3.10.35 \(\int \frac {(a+b x)^6 (A+B x)}{(d+e x)^{15}} \, dx\)

Optimal. Leaf size=292 \[ \frac {b^5 (-6 a B e-A b e+7 b B d)}{8 e^8 (d+e x)^8}-\frac {b^4 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{3 e^8 (d+e x)^9}+\frac {b^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{2 e^8 (d+e x)^{10}}-\frac {5 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{11 e^8 (d+e x)^{11}}+\frac {b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{4 e^8 (d+e x)^{12}}-\frac {(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{13 e^8 (d+e x)^{13}}+\frac {(b d-a e)^6 (B d-A e)}{14 e^8 (d+e x)^{14}}-\frac {b^6 B}{7 e^8 (d+e x)^7} \]

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Rubi [A]  time = 0.27, antiderivative size = 292, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} \frac {b^5 (-6 a B e-A b e+7 b B d)}{8 e^8 (d+e x)^8}-\frac {b^4 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{3 e^8 (d+e x)^9}+\frac {b^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{2 e^8 (d+e x)^{10}}-\frac {5 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{11 e^8 (d+e x)^{11}}+\frac {b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{4 e^8 (d+e x)^{12}}-\frac {(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{13 e^8 (d+e x)^{13}}+\frac {(b d-a e)^6 (B d-A e)}{14 e^8 (d+e x)^{14}}-\frac {b^6 B}{7 e^8 (d+e x)^7} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((a + b*x)^6*(A + B*x))/(d + e*x)^15,x]

[Out]

((b*d - a*e)^6*(B*d - A*e))/(14*e^8*(d + e*x)^14) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(13*e^8*(d + e
*x)^13) + (b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(4*e^8*(d + e*x)^12) - (5*b^2*(b*d - a*e)^3*(7*b*B*d
- 4*A*b*e - 3*a*B*e))/(11*e^8*(d + e*x)^11) + (b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e))/(2*e^8*(d + e
*x)^10) - (b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e))/(3*e^8*(d + e*x)^9) + (b^5*(7*b*B*d - A*b*e - 6*a*B*
e))/(8*e^8*(d + e*x)^8) - (b^6*B)/(7*e^8*(d + e*x)^7)

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin {align*} \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^{15}} \, dx &=\int \left (\frac {(-b d+a e)^6 (-B d+A e)}{e^7 (d+e x)^{15}}+\frac {(-b d+a e)^5 (-7 b B d+6 A b e+a B e)}{e^7 (d+e x)^{14}}+\frac {3 b (b d-a e)^4 (-7 b B d+5 A b e+2 a B e)}{e^7 (d+e x)^{13}}-\frac {5 b^2 (b d-a e)^3 (-7 b B d+4 A b e+3 a B e)}{e^7 (d+e x)^{12}}+\frac {5 b^3 (b d-a e)^2 (-7 b B d+3 A b e+4 a B e)}{e^7 (d+e x)^{11}}-\frac {3 b^4 (b d-a e) (-7 b B d+2 A b e+5 a B e)}{e^7 (d+e x)^{10}}+\frac {b^5 (-7 b B d+A b e+6 a B e)}{e^7 (d+e x)^9}+\frac {b^6 B}{e^7 (d+e x)^8}\right ) \, dx\\ &=\frac {(b d-a e)^6 (B d-A e)}{14 e^8 (d+e x)^{14}}-\frac {(b d-a e)^5 (7 b B d-6 A b e-a B e)}{13 e^8 (d+e x)^{13}}+\frac {b (b d-a e)^4 (7 b B d-5 A b e-2 a B e)}{4 e^8 (d+e x)^{12}}-\frac {5 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e)}{11 e^8 (d+e x)^{11}}+\frac {b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e)}{2 e^8 (d+e x)^{10}}-\frac {b^4 (b d-a e) (7 b B d-2 A b e-5 a B e)}{3 e^8 (d+e x)^9}+\frac {b^5 (7 b B d-A b e-6 a B e)}{8 e^8 (d+e x)^8}-\frac {b^6 B}{7 e^8 (d+e x)^7}\\ \end {align*}

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Mathematica [B]  time = 0.29, size = 602, normalized size = 2.06 \begin {gather*} -\frac {132 a^6 e^6 (13 A e+B (d+14 e x))+132 a^5 b e^5 \left (6 A e (d+14 e x)+B \left (d^2+14 d e x+91 e^2 x^2\right )\right )+30 a^4 b^2 e^4 \left (11 A e \left (d^2+14 d e x+91 e^2 x^2\right )+3 B \left (d^3+14 d^2 e x+91 d e^2 x^2+364 e^3 x^3\right )\right )+24 a^3 b^3 e^3 \left (5 A e \left (d^3+14 d^2 e x+91 d e^2 x^2+364 e^3 x^3\right )+2 B \left (d^4+14 d^3 e x+91 d^2 e^2 x^2+364 d e^3 x^3+1001 e^4 x^4\right )\right )+4 a^2 b^4 e^2 \left (9 A e \left (d^4+14 d^3 e x+91 d^2 e^2 x^2+364 d e^3 x^3+1001 e^4 x^4\right )+5 B \left (d^5+14 d^4 e x+91 d^3 e^2 x^2+364 d^2 e^3 x^3+1001 d e^4 x^4+2002 e^5 x^5\right )\right )+2 a b^5 e \left (4 A e \left (d^5+14 d^4 e x+91 d^3 e^2 x^2+364 d^2 e^3 x^3+1001 d e^4 x^4+2002 e^5 x^5\right )+3 B \left (d^6+14 d^5 e x+91 d^4 e^2 x^2+364 d^3 e^3 x^3+1001 d^2 e^4 x^4+2002 d e^5 x^5+3003 e^6 x^6\right )\right )+b^6 \left (A e \left (d^6+14 d^5 e x+91 d^4 e^2 x^2+364 d^3 e^3 x^3+1001 d^2 e^4 x^4+2002 d e^5 x^5+3003 e^6 x^6\right )+B \left (d^7+14 d^6 e x+91 d^5 e^2 x^2+364 d^4 e^3 x^3+1001 d^3 e^4 x^4+2002 d^2 e^5 x^5+3003 d e^6 x^6+3432 e^7 x^7\right )\right )}{24024 e^8 (d+e x)^{14}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^15,x]

[Out]

-1/24024*(132*a^6*e^6*(13*A*e + B*(d + 14*e*x)) + 132*a^5*b*e^5*(6*A*e*(d + 14*e*x) + B*(d^2 + 14*d*e*x + 91*e
^2*x^2)) + 30*a^4*b^2*e^4*(11*A*e*(d^2 + 14*d*e*x + 91*e^2*x^2) + 3*B*(d^3 + 14*d^2*e*x + 91*d*e^2*x^2 + 364*e
^3*x^3)) + 24*a^3*b^3*e^3*(5*A*e*(d^3 + 14*d^2*e*x + 91*d*e^2*x^2 + 364*e^3*x^3) + 2*B*(d^4 + 14*d^3*e*x + 91*
d^2*e^2*x^2 + 364*d*e^3*x^3 + 1001*e^4*x^4)) + 4*a^2*b^4*e^2*(9*A*e*(d^4 + 14*d^3*e*x + 91*d^2*e^2*x^2 + 364*d
*e^3*x^3 + 1001*e^4*x^4) + 5*B*(d^5 + 14*d^4*e*x + 91*d^3*e^2*x^2 + 364*d^2*e^3*x^3 + 1001*d*e^4*x^4 + 2002*e^
5*x^5)) + 2*a*b^5*e*(4*A*e*(d^5 + 14*d^4*e*x + 91*d^3*e^2*x^2 + 364*d^2*e^3*x^3 + 1001*d*e^4*x^4 + 2002*e^5*x^
5) + 3*B*(d^6 + 14*d^5*e*x + 91*d^4*e^2*x^2 + 364*d^3*e^3*x^3 + 1001*d^2*e^4*x^4 + 2002*d*e^5*x^5 + 3003*e^6*x
^6)) + b^6*(A*e*(d^6 + 14*d^5*e*x + 91*d^4*e^2*x^2 + 364*d^3*e^3*x^3 + 1001*d^2*e^4*x^4 + 2002*d*e^5*x^5 + 300
3*e^6*x^6) + B*(d^7 + 14*d^6*e*x + 91*d^5*e^2*x^2 + 364*d^4*e^3*x^3 + 1001*d^3*e^4*x^4 + 2002*d^2*e^5*x^5 + 30
03*d*e^6*x^6 + 3432*e^7*x^7)))/(e^8*(d + e*x)^14)

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^6 (A+B x)}{(d+e x)^{15}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^15,x]

[Out]

IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^15, x]

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fricas [B]  time = 1.09, size = 902, normalized size = 3.09 \begin {gather*} -\frac {3432 \, B b^{6} e^{7} x^{7} + B b^{6} d^{7} + 1716 \, A a^{6} e^{7} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{2} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{3} + 30 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{4} + 66 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{5} + 132 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{6} + 3003 \, {\left (B b^{6} d e^{6} + {\left (6 \, B a b^{5} + A b^{6}\right )} e^{7}\right )} x^{6} + 2002 \, {\left (B b^{6} d^{2} e^{5} + {\left (6 \, B a b^{5} + A b^{6}\right )} d e^{6} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{7}\right )} x^{5} + 1001 \, {\left (B b^{6} d^{3} e^{4} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e^{5} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{6} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{7}\right )} x^{4} + 364 \, {\left (B b^{6} d^{4} e^{3} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e^{4} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{5} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{6} + 30 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{7}\right )} x^{3} + 91 \, {\left (B b^{6} d^{5} e^{2} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e^{3} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{4} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{5} + 30 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{6} + 66 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{7}\right )} x^{2} + 14 \, {\left (B b^{6} d^{6} e + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} e^{2} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e^{3} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{4} + 30 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{5} + 66 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{6} + 132 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{7}\right )} x}{24024 \, {\left (e^{22} x^{14} + 14 \, d e^{21} x^{13} + 91 \, d^{2} e^{20} x^{12} + 364 \, d^{3} e^{19} x^{11} + 1001 \, d^{4} e^{18} x^{10} + 2002 \, d^{5} e^{17} x^{9} + 3003 \, d^{6} e^{16} x^{8} + 3432 \, d^{7} e^{15} x^{7} + 3003 \, d^{8} e^{14} x^{6} + 2002 \, d^{9} e^{13} x^{5} + 1001 \, d^{10} e^{12} x^{4} + 364 \, d^{11} e^{11} x^{3} + 91 \, d^{12} e^{10} x^{2} + 14 \, d^{13} e^{9} x + d^{14} e^{8}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)/(e*x+d)^15,x, algorithm="fricas")

[Out]

-1/24024*(3432*B*b^6*e^7*x^7 + B*b^6*d^7 + 1716*A*a^6*e^7 + (6*B*a*b^5 + A*b^6)*d^6*e + 4*(5*B*a^2*b^4 + 2*A*a
*b^5)*d^5*e^2 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 66*(2*B*a^5*
b + 5*A*a^4*b^2)*d^2*e^5 + 132*(B*a^6 + 6*A*a^5*b)*d*e^6 + 3003*(B*b^6*d*e^6 + (6*B*a*b^5 + A*b^6)*e^7)*x^6 +
2002*(B*b^6*d^2*e^5 + (6*B*a*b^5 + A*b^6)*d*e^6 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 1001*(B*b^6*d^3*e^4 +
(6*B*a*b^5 + A*b^6)*d^2*e^5 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 3
64*(B*b^6*d^4*e^3 + (6*B*a*b^5 + A*b^6)*d^3*e^4 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 12*(4*B*a^3*b^3 + 3*A*
a^2*b^4)*d*e^6 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 91*(B*b^6*d^5*e^2 + (6*B*a*b^5 + A*b^6)*d^4*e^3 + 4
*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d
*e^6 + 66*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 14*(B*b^6*d^6*e + (6*B*a*b^5 + A*b^6)*d^5*e^2 + 4*(5*B*a^2*b^4
+ 2*A*a*b^5)*d^4*e^3 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 66*(2
*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 132*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^22*x^14 + 14*d*e^21*x^13 + 91*d^2*e^20*x^12
+ 364*d^3*e^19*x^11 + 1001*d^4*e^18*x^10 + 2002*d^5*e^17*x^9 + 3003*d^6*e^16*x^8 + 3432*d^7*e^15*x^7 + 3003*d
^8*e^14*x^6 + 2002*d^9*e^13*x^5 + 1001*d^10*e^12*x^4 + 364*d^11*e^11*x^3 + 91*d^12*e^10*x^2 + 14*d^13*e^9*x +
d^14*e^8)

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giac [B]  time = 1.27, size = 854, normalized size = 2.92 \begin {gather*} -\frac {{\left (3432 \, B b^{6} x^{7} e^{7} + 3003 \, B b^{6} d x^{6} e^{6} + 2002 \, B b^{6} d^{2} x^{5} e^{5} + 1001 \, B b^{6} d^{3} x^{4} e^{4} + 364 \, B b^{6} d^{4} x^{3} e^{3} + 91 \, B b^{6} d^{5} x^{2} e^{2} + 14 \, B b^{6} d^{6} x e + B b^{6} d^{7} + 18018 \, B a b^{5} x^{6} e^{7} + 3003 \, A b^{6} x^{6} e^{7} + 12012 \, B a b^{5} d x^{5} e^{6} + 2002 \, A b^{6} d x^{5} e^{6} + 6006 \, B a b^{5} d^{2} x^{4} e^{5} + 1001 \, A b^{6} d^{2} x^{4} e^{5} + 2184 \, B a b^{5} d^{3} x^{3} e^{4} + 364 \, A b^{6} d^{3} x^{3} e^{4} + 546 \, B a b^{5} d^{4} x^{2} e^{3} + 91 \, A b^{6} d^{4} x^{2} e^{3} + 84 \, B a b^{5} d^{5} x e^{2} + 14 \, A b^{6} d^{5} x e^{2} + 6 \, B a b^{5} d^{6} e + A b^{6} d^{6} e + 40040 \, B a^{2} b^{4} x^{5} e^{7} + 16016 \, A a b^{5} x^{5} e^{7} + 20020 \, B a^{2} b^{4} d x^{4} e^{6} + 8008 \, A a b^{5} d x^{4} e^{6} + 7280 \, B a^{2} b^{4} d^{2} x^{3} e^{5} + 2912 \, A a b^{5} d^{2} x^{3} e^{5} + 1820 \, B a^{2} b^{4} d^{3} x^{2} e^{4} + 728 \, A a b^{5} d^{3} x^{2} e^{4} + 280 \, B a^{2} b^{4} d^{4} x e^{3} + 112 \, A a b^{5} d^{4} x e^{3} + 20 \, B a^{2} b^{4} d^{5} e^{2} + 8 \, A a b^{5} d^{5} e^{2} + 48048 \, B a^{3} b^{3} x^{4} e^{7} + 36036 \, A a^{2} b^{4} x^{4} e^{7} + 17472 \, B a^{3} b^{3} d x^{3} e^{6} + 13104 \, A a^{2} b^{4} d x^{3} e^{6} + 4368 \, B a^{3} b^{3} d^{2} x^{2} e^{5} + 3276 \, A a^{2} b^{4} d^{2} x^{2} e^{5} + 672 \, B a^{3} b^{3} d^{3} x e^{4} + 504 \, A a^{2} b^{4} d^{3} x e^{4} + 48 \, B a^{3} b^{3} d^{4} e^{3} + 36 \, A a^{2} b^{4} d^{4} e^{3} + 32760 \, B a^{4} b^{2} x^{3} e^{7} + 43680 \, A a^{3} b^{3} x^{3} e^{7} + 8190 \, B a^{4} b^{2} d x^{2} e^{6} + 10920 \, A a^{3} b^{3} d x^{2} e^{6} + 1260 \, B a^{4} b^{2} d^{2} x e^{5} + 1680 \, A a^{3} b^{3} d^{2} x e^{5} + 90 \, B a^{4} b^{2} d^{3} e^{4} + 120 \, A a^{3} b^{3} d^{3} e^{4} + 12012 \, B a^{5} b x^{2} e^{7} + 30030 \, A a^{4} b^{2} x^{2} e^{7} + 1848 \, B a^{5} b d x e^{6} + 4620 \, A a^{4} b^{2} d x e^{6} + 132 \, B a^{5} b d^{2} e^{5} + 330 \, A a^{4} b^{2} d^{2} e^{5} + 1848 \, B a^{6} x e^{7} + 11088 \, A a^{5} b x e^{7} + 132 \, B a^{6} d e^{6} + 792 \, A a^{5} b d e^{6} + 1716 \, A a^{6} e^{7}\right )} e^{\left (-8\right )}}{24024 \, {\left (x e + d\right )}^{14}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)/(e*x+d)^15,x, algorithm="giac")

[Out]

-1/24024*(3432*B*b^6*x^7*e^7 + 3003*B*b^6*d*x^6*e^6 + 2002*B*b^6*d^2*x^5*e^5 + 1001*B*b^6*d^3*x^4*e^4 + 364*B*
b^6*d^4*x^3*e^3 + 91*B*b^6*d^5*x^2*e^2 + 14*B*b^6*d^6*x*e + B*b^6*d^7 + 18018*B*a*b^5*x^6*e^7 + 3003*A*b^6*x^6
*e^7 + 12012*B*a*b^5*d*x^5*e^6 + 2002*A*b^6*d*x^5*e^6 + 6006*B*a*b^5*d^2*x^4*e^5 + 1001*A*b^6*d^2*x^4*e^5 + 21
84*B*a*b^5*d^3*x^3*e^4 + 364*A*b^6*d^3*x^3*e^4 + 546*B*a*b^5*d^4*x^2*e^3 + 91*A*b^6*d^4*x^2*e^3 + 84*B*a*b^5*d
^5*x*e^2 + 14*A*b^6*d^5*x*e^2 + 6*B*a*b^5*d^6*e + A*b^6*d^6*e + 40040*B*a^2*b^4*x^5*e^7 + 16016*A*a*b^5*x^5*e^
7 + 20020*B*a^2*b^4*d*x^4*e^6 + 8008*A*a*b^5*d*x^4*e^6 + 7280*B*a^2*b^4*d^2*x^3*e^5 + 2912*A*a*b^5*d^2*x^3*e^5
+ 1820*B*a^2*b^4*d^3*x^2*e^4 + 728*A*a*b^5*d^3*x^2*e^4 + 280*B*a^2*b^4*d^4*x*e^3 + 112*A*a*b^5*d^4*x*e^3 + 20
*B*a^2*b^4*d^5*e^2 + 8*A*a*b^5*d^5*e^2 + 48048*B*a^3*b^3*x^4*e^7 + 36036*A*a^2*b^4*x^4*e^7 + 17472*B*a^3*b^3*d
*x^3*e^6 + 13104*A*a^2*b^4*d*x^3*e^6 + 4368*B*a^3*b^3*d^2*x^2*e^5 + 3276*A*a^2*b^4*d^2*x^2*e^5 + 672*B*a^3*b^3
*d^3*x*e^4 + 504*A*a^2*b^4*d^3*x*e^4 + 48*B*a^3*b^3*d^4*e^3 + 36*A*a^2*b^4*d^4*e^3 + 32760*B*a^4*b^2*x^3*e^7 +
43680*A*a^3*b^3*x^3*e^7 + 8190*B*a^4*b^2*d*x^2*e^6 + 10920*A*a^3*b^3*d*x^2*e^6 + 1260*B*a^4*b^2*d^2*x*e^5 + 1
680*A*a^3*b^3*d^2*x*e^5 + 90*B*a^4*b^2*d^3*e^4 + 120*A*a^3*b^3*d^3*e^4 + 12012*B*a^5*b*x^2*e^7 + 30030*A*a^4*b
^2*x^2*e^7 + 1848*B*a^5*b*d*x*e^6 + 4620*A*a^4*b^2*d*x*e^6 + 132*B*a^5*b*d^2*e^5 + 330*A*a^4*b^2*d^2*e^5 + 184
8*B*a^6*x*e^7 + 11088*A*a^5*b*x*e^7 + 132*B*a^6*d*e^6 + 792*A*a^5*b*d*e^6 + 1716*A*a^6*e^7)*e^(-8)/(x*e + d)^1
4

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maple [B]  time = 0.01, size = 814, normalized size = 2.79 \begin {gather*} -\frac {B \,b^{6}}{7 \left (e x +d \right )^{7} e^{8}}-\frac {\left (A b e +6 B a e -7 B b d \right ) b^{5}}{8 \left (e x +d \right )^{8} e^{8}}-\frac {\left (2 A a b \,e^{2}-2 A d \,b^{2} e +5 B \,a^{2} e^{2}-12 B a b d e +7 B \,b^{2} d^{2}\right ) b^{4}}{3 \left (e x +d \right )^{9} e^{8}}-\frac {\left (3 A \,a^{2} b \,e^{3}-6 A d a \,b^{2} e^{2}+3 A \,b^{3} d^{2} e +4 B \,a^{3} e^{3}-15 B d \,a^{2} b \,e^{2}+18 B a \,b^{2} d^{2} e -7 B \,b^{3} d^{3}\right ) b^{3}}{2 \left (e x +d \right )^{10} e^{8}}-\frac {5 \left (4 A \,a^{3} b \,e^{4}-12 A \,a^{2} b^{2} d \,e^{3}+12 A a \,b^{3} d^{2} e^{2}-4 A \,b^{4} d^{3} e +3 B \,a^{4} e^{4}-16 B \,a^{3} b d \,e^{3}+30 B \,a^{2} b^{2} d^{2} e^{2}-24 B a \,b^{3} d^{3} e +7 B \,b^{4} d^{4}\right ) b^{2}}{11 \left (e x +d \right )^{11} e^{8}}-\frac {\left (5 A \,a^{4} b \,e^{5}-20 A \,a^{3} b^{2} d \,e^{4}+30 A \,a^{2} b^{3} d^{2} e^{3}-20 A a \,b^{4} d^{3} e^{2}+5 A \,b^{5} d^{4} e +2 B \,a^{5} e^{5}-15 B \,a^{4} b d \,e^{4}+40 B \,a^{3} b^{2} d^{2} e^{3}-50 B \,a^{2} b^{3} d^{3} e^{2}+30 B a \,b^{4} d^{4} e -7 B \,b^{5} d^{5}\right ) b}{4 \left (e x +d \right )^{12} e^{8}}-\frac {6 a^{5} b A \,e^{6}-30 A d \,a^{4} b^{2} e^{5}+60 A \,d^{2} a^{3} b^{3} e^{4}-60 A \,d^{3} a^{2} b^{4} e^{3}+30 A \,d^{4} a \,b^{5} e^{2}-6 A \,d^{5} b^{6} e +a^{6} B \,e^{6}-12 B d \,a^{5} b \,e^{5}+45 B \,d^{2} a^{4} b^{2} e^{4}-80 B \,d^{3} a^{3} b^{3} e^{3}+75 B \,d^{4} a^{2} b^{4} e^{2}-36 B \,d^{5} a \,b^{5} e +7 B \,b^{6} d^{6}}{13 \left (e x +d \right )^{13} e^{8}}-\frac {A \,a^{6} e^{7}-6 A d \,a^{5} b \,e^{6}+15 A \,d^{2} a^{4} b^{2} e^{5}-20 A \,d^{3} a^{3} b^{3} e^{4}+15 A \,d^{4} a^{2} b^{4} e^{3}-6 A \,d^{5} a \,b^{5} e^{2}+A \,d^{6} b^{6} e -B d \,a^{6} e^{6}+6 B \,d^{2} a^{5} b \,e^{5}-15 B \,d^{3} a^{4} b^{2} e^{4}+20 B \,d^{4} a^{3} b^{3} e^{3}-15 B \,d^{5} a^{2} b^{4} e^{2}+6 B \,d^{6} a \,b^{5} e -B \,b^{6} d^{7}}{14 \left (e x +d \right )^{14} e^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^6*(B*x+A)/(e*x+d)^15,x)

[Out]

-1/13*(6*A*a^5*b*e^6-30*A*a^4*b^2*d*e^5+60*A*a^3*b^3*d^2*e^4-60*A*a^2*b^4*d^3*e^3+30*A*a*b^5*d^4*e^2-6*A*b^6*d
^5*e+B*a^6*e^6-12*B*a^5*b*d*e^5+45*B*a^4*b^2*d^2*e^4-80*B*a^3*b^3*d^3*e^3+75*B*a^2*b^4*d^4*e^2-36*B*a*b^5*d^5*
e+7*B*b^6*d^6)/e^8/(e*x+d)^13-1/14*(A*a^6*e^7-6*A*a^5*b*d*e^6+15*A*a^4*b^2*d^2*e^5-20*A*a^3*b^3*d^3*e^4+15*A*a
^2*b^4*d^4*e^3-6*A*a*b^5*d^5*e^2+A*b^6*d^6*e-B*a^6*d*e^6+6*B*a^5*b*d^2*e^5-15*B*a^4*b^2*d^3*e^4+20*B*a^3*b^3*d
^4*e^3-15*B*a^2*b^4*d^5*e^2+6*B*a*b^5*d^6*e-B*b^6*d^7)/e^8/(e*x+d)^14-1/8*b^5*(A*b*e+6*B*a*e-7*B*b*d)/e^8/(e*x
+d)^8-1/4*b*(5*A*a^4*b*e^5-20*A*a^3*b^2*d*e^4+30*A*a^2*b^3*d^2*e^3-20*A*a*b^4*d^3*e^2+5*A*b^5*d^4*e+2*B*a^5*e^
5-15*B*a^4*b*d*e^4+40*B*a^3*b^2*d^2*e^3-50*B*a^2*b^3*d^3*e^2+30*B*a*b^4*d^4*e-7*B*b^5*d^5)/e^8/(e*x+d)^12-5/11
*b^2*(4*A*a^3*b*e^4-12*A*a^2*b^2*d*e^3+12*A*a*b^3*d^2*e^2-4*A*b^4*d^3*e+3*B*a^4*e^4-16*B*a^3*b*d*e^3+30*B*a^2*
b^2*d^2*e^2-24*B*a*b^3*d^3*e+7*B*b^4*d^4)/e^8/(e*x+d)^11-1/2*b^3*(3*A*a^2*b*e^3-6*A*a*b^2*d*e^2+3*A*b^3*d^2*e+
4*B*a^3*e^3-15*B*a^2*b*d*e^2+18*B*a*b^2*d^2*e-7*B*b^3*d^3)/e^8/(e*x+d)^10-1/3*b^4*(2*A*a*b*e^2-2*A*b^2*d*e+5*B
*a^2*e^2-12*B*a*b*d*e+7*B*b^2*d^2)/e^8/(e*x+d)^9-1/7*b^6*B/e^8/(e*x+d)^7

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maxima [B]  time = 0.86, size = 902, normalized size = 3.09 \begin {gather*} -\frac {3432 \, B b^{6} e^{7} x^{7} + B b^{6} d^{7} + 1716 \, A a^{6} e^{7} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{2} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{3} + 30 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{4} + 66 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{5} + 132 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{6} + 3003 \, {\left (B b^{6} d e^{6} + {\left (6 \, B a b^{5} + A b^{6}\right )} e^{7}\right )} x^{6} + 2002 \, {\left (B b^{6} d^{2} e^{5} + {\left (6 \, B a b^{5} + A b^{6}\right )} d e^{6} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{7}\right )} x^{5} + 1001 \, {\left (B b^{6} d^{3} e^{4} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e^{5} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{6} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{7}\right )} x^{4} + 364 \, {\left (B b^{6} d^{4} e^{3} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e^{4} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{5} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{6} + 30 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{7}\right )} x^{3} + 91 \, {\left (B b^{6} d^{5} e^{2} + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e^{3} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{4} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{5} + 30 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{6} + 66 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{7}\right )} x^{2} + 14 \, {\left (B b^{6} d^{6} e + {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} e^{2} + 4 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e^{3} + 12 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{4} + 30 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{5} + 66 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{6} + 132 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{7}\right )} x}{24024 \, {\left (e^{22} x^{14} + 14 \, d e^{21} x^{13} + 91 \, d^{2} e^{20} x^{12} + 364 \, d^{3} e^{19} x^{11} + 1001 \, d^{4} e^{18} x^{10} + 2002 \, d^{5} e^{17} x^{9} + 3003 \, d^{6} e^{16} x^{8} + 3432 \, d^{7} e^{15} x^{7} + 3003 \, d^{8} e^{14} x^{6} + 2002 \, d^{9} e^{13} x^{5} + 1001 \, d^{10} e^{12} x^{4} + 364 \, d^{11} e^{11} x^{3} + 91 \, d^{12} e^{10} x^{2} + 14 \, d^{13} e^{9} x + d^{14} e^{8}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)/(e*x+d)^15,x, algorithm="maxima")

[Out]

-1/24024*(3432*B*b^6*e^7*x^7 + B*b^6*d^7 + 1716*A*a^6*e^7 + (6*B*a*b^5 + A*b^6)*d^6*e + 4*(5*B*a^2*b^4 + 2*A*a
*b^5)*d^5*e^2 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 66*(2*B*a^5*
b + 5*A*a^4*b^2)*d^2*e^5 + 132*(B*a^6 + 6*A*a^5*b)*d*e^6 + 3003*(B*b^6*d*e^6 + (6*B*a*b^5 + A*b^6)*e^7)*x^6 +
2002*(B*b^6*d^2*e^5 + (6*B*a*b^5 + A*b^6)*d*e^6 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 1001*(B*b^6*d^3*e^4 +
(6*B*a*b^5 + A*b^6)*d^2*e^5 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 3
64*(B*b^6*d^4*e^3 + (6*B*a*b^5 + A*b^6)*d^3*e^4 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 12*(4*B*a^3*b^3 + 3*A*
a^2*b^4)*d*e^6 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 91*(B*b^6*d^5*e^2 + (6*B*a*b^5 + A*b^6)*d^4*e^3 + 4
*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d
*e^6 + 66*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 14*(B*b^6*d^6*e + (6*B*a*b^5 + A*b^6)*d^5*e^2 + 4*(5*B*a^2*b^4
+ 2*A*a*b^5)*d^4*e^3 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 66*(2
*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 132*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^22*x^14 + 14*d*e^21*x^13 + 91*d^2*e^20*x^12
+ 364*d^3*e^19*x^11 + 1001*d^4*e^18*x^10 + 2002*d^5*e^17*x^9 + 3003*d^6*e^16*x^8 + 3432*d^7*e^15*x^7 + 3003*d
^8*e^14*x^6 + 2002*d^9*e^13*x^5 + 1001*d^10*e^12*x^4 + 364*d^11*e^11*x^3 + 91*d^12*e^10*x^2 + 14*d^13*e^9*x +
d^14*e^8)

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mupad [B]  time = 2.21, size = 918, normalized size = 3.14 \begin {gather*} -\frac {\frac {132\,B\,a^6\,d\,e^6+1716\,A\,a^6\,e^7+132\,B\,a^5\,b\,d^2\,e^5+792\,A\,a^5\,b\,d\,e^6+90\,B\,a^4\,b^2\,d^3\,e^4+330\,A\,a^4\,b^2\,d^2\,e^5+48\,B\,a^3\,b^3\,d^4\,e^3+120\,A\,a^3\,b^3\,d^3\,e^4+20\,B\,a^2\,b^4\,d^5\,e^2+36\,A\,a^2\,b^4\,d^4\,e^3+6\,B\,a\,b^5\,d^6\,e+8\,A\,a\,b^5\,d^5\,e^2+B\,b^6\,d^7+A\,b^6\,d^6\,e}{24024\,e^8}+\frac {x\,\left (132\,B\,a^6\,e^6+132\,B\,a^5\,b\,d\,e^5+792\,A\,a^5\,b\,e^6+90\,B\,a^4\,b^2\,d^2\,e^4+330\,A\,a^4\,b^2\,d\,e^5+48\,B\,a^3\,b^3\,d^3\,e^3+120\,A\,a^3\,b^3\,d^2\,e^4+20\,B\,a^2\,b^4\,d^4\,e^2+36\,A\,a^2\,b^4\,d^3\,e^3+6\,B\,a\,b^5\,d^5\,e+8\,A\,a\,b^5\,d^4\,e^2+B\,b^6\,d^6+A\,b^6\,d^5\,e\right )}{1716\,e^7}+\frac {b^3\,x^4\,\left (48\,B\,a^3\,e^3+20\,B\,a^2\,b\,d\,e^2+36\,A\,a^2\,b\,e^3+6\,B\,a\,b^2\,d^2\,e+8\,A\,a\,b^2\,d\,e^2+B\,b^3\,d^3+A\,b^3\,d^2\,e\right )}{24\,e^4}+\frac {b^5\,x^6\,\left (A\,b\,e+6\,B\,a\,e+B\,b\,d\right )}{8\,e^2}+\frac {b\,x^2\,\left (132\,B\,a^5\,e^5+90\,B\,a^4\,b\,d\,e^4+330\,A\,a^4\,b\,e^5+48\,B\,a^3\,b^2\,d^2\,e^3+120\,A\,a^3\,b^2\,d\,e^4+20\,B\,a^2\,b^3\,d^3\,e^2+36\,A\,a^2\,b^3\,d^2\,e^3+6\,B\,a\,b^4\,d^4\,e+8\,A\,a\,b^4\,d^3\,e^2+B\,b^5\,d^5+A\,b^5\,d^4\,e\right )}{264\,e^6}+\frac {b^2\,x^3\,\left (90\,B\,a^4\,e^4+48\,B\,a^3\,b\,d\,e^3+120\,A\,a^3\,b\,e^4+20\,B\,a^2\,b^2\,d^2\,e^2+36\,A\,a^2\,b^2\,d\,e^3+6\,B\,a\,b^3\,d^3\,e+8\,A\,a\,b^3\,d^2\,e^2+B\,b^4\,d^4+A\,b^4\,d^3\,e\right )}{66\,e^5}+\frac {b^4\,x^5\,\left (20\,B\,a^2\,e^2+6\,B\,a\,b\,d\,e+8\,A\,a\,b\,e^2+B\,b^2\,d^2+A\,b^2\,d\,e\right )}{12\,e^3}+\frac {B\,b^6\,x^7}{7\,e}}{d^{14}+14\,d^{13}\,e\,x+91\,d^{12}\,e^2\,x^2+364\,d^{11}\,e^3\,x^3+1001\,d^{10}\,e^4\,x^4+2002\,d^9\,e^5\,x^5+3003\,d^8\,e^6\,x^6+3432\,d^7\,e^7\,x^7+3003\,d^6\,e^8\,x^8+2002\,d^5\,e^9\,x^9+1001\,d^4\,e^{10}\,x^{10}+364\,d^3\,e^{11}\,x^{11}+91\,d^2\,e^{12}\,x^{12}+14\,d\,e^{13}\,x^{13}+e^{14}\,x^{14}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((A + B*x)*(a + b*x)^6)/(d + e*x)^15,x)

[Out]

-((1716*A*a^6*e^7 + B*b^6*d^7 + A*b^6*d^6*e + 132*B*a^6*d*e^6 + 8*A*a*b^5*d^5*e^2 + 132*B*a^5*b*d^2*e^5 + 36*A
*a^2*b^4*d^4*e^3 + 120*A*a^3*b^3*d^3*e^4 + 330*A*a^4*b^2*d^2*e^5 + 20*B*a^2*b^4*d^5*e^2 + 48*B*a^3*b^3*d^4*e^3
+ 90*B*a^4*b^2*d^3*e^4 + 792*A*a^5*b*d*e^6 + 6*B*a*b^5*d^6*e)/(24024*e^8) + (x*(132*B*a^6*e^6 + B*b^6*d^6 + 7
92*A*a^5*b*e^6 + A*b^6*d^5*e + 8*A*a*b^5*d^4*e^2 + 330*A*a^4*b^2*d*e^5 + 36*A*a^2*b^4*d^3*e^3 + 120*A*a^3*b^3*
d^2*e^4 + 20*B*a^2*b^4*d^4*e^2 + 48*B*a^3*b^3*d^3*e^3 + 90*B*a^4*b^2*d^2*e^4 + 6*B*a*b^5*d^5*e + 132*B*a^5*b*d
*e^5))/(1716*e^7) + (b^3*x^4*(48*B*a^3*e^3 + B*b^3*d^3 + 36*A*a^2*b*e^3 + A*b^3*d^2*e + 8*A*a*b^2*d*e^2 + 6*B*
a*b^2*d^2*e + 20*B*a^2*b*d*e^2))/(24*e^4) + (b^5*x^6*(A*b*e + 6*B*a*e + B*b*d))/(8*e^2) + (b*x^2*(132*B*a^5*e^
5 + B*b^5*d^5 + 330*A*a^4*b*e^5 + A*b^5*d^4*e + 8*A*a*b^4*d^3*e^2 + 120*A*a^3*b^2*d*e^4 + 36*A*a^2*b^3*d^2*e^3
+ 20*B*a^2*b^3*d^3*e^2 + 48*B*a^3*b^2*d^2*e^3 + 6*B*a*b^4*d^4*e + 90*B*a^4*b*d*e^4))/(264*e^6) + (b^2*x^3*(90
*B*a^4*e^4 + B*b^4*d^4 + 120*A*a^3*b*e^4 + A*b^4*d^3*e + 8*A*a*b^3*d^2*e^2 + 36*A*a^2*b^2*d*e^3 + 20*B*a^2*b^2
*d^2*e^2 + 6*B*a*b^3*d^3*e + 48*B*a^3*b*d*e^3))/(66*e^5) + (b^4*x^5*(20*B*a^2*e^2 + B*b^2*d^2 + 8*A*a*b*e^2 +
A*b^2*d*e + 6*B*a*b*d*e))/(12*e^3) + (B*b^6*x^7)/(7*e))/(d^14 + e^14*x^14 + 14*d*e^13*x^13 + 91*d^12*e^2*x^2 +
364*d^11*e^3*x^3 + 1001*d^10*e^4*x^4 + 2002*d^9*e^5*x^5 + 3003*d^8*e^6*x^6 + 3432*d^7*e^7*x^7 + 3003*d^6*e^8*
x^8 + 2002*d^5*e^9*x^9 + 1001*d^4*e^10*x^10 + 364*d^3*e^11*x^11 + 91*d^2*e^12*x^12 + 14*d^13*e*x)

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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((b*x+a)**6*(B*x+A)/(e*x+d)**15,x)

[Out]

Timed out

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