^{10} x^{3} + 3510 \, b^{10} c^{8} d^{2} x^{2} + 2808 \, a b^{9} c^{7} d^{3} x^{2} + 2184 \, a^{2} b^{8} c^{6} d^{4} x^{2} + 1638 \, a^{3} b^{7} c^{5} d^{5} x^{2} + 1170 \, a^{4} b^{6} c^{4} d^{6} x^{2} + 780 \, a^{5} b^{5} c^{3} d^{7} x^{2} + 468 \, a^{6} b^{4} c^{2} d^{8} x^{2} + 234 \, a^{7} b^{3} c d^{9} x^{2} + 78 \, a^{8} b^{2} d^{10} x^{2} + 715 \, b^{10} c^{9} d x + 585 \, a b^{9} c^{8} d^{2} x + 468 \, a^{2} b^{8} c^{7} d^{3} x + 364 \, a^{3} b^{7} c^{6} d^{4} x + 273 \, a^{4} b^{6} c^{5} d^{5} x + 195 \, a^{5} b^{5} c^{4} d^{6} x + 130 \, a^{6} b^{4} c^{3} d^{7} x + 78 \, a^{7} b^{3} c^{2} d^{8} x + 39 \, a^{8} b^{2} c d^{9} x + 13 \, a^{9} b d^{10} x + 66 \, b^{10} c^{10} + 55 \, a b^{9} c^{9} d + 45 \, a^{2} b^{8} c^{8} d^{2} + 36 \, a^{3} b^{7} c^{7} d^{3} + 28 \, a^{4} b^{6} c^{6} d^{4} + 21 \, a^{5} b^{5} c^{5} d^{5} + 15 \, a^{6} b^{4} c^{4} d^{6} + 10 \, a^{7} b^{3} c^{3} d^{7} + 6 \, a^{8} b^{2} c^{2} d^{8} + 3 \, a^{9} b c d^{9} + a^{10} d^{10}}{858 \, {\left (b x + a\right )}^{13} b^{11}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^10/(b*x+a)^14,x, algorithm="giac")

[Out]

-1/858*(286*b^10*d^10*x^10 + 2145*b^10*c*d^9*x^9 + 715*a*b^9*d^10*x^9 + 7722*b^10*c^2*d^8*x^8 + 3861*a*b^9*c*d
^9*x^8 + 1287*a^2*b^8*d^10*x^8 + 17160*b^10*c^3*d^7*x^7 + 10296*a*b^9*c^2*d^8*x^7 + 5148*a^2*b^8*c*d^9*x^7 + 1
716*a^3*b^7*d^10*x^7 + 25740*b^10*c^4*d^6*x^6 + 17160*a*b^9*c^3*d^7*x^6 + 10296*a^2*b^8*c^2*d^8*x^6 + 5148*a^3
*b^7*c*d^9*x^6 + 1716*a^4*b^6*d^10*x^6 + 27027*b^10*c^5*d^5*x^5 + 19305*a*b^9*c^4*d^6*x^5 + 12870*a^2*b^8*c^3*
d^7*x^5 + 7722*a^3*b^7*c^2*d^8*x^5 + 3861*a^4*b^6*c*d^9*x^5 + 1287*a^5*b^5*d^10*x^5 + 20020*b^10*c^6*d^4*x^4 +
15015*a*b^9*c^5*d^5*x^4 + 10725*a^2*b^8*c^4*d^6*x^4 + 7150*a^3*b^7*c^3*d^7*x^4 + 4290*a^4*b^6*c^2*d^8*x^4 + 2
145*a^5*b^5*c*d^9*x^4 + 715*a^6*b^4*d^10*x^4 + 10296*b^10*c^7*d^3*x^3 + 8008*a*b^9*c^6*d^4*x^3 + 6006*a^2*b^8*
c^5*d^5*x^3 + 4290*a^3*b^7*c^4*d^6*x^3 + 2860*a^4*b^6*c^3*d^7*x^3 + 1716*a^5*b^5*c^2*d^8*x^3 + 858*a^6*b^4*c*d
^9*x^3 + 286*a^7*b^3*d^10*x^3 + 3510*b^10*c^8*d^2*x^2 + 2808*a*b^9*c^7*d^3*x^2 + 2184*a^2*b^8*c^6*d^4*x^2 + 16
38*a^3*b^7*c^5*d^5*x^2 + 1170*a^4*b^6*c^4*d^6*x^2 + 780*a^5*b^5*c^3*d^7*x^2 + 468*a^6*b^4*c^2*d^8*x^2 + 234*a^
7*b^3*c*d^9*x^2 + 78*a^8*b^2*d^10*x^2 + 715*b^10*c^9*d*x + 585*a*b^9*c^8*d^2*x + 468*a^2*b^8*c^7*d^3*x + 364*a
^3*b^7*c^6*d^4*x + 273*a^4*b^6*c^5*d^5*x + 195*a^5*b^5*c^4*d^6*x + 130*a^6*b^4*c^3*d^7*x + 78*a^7*b^3*c^2*d^8*
x + 39*a^8*b^2*c*d^9*x + 13*a^9*b*d^10*x + 66*b^10*c^10 + 55*a*b^9*c^9*d + 45*a^2*b^8*c^8*d^2 + 36*a^3*b^7*c^7
*d^3 + 28*a^4*b^6*c^6*d^4 + 21*a^5*b^5*c^5*d^5 + 15*a^6*b^4*c^4*d^6 + 10*a^7*b^3*c^3*d^7 + 6*a^8*b^2*c^2*d^8 +
3*a^9*b*c*d^9 + a^10*d^10)/((b*x + a)^13*b^11)

________________________________________________________________________________________

maple [B]  time = 0.01, size = 867, normalized size = 9.74 \begin {gather*} -\frac {d^{10}}{3 \left (b x +a \right )^{3} b^{11}}+\frac {5 \left (a d -b c \right ) d^{9}}{2 \left (b x +a \right )^{4} b^{11}}-\frac {9 \left (a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right ) d^{8}}{\left (b x +a \right )^{5} b^{11}}+\frac {20 \left (a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right ) d^{7}}{\left (b x +a \right )^{6} b^{11}}-\frac {30 \left (a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}-4 a \,b^{3} c^{3} d +b^{4} c^{4}\right ) d^{6}}{\left (b x +a \right )^{7} b^{11}}+\frac {63 \left (a^{5} d^{5}-5 a^{4} b c \,d^{4}+10 a^{3} b^{2} c^{2} d^{3}-10 a^{2} b^{3} c^{3} d^{2}+5 a \,b^{4} c^{4} d -b^{5} c^{5}\right ) d^{5}}{2 \left (b x +a \right )^{8} b^{11}}-\frac {70 \left (a^{6} d^{6}-6 a^{5} b c \,d^{5}+15 a^{4} b^{2} c^{2} d^{4}-20 a^{3} b^{3} c^{3} d^{3}+15 a^{2} b^{4} c^{4} d^{2}-6 a \,b^{5} c^{5} d +b^{6} c^{6}\right ) d^{4}}{3 \left (b x +a \right )^{9} b^{11}}+\frac {12 \left (a^{7} d^{7}-7 a^{6} b c \,d^{6}+21 a^{5} b^{2} c^{2} d^{5}-35 a^{4} b^{3} c^{3} d^{4}+35 a^{3} b^{4} c^{4} d^{3}-21 a^{2} b^{5} c^{5} d^{2}+7 a \,b^{6} c^{6} d -b^{7} c^{7}\right ) d^{3}}{\left (b x +a \right )^{10} b^{11}}-\frac {45 \left (a^{8} d^{8}-8 a^{7} b c \,d^{7}+28 a^{6} b^{2} c^{2} d^{6}-56 a^{5} b^{3} c^{3} d^{5}+70 a^{4} b^{4} c^{4} d^{4}-56 a^{3} b^{5} c^{5} d^{3}+28 a^{2} b^{6} c^{6} d^{2}-8 a \,b^{7} c^{7} d +b^{8} c^{8}\right ) d^{2}}{11 \left (b x +a \right )^{11} b^{11}}+\frac {5 \left (a^{9} d^{9}-9 a^{8} b c \,d^{8}+36 a^{7} b^{2} c^{2} d^{7}-84 a^{6} b^{3} c^{3} d^{6}+126 a^{5} b^{4} c^{4} d^{5}-126 a^{4} b^{5} c^{5} d^{4}+84 a^{3} b^{6} c^{6} d^{3}-36 a^{2} b^{7} c^{7} d^{2}+9 a \,b^{8} c^{8} d -b^{9} c^{9}\right ) d}{6 \left (b x +a \right )^{12} b^{11}}-\frac {d^{10} a^{10}-10 c \,d^{9} a^{9} b +45 c^{2} d^{8} a^{8} b^{2}-120 a^{7} c^{3} d^{7} b^{3}+210 c^{4} d^{6} a^{6} b^{4}-252 a^{5} c^{5} d^{5} b^{5}+210 a^{4} c^{6} d^{4} b^{6}-120 a^{3} c^{7} d^{3} b^{7}+45 a^{2} c^{8} d^{2} b^{8}-10 a \,b^{9} c^{9} d +c^{10} b^{10}}{13 \left (b x +a \right )^{13} b^{11}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x+c)^10/(b*x+a)^14,x)

[Out]

63/2*d^5*(a^5*d^5-5*a^4*b*c*d^4+10*a^3*b^2*c^2*d^3-10*a^2*b^3*c^3*d^2+5*a*b^4*c^4*d-b^5*c^5)/b^11/(b*x+a)^8-1/
13*(a^10*d^10-10*a^9*b*c*d^9+45*a^8*b^2*c^2*d^8-120*a^7*b^3*c^3*d^7+210*a^6*b^4*c^4*d^6-252*a^5*b^5*c^5*d^5+21
0*a^4*b^6*c^6*d^4-120*a^3*b^7*c^7*d^3+45*a^2*b^8*c^8*d^2-10*a*b^9*c^9*d+b^10*c^10)/b^11/(b*x+a)^13-1/3*d^10/b^
11/(b*x+a)^3-30*d^6*(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/b^11/(b*x+a)^7-70/3*d^4*(a
^6*d^6-6*a^5*b*c*d^5+15*a^4*b^2*c^2*d^4-20*a^3*b^3*c^3*d^3+15*a^2*b^4*c^4*d^2-6*a*b^5*c^5*d+b^6*c^6)/b^11/(b*x
+a)^9-9*d^8*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^11/(b*x+a)^5+5/2*d^9*(a*d-b*c)/b^11/(b*x+a)^4-45/11*d^2*(a^8*d^8-8*a
^7*b*c*d^7+28*a^6*b^2*c^2*d^6-56*a^5*b^3*c^3*d^5+70*a^4*b^4*c^4*d^4-56*a^3*b^5*c^5*d^3+28*a^2*b^6*c^6*d^2-8*a*
b^7*c^7*d+b^8*c^8)/b^11/(b*x+a)^11+5/6*d*(a^9*d^9-9*a^8*b*c*d^8+36*a^7*b^2*c^2*d^7-84*a^6*b^3*c^3*d^6+126*a^5*
b^4*c^4*d^5-126*a^4*b^5*c^5*d^4+84*a^3*b^6*c^6*d^3-36*a^2*b^7*c^7*d^2+9*a*b^8*c^8*d-b^9*c^9)/b^11/(b*x+a)^12+2
0*d^7*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/b^11/(b*x+a)^6+12*d^3*(a^7*d^7-7*a^6*b*c*d^6+21*a^5*b^2*c^
2*d^5-35*a^4*b^3*c^3*d^4+35*a^3*b^4*c^4*d^3-21*a^2*b^5*c^5*d^2+7*a*b^6*c^6*d-b^7*c^7)/b^11/(b*x+a)^10

________________________________________________________________________________________

maxima [B]  time = 2.21, size = 997, normalized size = 11.20 \begin {gather*} -\frac {286 \, b^{10} d^{10} x^{10} + 66 \, b^{10} c^{10} + 55 \, a b^{9} c^{9} d + 45 \, a^{2} b^{8} c^{8} d^{2} + 36 \, a^{3} b^{7} c^{7} d^{3} + 28 \, a^{4} b^{6} c^{6} d^{4} + 21 \, a^{5} b^{5} c^{5} d^{5} + 15 \, a^{6} b^{4} c^{4} d^{6} + 10 \, a^{7} b^{3} c^{3} d^{7} + 6 \, a^{8} b^{2} c^{2} d^{8} + 3 \, a^{9} b c d^{9} + a^{10} d^{10} + 715 \, {\left (3 \, b^{10} c d^{9} + a b^{9} d^{10}\right )} x^{9} + 1287 \, {\left (6 \, b^{10} c^{2} d^{8} + 3 \, a b^{9} c d^{9} + a^{2} b^{8} d^{10}\right )} x^{8} + 1716 \, {\left (10 \, b^{10} c^{3} d^{7} + 6 \, a b^{9} c^{2} d^{8} + 3 \, a^{2} b^{8} c d^{9} + a^{3} b^{7} d^{10}\right )} x^{7} + 1716 \, {\left (15 \, b^{10} c^{4} d^{6} + 10 \, a b^{9} c^{3} d^{7} + 6 \, a^{2} b^{8} c^{2} d^{8} + 3 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right )} x^{6} + 1287 \, {\left (21 \, b^{10} c^{5} d^{5} + 15 \, a b^{9} c^{4} d^{6} + 10 \, a^{2} b^{8} c^{3} d^{7} + 6 \, a^{3} b^{7} c^{2} d^{8} + 3 \, a^{4} b^{6} c d^{9} + a^{5} b^{5} d^{10}\right )} x^{5} + 715 \, {\left (28 \, b^{10} c^{6} d^{4} + 21 \, a b^{9} c^{5} d^{5} + 15 \, a^{2} b^{8} c^{4} d^{6} + 10 \, a^{3} b^{7} c^{3} d^{7} + 6 \, a^{4} b^{6} c^{2} d^{8} + 3 \, a^{5} b^{5} c d^{9} + a^{6} b^{4} d^{10}\right )} x^{4} + 286 \, {\left (36 \, b^{10} c^{7} d^{3} + 28 \, a b^{9} c^{6} d^{4} + 21 \, a^{2} b^{8} c^{5} d^{5} + 15 \, a^{3} b^{7} c^{4} d^{6} + 10 \, a^{4} b^{6} c^{3} d^{7} + 6 \, a^{5} b^{5} c^{2} d^{8} + 3 \, a^{6} b^{4} c d^{9} + a^{7} b^{3} d^{10}\right )} x^{3} + 78 \, {\left (45 \, b^{10} c^{8} d^{2} + 36 \, a b^{9} c^{7} d^{3} + 28 \, a^{2} b^{8} c^{6} d^{4} + 21 \, a^{3} b^{7} c^{5} d^{5} + 15 \, a^{4} b^{6} c^{4} d^{6} + 10 \, a^{5} b^{5} c^{3} d^{7} + 6 \, a^{6} b^{4} c^{2} d^{8} + 3 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 13 \, {\left (55 \, b^{10} c^{9} d + 45 \, a b^{9} c^{8} d^{2} + 36 \, a^{2} b^{8} c^{7} d^{3} + 28 \, a^{3} b^{7} c^{6} d^{4} + 21 \, a^{4} b^{6} c^{5} d^{5} + 15 \, a^{5} b^{5} c^{4} d^{6} + 10 \, a^{6} b^{4} c^{3} d^{7} + 6 \, a^{7} b^{3} c^{2} d^{8} + 3 \, a^{8} b^{2} c d^{9} + a^{9} b d^{10}\right )} x}{858 \, {\left (b^{24} x^{13} + 13 \, a b^{23} x^{12} + 78 \, a^{2} b^{22} x^{11} + 286 \, a^{3} b^{21} x^{10} + 715 \, a^{4} b^{20} x^{9} + 1287 \, a^{5} b^{19} x^{8} + 1716 \, a^{6} b^{18} x^{7} + 1716 \, a^{7} b^{17} x^{6} + 1287 \, a^{8} b^{16} x^{5} + 715 \, a^{9} b^{15} x^{4} + 286 \, a^{10} b^{14} x^{3} + 78 \, a^{11} b^{13} x^{2} + 13 \, a^{12} b^{12} x + a^{13} b^{11}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^10/(b*x+a)^14,x, algorithm="maxima")

[Out]

-1/858*(286*b^10*d^10*x^10 + 66*b^10*c^10 + 55*a*b^9*c^9*d + 45*a^2*b^8*c^8*d^2 + 36*a^3*b^7*c^7*d^3 + 28*a^4*
b^6*c^6*d^4 + 21*a^5*b^5*c^5*d^5 + 15*a^6*b^4*c^4*d^6 + 10*a^7*b^3*c^3*d^7 + 6*a^8*b^2*c^2*d^8 + 3*a^9*b*c*d^9
+ a^10*d^10 + 715*(3*b^10*c*d^9 + a*b^9*d^10)*x^9 + 1287*(6*b^10*c^2*d^8 + 3*a*b^9*c*d^9 + a^2*b^8*d^10)*x^8
+ 1716*(10*b^10*c^3*d^7 + 6*a*b^9*c^2*d^8 + 3*a^2*b^8*c*d^9 + a^3*b^7*d^10)*x^7 + 1716*(15*b^10*c^4*d^6 + 10*a
*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 + 3*a^3*b^7*c*d^9 + a^4*b^6*d^10)*x^6 + 1287*(21*b^10*c^5*d^5 + 15*a*b^9*c^4*
d^6 + 10*a^2*b^8*c^3*d^7 + 6*a^3*b^7*c^2*d^8 + 3*a^4*b^6*c*d^9 + a^5*b^5*d^10)*x^5 + 715*(28*b^10*c^6*d^4 + 21
*a*b^9*c^5*d^5 + 15*a^2*b^8*c^4*d^6 + 10*a^3*b^7*c^3*d^7 + 6*a^4*b^6*c^2*d^8 + 3*a^5*b^5*c*d^9 + a^6*b^4*d^10)
*x^4 + 286*(36*b^10*c^7*d^3 + 28*a*b^9*c^6*d^4 + 21*a^2*b^8*c^5*d^5 + 15*a^3*b^7*c^4*d^6 + 10*a^4*b^6*c^3*d^7
+ 6*a^5*b^5*c^2*d^8 + 3*a^6*b^4*c*d^9 + a^7*b^3*d^10)*x^3 + 78*(45*b^10*c^8*d^2 + 36*a*b^9*c^7*d^3 + 28*a^2*b^
8*c^6*d^4 + 21*a^3*b^7*c^5*d^5 + 15*a^4*b^6*c^4*d^6 + 10*a^5*b^5*c^3*d^7 + 6*a^6*b^4*c^2*d^8 + 3*a^7*b^3*c*d^9
+ a^8*b^2*d^10)*x^2 + 13*(55*b^10*c^9*d + 45*a*b^9*c^8*d^2 + 36*a^2*b^8*c^7*d^3 + 28*a^3*b^7*c^6*d^4 + 21*a^4
*b^6*c^5*d^5 + 15*a^5*b^5*c^4*d^6 + 10*a^6*b^4*c^3*d^7 + 6*a^7*b^3*c^2*d^8 + 3*a^8*b^2*c*d^9 + a^9*b*d^10)*x)/
(b^24*x^13 + 13*a*b^23*x^12 + 78*a^2*b^22*x^11 + 286*a^3*b^21*x^10 + 715*a^4*b^20*x^9 + 1287*a^5*b^19*x^8 + 17
16*a^6*b^18*x^7 + 1716*a^7*b^17*x^6 + 1287*a^8*b^16*x^5 + 715*a^9*b^15*x^4 + 286*a^10*b^14*x^3 + 78*a^11*b^13*
x^2 + 13*a^12*b^12*x + a^13*b^11)

________________________________________________________________________________________

mupad [B]  time = 0.48, size = 1098, normalized size = 12.34 \begin {gather*} -\frac {a^{10}\,d^{10}+3\,a^9\,b\,c\,d^9+13\,a^9\,b\,d^{10}\,x+6\,a^8\,b^2\,c^2\,d^8+39\,a^8\,b^2\,c\,d^9\,x+78\,a^8\,b^2\,d^{10}\,x^2+10\,a^7\,b^3\,c^3\,d^7+78\,a^7\,b^3\,c^2\,d^8\,x+234\,a^7\,b^3\,c\,d^9\,x^2+286\,a^7\,b^3\,d^{10}\,x^3+15\,a^6\,b^4\,c^4\,d^6+130\,a^6\,b^4\,c^3\,d^7\,x+468\,a^6\,b^4\,c^2\,d^8\,x^2+858\,a^6\,b^4\,c\,d^9\,x^3+715\,a^6\,b^4\,d^{10}\,x^4+21\,a^5\,b^5\,c^5\,d^5+195\,a^5\,b^5\,c^4\,d^6\,x+780\,a^5\,b^5\,c^3\,d^7\,x^2+1716\,a^5\,b^5\,c^2\,d^8\,x^3+2145\,a^5\,b^5\,c\,d^9\,x^4+1287\,a^5\,b^5\,d^{10}\,x^5+28\,a^4\,b^6\,c^6\,d^4+273\,a^4\,b^6\,c^5\,d^5\,x+1170\,a^4\,b^6\,c^4\,d^6\,x^2+2860\,a^4\,b^6\,c^3\,d^7\,x^3+4290\,a^4\,b^6\,c^2\,d^8\,x^4+3861\,a^4\,b^6\,c\,d^9\,x^5+1716\,a^4\,b^6\,d^{10}\,x^6+36\,a^3\,b^7\,c^7\,d^3+364\,a^3\,b^7\,c^6\,d^4\,x+1638\,a^3\,b^7\,c^5\,d^5\,x^2+4290\,a^3\,b^7\,c^4\,d^6\,x^3+7150\,a^3\,b^7\,c^3\,d^7\,x^4+7722\,a^3\,b^7\,c^2\,d^8\,x^5+5148\,a^3\,b^7\,c\,d^9\,x^6+1716\,a^3\,b^7\,d^{10}\,x^7+45\,a^2\,b^8\,c^8\,d^2+468\,a^2\,b^8\,c^7\,d^3\,x+2184\,a^2\,b^8\,c^6\,d^4\,x^2+6006\,a^2\,b^8\,c^5\,d^5\,x^3+10725\,a^2\,b^8\,c^4\,d^6\,x^4+12870\,a^2\,b^8\,c^3\,d^7\,x^5+10296\,a^2\,b^8\,c^2\,d^8\,x^6+5148\,a^2\,b^8\,c\,d^9\,x^7+1287\,a^2\,b^8\,d^{10}\,x^8+55\,a\,b^9\,c^9\,d+585\,a\,b^9\,c^8\,d^2\,x+2808\,a\,b^9\,c^7\,d^3\,x^2+8008\,a\,b^9\,c^6\,d^4\,x^3+15015\,a\,b^9\,c^5\,d^5\,x^4+19305\,a\,b^9\,c^4\,d^6\,x^5+17160\,a\,b^9\,c^3\,d^7\,x^6+10296\,a\,b^9\,c^2\,d^8\,x^7+3861\,a\,b^9\,c\,d^9\,x^8+715\,a\,b^9\,d^{10}\,x^9+66\,b^{10}\,c^{10}+715\,b^{10}\,c^9\,d\,x+3510\,b^{10}\,c^8\,d^2\,x^2+10296\,b^{10}\,c^7\,d^3\,x^3+20020\,b^{10}\,c^6\,d^4\,x^4+27027\,b^{10}\,c^5\,d^5\,x^5+25740\,b^{10}\,c^4\,d^6\,x^6+17160\,b^{10}\,c^3\,d^7\,x^7+7722\,b^{10}\,c^2\,d^8\,x^8+2145\,b^{10}\,c\,d^9\,x^9+286\,b^{10}\,d^{10}\,x^{10}}{858\,a^{13}\,b^{11}+11154\,a^{12}\,b^{12}\,x+66924\,a^{11}\,b^{13}\,x^2+245388\,a^{10}\,b^{14}\,x^3+613470\,a^9\,b^{15}\,x^4+1104246\,a^8\,b^{16}\,x^5+1472328\,a^7\,b^{17}\,x^6+1472328\,a^6\,b^{18}\,x^7+1104246\,a^5\,b^{19}\,x^8+613470\,a^4\,b^{20}\,x^9+245388\,a^3\,b^{21}\,x^{10}+66924\,a^2\,b^{22}\,x^{11}+11154\,a\,b^{23}\,x^{12}+858\,b^{24}\,x^{13}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c + d*x)^10/(a + b*x)^14,x)

[Out]

-(a^10*d^10 + 66*b^10*c^10 + 286*b^10*d^10*x^10 + 715*a*b^9*d^10*x^9 + 2145*b^10*c*d^9*x^9 + 45*a^2*b^8*c^8*d^
2 + 36*a^3*b^7*c^7*d^3 + 28*a^4*b^6*c^6*d^4 + 21*a^5*b^5*c^5*d^5 + 15*a^6*b^4*c^4*d^6 + 10*a^7*b^3*c^3*d^7 + 6
*a^8*b^2*c^2*d^8 + 78*a^8*b^2*d^10*x^2 + 286*a^7*b^3*d^10*x^3 + 715*a^6*b^4*d^10*x^4 + 1287*a^5*b^5*d^10*x^5 +
1716*a^4*b^6*d^10*x^6 + 1716*a^3*b^7*d^10*x^7 + 1287*a^2*b^8*d^10*x^8 + 3510*b^10*c^8*d^2*x^2 + 10296*b^10*c^
7*d^3*x^3 + 20020*b^10*c^6*d^4*x^4 + 27027*b^10*c^5*d^5*x^5 + 25740*b^10*c^4*d^6*x^6 + 17160*b^10*c^3*d^7*x^7
+ 7722*b^10*c^2*d^8*x^8 + 55*a*b^9*c^9*d + 3*a^9*b*c*d^9 + 13*a^9*b*d^10*x + 715*b^10*c^9*d*x + 2184*a^2*b^8*c
^6*d^4*x^2 + 1638*a^3*b^7*c^5*d^5*x^2 + 1170*a^4*b^6*c^4*d^6*x^2 + 780*a^5*b^5*c^3*d^7*x^2 + 468*a^6*b^4*c^2*d
^8*x^2 + 6006*a^2*b^8*c^5*d^5*x^3 + 4290*a^3*b^7*c^4*d^6*x^3 + 2860*a^4*b^6*c^3*d^7*x^3 + 1716*a^5*b^5*c^2*d^8
*x^3 + 10725*a^2*b^8*c^4*d^6*x^4 + 7150*a^3*b^7*c^3*d^7*x^4 + 4290*a^4*b^6*c^2*d^8*x^4 + 12870*a^2*b^8*c^3*d^7
*x^5 + 7722*a^3*b^7*c^2*d^8*x^5 + 10296*a^2*b^8*c^2*d^8*x^6 + 585*a*b^9*c^8*d^2*x + 39*a^8*b^2*c*d^9*x + 3861*
a*b^9*c*d^9*x^8 + 468*a^2*b^8*c^7*d^3*x + 364*a^3*b^7*c^6*d^4*x + 273*a^4*b^6*c^5*d^5*x + 195*a^5*b^5*c^4*d^6*
x + 130*a^6*b^4*c^3*d^7*x + 78*a^7*b^3*c^2*d^8*x + 2808*a*b^9*c^7*d^3*x^2 + 234*a^7*b^3*c*d^9*x^2 + 8008*a*b^9
*c^6*d^4*x^3 + 858*a^6*b^4*c*d^9*x^3 + 15015*a*b^9*c^5*d^5*x^4 + 2145*a^5*b^5*c*d^9*x^4 + 19305*a*b^9*c^4*d^6*
x^5 + 3861*a^4*b^6*c*d^9*x^5 + 17160*a*b^9*c^3*d^7*x^6 + 5148*a^3*b^7*c*d^9*x^6 + 10296*a*b^9*c^2*d^8*x^7 + 51
48*a^2*b^8*c*d^9*x^7)/(858*a^13*b^11 + 858*b^24*x^13 + 11154*a^12*b^12*x + 11154*a*b^23*x^12 + 66924*a^11*b^13
*x^2 + 245388*a^10*b^14*x^3 + 613470*a^9*b^15*x^4 + 1104246*a^8*b^16*x^5 + 1472328*a^7*b^17*x^6 + 1472328*a^6*
b^18*x^7 + 1104246*a^5*b^19*x^8 + 613470*a^4*b^20*x^9 + 245388*a^3*b^21*x^10 + 66924*a^2*b^22*x^11)

________________________________________________________________________________________

sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)**10/(b*x+a)**14,x)

[Out]

Timed out

________________________________________________________________________________________