Integrand size = 20, antiderivative size = 135 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx=-\frac {(B d-A e) (a+b x)^{11}}{13 e (b d-a e) (d+e x)^{13}}+\frac {(11 b B d+2 A b e-13 a B e) (a+b x)^{11}}{156 e (b d-a e)^2 (d+e x)^{12}}+\frac {b (11 b B d+2 A b e-13 a B e) (a+b x)^{11}}{1716 e (b d-a e)^3 (d+e x)^{11}} \] Output:
-1/13*(-A*e+B*d)*(b*x+a)^11/e/(-a*e+b*d)/(e*x+d)^13+1/156*(2*A*b*e-13*B*a* e+11*B*b*d)*(b*x+a)^11/e/(-a*e+b*d)^2/(e*x+d)^12+1/1716*b*(2*A*b*e-13*B*a* e+11*B*b*d)*(b*x+a)^11/e/(-a*e+b*d)^3/(e*x+d)^11
Leaf count is larger than twice the leaf count of optimal. \(1433\) vs. \(2(135)=270\).
Time = 0.48 (sec) , antiderivative size = 1433, normalized size of antiderivative = 10.61 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx =\text {Too large to display} \] Input:
Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^14,x]
Output:
-1/1716*(11*a^10*e^10*(12*A*e + B*(d + 13*e*x)) + 10*a^9*b*e^9*(11*A*e*(d + 13*e*x) + 2*B*(d^2 + 13*d*e*x + 78*e^2*x^2)) + 9*a^8*b^2*e^8*(10*A*e*(d^ 2 + 13*d*e*x + 78*e^2*x^2) + 3*B*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^ 3*x^3)) + 8*a^7*b^3*e^7*(9*A*e*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^3* x^3) + 4*B*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3*x^3 + 715*e^4*x^ 4)) + 7*a^6*b^4*e^6*(8*A*e*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3* x^3 + 715*e^4*x^4) + 5*B*(d^5 + 13*d^4*e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3* x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5)) + 6*a^5*b^5*e^5*(7*A*e*(d^5 + 13*d^4* e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3*x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5) + 6 *B*(d^6 + 13*d^5*e*x + 78*d^4*e^2*x^2 + 286*d^3*e^3*x^3 + 715*d^2*e^4*x^4 + 1287*d*e^5*x^5 + 1716*e^6*x^6)) + 5*a^4*b^6*e^4*(6*A*e*(d^6 + 13*d^5*e*x + 78*d^4*e^2*x^2 + 286*d^3*e^3*x^3 + 715*d^2*e^4*x^4 + 1287*d*e^5*x^5 + 1 716*e^6*x^6) + 7*B*(d^7 + 13*d^6*e*x + 78*d^5*e^2*x^2 + 286*d^4*e^3*x^3 + 715*d^3*e^4*x^4 + 1287*d^2*e^5*x^5 + 1716*d*e^6*x^6 + 1716*e^7*x^7)) + 4*a ^3*b^7*e^3*(5*A*e*(d^7 + 13*d^6*e*x + 78*d^5*e^2*x^2 + 286*d^4*e^3*x^3 + 7 15*d^3*e^4*x^4 + 1287*d^2*e^5*x^5 + 1716*d*e^6*x^6 + 1716*e^7*x^7) + 8*B*( d^8 + 13*d^7*e*x + 78*d^6*e^2*x^2 + 286*d^5*e^3*x^3 + 715*d^4*e^4*x^4 + 12 87*d^3*e^5*x^5 + 1716*d^2*e^6*x^6 + 1716*d*e^7*x^7 + 1287*e^8*x^8)) + 3*a^ 2*b^8*e^2*(4*A*e*(d^8 + 13*d^7*e*x + 78*d^6*e^2*x^2 + 286*d^5*e^3*x^3 + 71 5*d^4*e^4*x^4 + 1287*d^3*e^5*x^5 + 1716*d^2*e^6*x^6 + 1716*d*e^7*x^7 + ...
Time = 0.22 (sec) , antiderivative size = 131, normalized size of antiderivative = 0.97, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {87, 55, 48}
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.
\(\displaystyle \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx\) |
\(\Big \downarrow \) 87 |
\(\displaystyle \frac {(-13 a B e+2 A b e+11 b B d) \int \frac {(a+b x)^{10}}{(d+e x)^{13}}dx}{13 e (b d-a e)}-\frac {(a+b x)^{11} (B d-A e)}{13 e (d+e x)^{13} (b d-a e)}\) |
\(\Big \downarrow \) 55 |
\(\displaystyle \frac {(-13 a B e+2 A b e+11 b B d) \left (\frac {b \int \frac {(a+b x)^{10}}{(d+e x)^{12}}dx}{12 (b d-a e)}+\frac {(a+b x)^{11}}{12 (d+e x)^{12} (b d-a e)}\right )}{13 e (b d-a e)}-\frac {(a+b x)^{11} (B d-A e)}{13 e (d+e x)^{13} (b d-a e)}\) |
\(\Big \downarrow \) 48 |
\(\displaystyle \frac {\left (\frac {b (a+b x)^{11}}{132 (d+e x)^{11} (b d-a e)^2}+\frac {(a+b x)^{11}}{12 (d+e x)^{12} (b d-a e)}\right ) (-13 a B e+2 A b e+11 b B d)}{13 e (b d-a e)}-\frac {(a+b x)^{11} (B d-A e)}{13 e (d+e x)^{13} (b d-a e)}\) |
Input:
Int[((a + b*x)^10*(A + B*x))/(d + e*x)^14,x]
Output:
-1/13*((B*d - A*e)*(a + b*x)^11)/(e*(b*d - a*e)*(d + e*x)^13) + ((11*b*B*d + 2*A*b*e - 13*a*B*e)*((a + b*x)^11/(12*(b*d - a*e)*(d + e*x)^12) + (b*(a + b*x)^11)/(132*(b*d - a*e)^2*(d + e*x)^11)))/(13*e*(b*d - a*e))
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] && EqQ[m + n + 2, 0] && NeQ[m, -1]
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] - Simp[d*(S implify[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] && 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] || !SumSimp lerQ[n, 1])
Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p _.), x_] :> Simp[(-(b*e - a*f))*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(f*(p + 1)*(c*f - d*e))), x] - Simp[(a*d*f*(n + p + 2) - b*(d*e*(n + 1) + c*f*(p + 1)))/(f*(p + 1)*(c*f - d*e)) Int[(c + d*x)^n*(e + f*x)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && LtQ[p, -1] && ( !LtQ[n, -1] || Intege rQ[p] || !(IntegerQ[n] || !(EqQ[e, 0] || !(EqQ[c, 0] || LtQ[p, n]))))
Leaf count of result is larger than twice the leaf count of optimal. \(1900\) vs. \(2(129)=258\).
Time = 0.27 (sec) , antiderivative size = 1901, normalized size of antiderivative = 14.08
method | result | size |
risch | \(\text {Expression too large to display}\) | \(1901\) |
default | \(\text {Expression too large to display}\) | \(1942\) |
norman | \(\text {Expression too large to display}\) | \(1992\) |
gosper | \(\text {Expression too large to display}\) | \(2233\) |
orering | \(\text {Expression too large to display}\) | \(2233\) |
parallelrisch | \(\text {Expression too large to display}\) | \(2240\) |
Input:
int((b*x+a)^10*(B*x+A)/(e*x+d)^14,x,method=_RETURNVERBOSE)
Output:
(-1/2*b^10*B/e*x^11-1/6*b^9/e^2*(2*A*b*e+20*B*a*e+11*B*b*d)*x^10-5/12*b^8/ e^3*(6*A*a*b*e^2+2*A*b^2*d*e+27*B*a^2*e^2+20*B*a*b*d*e+11*B*b^2*d^2)*x^9-3 /4*b^7/e^4*(12*A*a^2*b*e^3+6*A*a*b^2*d*e^2+2*A*b^3*d^2*e+32*B*a^3*e^3+27*B *a^2*b*d*e^2+20*B*a*b^2*d^2*e+11*B*b^3*d^3)*x^8-b^6/e^5*(20*A*a^3*b*e^4+12 *A*a^2*b^2*d*e^3+6*A*a*b^3*d^2*e^2+2*A*b^4*d^3*e+35*B*a^4*e^4+32*B*a^3*b*d *e^3+27*B*a^2*b^2*d^2*e^2+20*B*a*b^3*d^3*e+11*B*b^4*d^4)*x^7-b^5/e^6*(30*A *a^4*b*e^5+20*A*a^3*b^2*d*e^4+12*A*a^2*b^3*d^2*e^3+6*A*a*b^4*d^3*e^2+2*A*b ^5*d^4*e+36*B*a^5*e^5+35*B*a^4*b*d*e^4+32*B*a^3*b^2*d^2*e^3+27*B*a^2*b^3*d ^3*e^2+20*B*a*b^4*d^4*e+11*B*b^5*d^5)*x^6-3/4*b^4/e^7*(42*A*a^5*b*e^6+30*A *a^4*b^2*d*e^5+20*A*a^3*b^3*d^2*e^4+12*A*a^2*b^4*d^3*e^3+6*A*a*b^5*d^4*e^2 +2*A*b^6*d^5*e+35*B*a^6*e^6+36*B*a^5*b*d*e^5+35*B*a^4*b^2*d^2*e^4+32*B*a^3 *b^3*d^3*e^3+27*B*a^2*b^4*d^4*e^2+20*B*a*b^5*d^5*e+11*B*b^6*d^6)*x^5-5/12* b^3/e^8*(56*A*a^6*b*e^7+42*A*a^5*b^2*d*e^6+30*A*a^4*b^3*d^2*e^5+20*A*a^3*b ^4*d^3*e^4+12*A*a^2*b^5*d^4*e^3+6*A*a*b^6*d^5*e^2+2*A*b^7*d^6*e+32*B*a^7*e ^7+35*B*a^6*b*d*e^6+36*B*a^5*b^2*d^2*e^5+35*B*a^4*b^3*d^3*e^4+32*B*a^3*b^4 *d^4*e^3+27*B*a^2*b^5*d^5*e^2+20*B*a*b^6*d^6*e+11*B*b^7*d^7)*x^4-1/6*b^2/e ^9*(72*A*a^7*b*e^8+56*A*a^6*b^2*d*e^7+42*A*a^5*b^3*d^2*e^6+30*A*a^4*b^4*d^ 3*e^5+20*A*a^3*b^5*d^4*e^4+12*A*a^2*b^6*d^5*e^3+6*A*a*b^7*d^6*e^2+2*A*b^8* d^7*e+27*B*a^8*e^8+32*B*a^7*b*d*e^7+35*B*a^6*b^2*d^2*e^6+36*B*a^5*b^3*d^3* e^5+35*B*a^4*b^4*d^4*e^4+32*B*a^3*b^5*d^5*e^3+27*B*a^2*b^6*d^6*e^2+20*B...
Leaf count of result is larger than twice the leaf count of optimal. 1951 vs. \(2 (129) = 258\).
Time = 0.13 (sec) , antiderivative size = 1951, normalized size of antiderivative = 14.45 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx=\text {Too large to display} \] Input:
integrate((b*x+a)^10*(B*x+A)/(e*x+d)^14,x, algorithm="fricas")
Output:
-1/1716*(858*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 132*A*a^10*e^11 + 2*(10*B *a*b^9 + A*b^10)*d^10*e + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 4*(8*B*a^3 *b^7 + 3*A*a^2*b^8)*d^8*e^3 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 6*(6 *B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^ 3*e^8 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 11*(B*a^10 + 10*A*a^9*b)*d* e^10 + 286*(11*B*b^10*d*e^10 + 2*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 715*(1 1*B*b^10*d^2*e^9 + 2*(10*B*a*b^9 + A*b^10)*d*e^10 + 3*(9*B*a^2*b^8 + 2*A*a *b^9)*e^11)*x^9 + 1287*(11*B*b^10*d^3*e^8 + 2*(10*B*a*b^9 + A*b^10)*d^2*e^ 9 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^1 1)*x^8 + 1716*(11*B*b^10*d^4*e^7 + 2*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 3*(9* B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 5* (7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 1716*(11*B*b^10*d^5*e^6 + 2*(10*B* a*b^9 + A*b^10)*d^4*e^7 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 4*(8*B*a^3 *b^7 + 3*A*a^2*b^8)*d^2*e^9 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 6*(6* B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 1287*(11*B*b^10*d^6*e^5 + 2*(10*B*a*b ^9 + A*b^10)*d^5*e^6 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 4*(8*B*a^3*b^ 7 + 3*A*a^2*b^8)*d^3*e^8 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 6*(6*B* a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 715*(11*B*b^10*d^7*e^4 + 2*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 3*(9*B*a^2*b...
Timed out. \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx=\text {Timed out} \] Input:
integrate((b*x+a)**10*(B*x+A)/(e*x+d)**14,x)
Output:
Timed out
Leaf count of result is larger than twice the leaf count of optimal. 1951 vs. \(2 (129) = 258\).
Time = 0.13 (sec) , antiderivative size = 1951, normalized size of antiderivative = 14.45 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx=\text {Too large to display} \] Input:
integrate((b*x+a)^10*(B*x+A)/(e*x+d)^14,x, algorithm="maxima")
Output:
-1/1716*(858*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 132*A*a^10*e^11 + 2*(10*B *a*b^9 + A*b^10)*d^10*e + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 4*(8*B*a^3 *b^7 + 3*A*a^2*b^8)*d^8*e^3 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 6*(6 *B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^ 3*e^8 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 11*(B*a^10 + 10*A*a^9*b)*d* e^10 + 286*(11*B*b^10*d*e^10 + 2*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 715*(1 1*B*b^10*d^2*e^9 + 2*(10*B*a*b^9 + A*b^10)*d*e^10 + 3*(9*B*a^2*b^8 + 2*A*a *b^9)*e^11)*x^9 + 1287*(11*B*b^10*d^3*e^8 + 2*(10*B*a*b^9 + A*b^10)*d^2*e^ 9 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^1 1)*x^8 + 1716*(11*B*b^10*d^4*e^7 + 2*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 3*(9* B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 5* (7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 1716*(11*B*b^10*d^5*e^6 + 2*(10*B* a*b^9 + A*b^10)*d^4*e^7 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 4*(8*B*a^3 *b^7 + 3*A*a^2*b^8)*d^2*e^9 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 6*(6* B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 1287*(11*B*b^10*d^6*e^5 + 2*(10*B*a*b ^9 + A*b^10)*d^5*e^6 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 4*(8*B*a^3*b^ 7 + 3*A*a^2*b^8)*d^3*e^8 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 6*(6*B* a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 715*(11*B*b^10*d^7*e^4 + 2*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 3*(9*B*a^2*b...
Leaf count of result is larger than twice the leaf count of optimal. 2232 vs. \(2 (129) = 258\).
Time = 0.13 (sec) , antiderivative size = 2232, normalized size of antiderivative = 16.53 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx=\text {Too large to display} \] Input:
integrate((b*x+a)^10*(B*x+A)/(e*x+d)^14,x, algorithm="giac")
Output:
-1/1716*(858*B*b^10*e^11*x^11 + 3146*B*b^10*d*e^10*x^10 + 5720*B*a*b^9*e^1 1*x^10 + 572*A*b^10*e^11*x^10 + 7865*B*b^10*d^2*e^9*x^9 + 14300*B*a*b^9*d* e^10*x^9 + 1430*A*b^10*d*e^10*x^9 + 19305*B*a^2*b^8*e^11*x^9 + 4290*A*a*b^ 9*e^11*x^9 + 14157*B*b^10*d^3*e^8*x^8 + 25740*B*a*b^9*d^2*e^9*x^8 + 2574*A *b^10*d^2*e^9*x^8 + 34749*B*a^2*b^8*d*e^10*x^8 + 7722*A*a*b^9*d*e^10*x^8 + 41184*B*a^3*b^7*e^11*x^8 + 15444*A*a^2*b^8*e^11*x^8 + 18876*B*b^10*d^4*e^ 7*x^7 + 34320*B*a*b^9*d^3*e^8*x^7 + 3432*A*b^10*d^3*e^8*x^7 + 46332*B*a^2* b^8*d^2*e^9*x^7 + 10296*A*a*b^9*d^2*e^9*x^7 + 54912*B*a^3*b^7*d*e^10*x^7 + 20592*A*a^2*b^8*d*e^10*x^7 + 60060*B*a^4*b^6*e^11*x^7 + 34320*A*a^3*b^7*e ^11*x^7 + 18876*B*b^10*d^5*e^6*x^6 + 34320*B*a*b^9*d^4*e^7*x^6 + 3432*A*b^ 10*d^4*e^7*x^6 + 46332*B*a^2*b^8*d^3*e^8*x^6 + 10296*A*a*b^9*d^3*e^8*x^6 + 54912*B*a^3*b^7*d^2*e^9*x^6 + 20592*A*a^2*b^8*d^2*e^9*x^6 + 60060*B*a^4*b ^6*d*e^10*x^6 + 34320*A*a^3*b^7*d*e^10*x^6 + 61776*B*a^5*b^5*e^11*x^6 + 51 480*A*a^4*b^6*e^11*x^6 + 14157*B*b^10*d^6*e^5*x^5 + 25740*B*a*b^9*d^5*e^6* x^5 + 2574*A*b^10*d^5*e^6*x^5 + 34749*B*a^2*b^8*d^4*e^7*x^5 + 7722*A*a*b^9 *d^4*e^7*x^5 + 41184*B*a^3*b^7*d^3*e^8*x^5 + 15444*A*a^2*b^8*d^3*e^8*x^5 + 45045*B*a^4*b^6*d^2*e^9*x^5 + 25740*A*a^3*b^7*d^2*e^9*x^5 + 46332*B*a^5*b ^5*d*e^10*x^5 + 38610*A*a^4*b^6*d*e^10*x^5 + 45045*B*a^6*b^4*e^11*x^5 + 54 054*A*a^5*b^5*e^11*x^5 + 7865*B*b^10*d^7*e^4*x^4 + 14300*B*a*b^9*d^6*e^5*x ^4 + 1430*A*b^10*d^6*e^5*x^4 + 19305*B*a^2*b^8*d^5*e^6*x^4 + 4290*A*a*b...
Time = 1.54 (sec) , antiderivative size = 2031, normalized size of antiderivative = 15.04 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx=\text {Too large to display} \] Input:
int(((A + B*x)*(a + b*x)^10)/(d + e*x)^14,x)
Output:
-((132*A*a^10*e^11 + 11*B*b^10*d^11 + 2*A*b^10*d^10*e + 11*B*a^10*d*e^10 + 6*A*a*b^9*d^9*e^2 + 20*B*a^9*b*d^2*e^9 + 12*A*a^2*b^8*d^8*e^3 + 20*A*a^3* b^7*d^7*e^4 + 30*A*a^4*b^6*d^6*e^5 + 42*A*a^5*b^5*d^5*e^6 + 56*A*a^6*b^4*d ^4*e^7 + 72*A*a^7*b^3*d^3*e^8 + 90*A*a^8*b^2*d^2*e^9 + 27*B*a^2*b^8*d^9*e^ 2 + 32*B*a^3*b^7*d^8*e^3 + 35*B*a^4*b^6*d^7*e^4 + 36*B*a^5*b^5*d^6*e^5 + 3 5*B*a^6*b^4*d^5*e^6 + 32*B*a^7*b^3*d^4*e^7 + 27*B*a^8*b^2*d^3*e^8 + 110*A* a^9*b*d*e^10 + 20*B*a*b^9*d^10*e)/(1716*e^12) + (x*(11*B*a^10*e^10 + 11*B* b^10*d^10 + 110*A*a^9*b*e^10 + 2*A*b^10*d^9*e + 6*A*a*b^9*d^8*e^2 + 90*A*a ^8*b^2*d*e^9 + 12*A*a^2*b^8*d^7*e^3 + 20*A*a^3*b^7*d^6*e^4 + 30*A*a^4*b^6* d^5*e^5 + 42*A*a^5*b^5*d^4*e^6 + 56*A*a^6*b^4*d^3*e^7 + 72*A*a^7*b^3*d^2*e ^8 + 27*B*a^2*b^8*d^8*e^2 + 32*B*a^3*b^7*d^7*e^3 + 35*B*a^4*b^6*d^6*e^4 + 36*B*a^5*b^5*d^5*e^5 + 35*B*a^6*b^4*d^4*e^6 + 32*B*a^7*b^3*d^3*e^7 + 27*B* a^8*b^2*d^2*e^8 + 20*B*a*b^9*d^9*e + 20*B*a^9*b*d*e^9))/(132*e^11) + (3*b^ 7*x^8*(32*B*a^3*e^3 + 11*B*b^3*d^3 + 12*A*a^2*b*e^3 + 2*A*b^3*d^2*e + 6*A* a*b^2*d*e^2 + 20*B*a*b^2*d^2*e + 27*B*a^2*b*d*e^2))/(4*e^4) + (3*b^4*x^5*( 35*B*a^6*e^6 + 11*B*b^6*d^6 + 42*A*a^5*b*e^6 + 2*A*b^6*d^5*e + 6*A*a*b^5*d ^4*e^2 + 30*A*a^4*b^2*d*e^5 + 12*A*a^2*b^4*d^3*e^3 + 20*A*a^3*b^3*d^2*e^4 + 27*B*a^2*b^4*d^4*e^2 + 32*B*a^3*b^3*d^3*e^3 + 35*B*a^4*b^2*d^2*e^4 + 20* B*a*b^5*d^5*e + 36*B*a^5*b*d*e^5))/(4*e^7) + (b^9*x^10*(2*A*b*e + 20*B*a*e + 11*B*b*d))/(6*e^2) + (b^6*x^7*(35*B*a^4*e^4 + 11*B*b^4*d^4 + 20*A*a^...
Time = 0.17 (sec) , antiderivative size = 1283, normalized size of antiderivative = 9.50 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx =\text {Too large to display} \] Input:
int((b*x+a)^10*(B*x+A)/(e*x+d)^14,x)
Output:
( - 12*a**11*e**11 - 11*a**10*b*d*e**10 - 143*a**10*b*e**11*x - 10*a**9*b* *2*d**2*e**9 - 130*a**9*b**2*d*e**10*x - 780*a**9*b**2*e**11*x**2 - 9*a**8 *b**3*d**3*e**8 - 117*a**8*b**3*d**2*e**9*x - 702*a**8*b**3*d*e**10*x**2 - 2574*a**8*b**3*e**11*x**3 - 8*a**7*b**4*d**4*e**7 - 104*a**7*b**4*d**3*e* *8*x - 624*a**7*b**4*d**2*e**9*x**2 - 2288*a**7*b**4*d*e**10*x**3 - 5720*a **7*b**4*e**11*x**4 - 7*a**6*b**5*d**5*e**6 - 91*a**6*b**5*d**4*e**7*x - 5 46*a**6*b**5*d**3*e**8*x**2 - 2002*a**6*b**5*d**2*e**9*x**3 - 5005*a**6*b* *5*d*e**10*x**4 - 9009*a**6*b**5*e**11*x**5 - 6*a**5*b**6*d**6*e**5 - 78*a **5*b**6*d**5*e**6*x - 468*a**5*b**6*d**4*e**7*x**2 - 1716*a**5*b**6*d**3* e**8*x**3 - 4290*a**5*b**6*d**2*e**9*x**4 - 7722*a**5*b**6*d*e**10*x**5 - 10296*a**5*b**6*e**11*x**6 - 5*a**4*b**7*d**7*e**4 - 65*a**4*b**7*d**6*e** 5*x - 390*a**4*b**7*d**5*e**6*x**2 - 1430*a**4*b**7*d**4*e**7*x**3 - 3575* a**4*b**7*d**3*e**8*x**4 - 6435*a**4*b**7*d**2*e**9*x**5 - 8580*a**4*b**7* d*e**10*x**6 - 8580*a**4*b**7*e**11*x**7 - 4*a**3*b**8*d**8*e**3 - 52*a**3 *b**8*d**7*e**4*x - 312*a**3*b**8*d**6*e**5*x**2 - 1144*a**3*b**8*d**5*e** 6*x**3 - 2860*a**3*b**8*d**4*e**7*x**4 - 5148*a**3*b**8*d**3*e**8*x**5 - 6 864*a**3*b**8*d**2*e**9*x**6 - 6864*a**3*b**8*d*e**10*x**7 - 5148*a**3*b** 8*e**11*x**8 - 3*a**2*b**9*d**9*e**2 - 39*a**2*b**9*d**8*e**3*x - 234*a**2 *b**9*d**7*e**4*x**2 - 858*a**2*b**9*d**6*e**5*x**3 - 2145*a**2*b**9*d**5* e**6*x**4 - 3861*a**2*b**9*d**4*e**7*x**5 - 5148*a**2*b**9*d**3*e**8*x*...