3.3.0 ∫ A+B log(e(a+bx) c+dx ) _______________________

Integrand size = 27, antiderivative size = 379 \[ \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^5} \, dx=-\frac {B (b c-a d)}{12 (b f-a g) (d f-c g) (f+g x)^3}-\frac {B (b c-a d) (2 b d f-b c g-a d g)}{8 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}-\frac {B (b c-a d) \left (a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left (3 d^2 f^2-3 c d f g+c^2 g^2\right )\right )}{4 (b f-a g)^3 (d f-c g)^3 (f+g x)}+\frac {b^4 B \log (a+b x)}{4 g (b f-a g)^4}-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{4 g (f+g x)^4}-\frac {B d^4 \log (c+d x)}{4 g (d f-c g)^4}-\frac {B (b c-a d) (2 b d f-b c g-a d g) \left (2 a b d^2 f g-a^2 d^2 g^2-b^2 \left (2 d^2 f^2-2 c d f g+c^2 g^2\right )\right ) \log (f+g x)}{4 (b f-a g)^4 (d f-c g)^4} \]

-1/12*B*(-a*d+b*c)/(-a*g+b*f)/(-c*g+d*f)/(g*x+f)^3-1/8*B*(-a*d+b*c)*(-a*d*g-b*c*g+2*b*d*f)/(-a*g+b*f)^2/(-c*g+

d*f)^2/(g*x+f)^2-1/4*B*(-a*d+b*c)*(a^2*d^2*g^2-a*b*d*g*(-c*g+3*d*f)+b^2*(c^2*g^2-3*c*d*f*g+3*d^2*f^2))/(-a*g+b

*f)^3/(-c*g+d*f)^3/(g*x+f)+1/4*b^4*B*ln(b*x+a)/g/(-a*g+b*f)^4+1/4*(-A-B*ln(e*(b*x+a)/(d*x+c)))/g/(g*x+f)^4-1/4

*B*d^4*ln(d*x+c)/g/(-c*g+d*f)^4-1/4*B*(-a*d+b*c)*(-a*d*g-b*c*g+2*b*d*f)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(c^2*g^

Rubi [A] (veriﬁed)

Time = 0.33 (sec) , antiderivative size = 379, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {2548, 84} \[ \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^5} \, dx=-\frac {B (b c-a d) \left (a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left (c^2 g^2-3 c d f g+3 d^2 f^2\right )\right )}{4 (f+g x) (b f-a g)^3 (d f-c g)^3}-\frac {B (b c-a d) \log (f+g x) (-a d g-b c g+2 b d f) \left (-a^2 d^2 g^2+2 a b d^2 f g-\left (b^2 \left (c^2 g^2-2 c d f g+2 d^2 f^2\right )\right )\right )}{4 (b f-a g)^4 (d f-c g)^4}-\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right )+A}{4 g (f+g x)^4}+\frac {b^4 B \log (a+b x)}{4 g (b f-a g)^4}-\frac {B (b c-a d) (-a d g-b c g+2 b d f)}{8 (f+g x)^2 (b f-a g)^2 (d f-c g)^2}-\frac {B (b c-a d)}{12 (f+g x)^3 (b f-a g) (d f-c g)}-\frac {B d^4 \log (c+d x)}{4 g (d f-c g)^4} \]

-1/12*(B*(b*c - a*d))/((b*f - a*g)*(d*f - c*g)*(f + g*x)^3) - (B*(b*c - a*d)*(2*b*d*f - b*c*g - a*d*g))/(8*(b*

f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (B*(b*c - a*d)*(a^2*d^2*g^2 - a*b*d*g*(3*d*f - c*g) + b^2*(3*d^2*f^2 -

3*c*d*f*g + c^2*g^2)))/(4*(b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*B*Log[a + b*x])/(4*g*(b*f - a*g)^4) -

(A + B*Log[(e*(a + b*x))/(c + d*x)])/(4*g*(f + g*x)^4) - (B*d^4*Log[c + d*x])/(4*g*(d*f - c*g)^4) - (B*(b*c -

a*d)*(2*b*d*f - b*c*g - a*d*g)*(2*a*b*d^2*f*g - a^2*d^2*g^2 - b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*Log[f +

Int[((e_.) + (f_.)*(x_))^(p_.)/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :> Int[ExpandIntegrand[(

e + f*x)^p/((a + b*x)*(c + d*x)), x], x] /; FreeQ[{a, b, c, d, e, f}, x] && IntegerQ[p]

Int[((A_.) + Log[(e_.)*((a_.) + (b_.)*(x_))^(n_.)*((c_.) + (d_.)*(x_))^(mn_)]*(B_.))*((f_.) + (g_.)*(x_))^(m_.

), x_Symbol] :> Simp[(f + g*x)^(m + 1)*((A + B*Log[e*((a + b*x)^n/(c + d*x)^n)])/(g*(m + 1))), x] - Dist[B*n*(

(b*c - a*d)/(g*(m + 1))), Int[(f + g*x)^(m + 1)/((a + b*x)*(c + d*x)), x], x] /; FreeQ[{a, b, c, d, e, f, g, A

, B, m, n}, x] && EqQ[n + mn, 0] && NeQ[b*c - a*d, 0] && NeQ[m, -1] && !(EqQ[m, -2] && IntegerQ[n])

Rubi steps \begin{align*} \text {integral}& = -\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{4 g (f+g x)^4}+\frac {(B (b c-a d)) \int \frac {1}{(a+b x) (c+d x) (f+g x)^4} \, dx}{4 g} \\ & = -\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{4 g (f+g x)^4}+\frac {(B (b c-a d)) \int \left (\frac {b^5}{(b c-a d) (b f-a g)^4 (a+b x)}-\frac {d^5}{(b c-a d) (-d f+c g)^4 (c+d x)}+\frac {g^2}{(b f-a g) (d f-c g) (f+g x)^4}-\frac {g^2 (-2 b d f+b c g+a d g)}{(b f-a g)^2 (d f-c g)^2 (f+g x)^3}+\frac {g^2 \left (a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left (3 d^2 f^2-3 c d f g+c^2 g^2\right )\right )}{(b f-a g)^3 (d f-c g)^3 (f+g x)^2}+\frac {g^2 (2 b d f-b c g-a d g) \left (2 b^2 d^2 f^2-2 b^2 c d f g-2 a b d^2 f g+b^2 c^2 g^2+a^2 d^2 g^2\right )}{(b f-a g)^4 (d f-c g)^4 (f+g x)}\right ) \, dx}{4 g} \\ & = -\frac {B (b c-a d)}{12 (b f-a g) (d f-c g) (f+g x)^3}-\frac {B (b c-a d) (2 b d f-b c g-a d g)}{8 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}-\frac {B (b c-a d) \left (a^2 d^2 g^2-a b d g (3 d f-c g)+b^2 \left (3 d^2 f^2-3 c d f g+c^2 g^2\right )\right )}{4 (b f-a g)^3 (d f-c g)^3 (f+g x)}+\frac {b^4 B \log (a+b x)}{4 g (b f-a g)^4}-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{4 g (f+g x)^4}-\frac {B d^4 \log (c+d x)}{4 g (d f-c g)^4}-\frac {B (b c-a d) (2 b d f-b c g-a d g) \left (2 a b d^2 f g-a^2 d^2 g^2-b^2 \left (2 d^2 f^2-2 c d f g+c^2 g^2\right )\right ) \log (f+g x)}{4 (b f-a g)^4 (d f-c g)^4} \\ \end{align*}

Mathematica [A] (veriﬁed)

Time = 0.53 (sec) , antiderivative size = 355, normalized size of antiderivative = 0.94 \[ \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^5} \, dx=\frac {-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^4}+B (b c-a d) \left (-\frac {g}{3 (b f-a g) (d f-c g) (f+g x)^3}+\frac {g (-2 b d f+b c g+a d g)}{2 (b f-a g)^2 (d f-c g)^2 (f+g x)^2}-\frac {g \left (a^2 d^2 g^2+a b d g (-3 d f+c g)+b^2 \left (3 d^2 f^2-3 c d f g+c^2 g^2\right )\right )}{(b f-a g)^3 (d f-c g)^3 (f+g x)}+\frac {b^4 \log (a+b x)}{(b c-a d) (b f-a g)^4}-\frac {d^4 \log (c+d x)}{(b c-a d) (d f-c g)^4}-\frac {g (-2 b d f+b c g+a d g) \left (-2 a b d^2 f g+a^2 d^2 g^2+b^2 \left (2 d^2 f^2-2 c d f g+c^2 g^2\right )\right ) \log (f+g x)}{(b f-a g)^4 (d f-c g)^4}\right )}{4 g} \]

(-((A + B*Log[(e*(a + b*x))/(c + d*x)])/(f + g*x)^4) + B*(b*c - a*d)*(-1/3*g/((b*f - a*g)*(d*f - c*g)*(f + g*x

)^3) + (g*(-2*b*d*f + b*c*g + a*d*g))/(2*(b*f - a*g)^2*(d*f - c*g)^2*(f + g*x)^2) - (g*(a^2*d^2*g^2 + a*b*d*g*

(-3*d*f + c*g) + b^2*(3*d^2*f^2 - 3*c*d*f*g + c^2*g^2)))/((b*f - a*g)^3*(d*f - c*g)^3*(f + g*x)) + (b^4*Log[a

+ b*x])/((b*c - a*d)*(b*f - a*g)^4) - (d^4*Log[c + d*x])/((b*c - a*d)*(d*f - c*g)^4) - (g*(-2*b*d*f + b*c*g +

a*d*g)*(-2*a*b*d^2*f*g + a^2*d^2*g^2 + b^2*(2*d^2*f^2 - 2*c*d*f*g + c^2*g^2))*Log[f + g*x])/((b*f - a*g)^4*(d*

Maple [B] (veriﬁed)

Leaf count of result is larger than twice the leaf count of optimal. \(2849\) vs. \(2(368)=736\).

Time = 6.65 (sec) , antiderivative size = 2850, normalized size of antiderivative = 7.52


method	result	size

parts	\(\text {Expression too large to display}\)	\(2850\)
derivativedivides	\(\text {Expression too large to display}\)	\(3309\)
default	\(\text {Expression too large to display}\)	\(3309\)
risch	\(\text {Expression too large to display}\)	\(4450\)
parallelrisch	\(\text {Expression too large to display}\)	\(5539\)

-1/4*A/(g*x+f)^4/g-B/d^2*(a*d-b*c)*e*(-3*d^4*e*(a*d-b*c)*g/(c*g-d*f)^3*(-1/2/(a*g-b*f)^2/e^2*(1/(c*g-d*f)*ln(c

*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f)+e*(a*g-b*f)/(c*g-d*f)/(c*g*(b*

e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f))+1/2*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))

*(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-2*a*e*g+2*b*e*f)*(b*e/d+(a*d-b*c)*e/d/(d

*x+c))/(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f)^2/(a*g-b*f)^2/e^2)-3*

d^3*e^2*g^2*(a^2*d^2-2*a*b*c*d+b^2*c^2)/(c*g-d*f)^3*(-1/3/(a*g-b*f)/(a^2*g^2-2*a*b*f*g+b^2*f^2)/e^3*(1/2*e^2*(

a^2*g^2-2*a*b*f*g+b^2*f^2)/(c*g-d*f)/(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*

g+b*e*f)^2-1/(c*g-d*f)*ln(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f)-e*(

a*g-b*f)/(c*g-d*f)/(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f))-1/3*ln(b

*e/d+(a*d-b*c)*e/d/(d*x+c))*(3*a^2*e^2*g^2-6*a*b*e^2*f*g-3*a*c*e*g^2*(b*e/d+(a*d-b*c)*e/d/(d*x+c))+3*a*d*e*f*g

*(b*e/d+(a*d-b*c)*e/d/(d*x+c))+3*b^2*e^2*f^2+3*b*c*e*f*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-3*b*d*e*f^2*(b*e/d+(a*d

-b*c)*e/d/(d*x+c))+c^2*g^2*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2-2*c*d*f*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2+d^2*f^2*(

b*e/d+(a*d-b*c)*e/d/(d*x+c))^2)*(b*e/d+(a*d-b*c)*e/d/(d*x+c))/(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a

*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f)^3/(a*g-b*f)/(a^2*g^2-2*a*b*f*g+b^2*f^2)/e^3)-d^5/(c*g-d*f)^3*(1/e/(a*g-b*f)*

ln((c*g-d*f)*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f)/(c*g-d*f)-ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*(b*e/d+(a*d-

b*c)*e/d/(d*x+c))/e/(a*g-b*f)/(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f

))-d^2*e^3*g^3*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/(c*g-d*f)^3*(-1/4/(a*g-b*f)^2/(a^2*g^2-2*a*b*f*g+

b^2*f^2)/e^4*(-1/2*e^2*(a^2*g^2-2*a*b*f*g+b^2*f^2)/(c*g-d*f)/(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*

d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f)^2+1/(c*g-d*f)*ln(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(

d*x+c))-a*e*g+b*e*f)+1/3*e^3*(a^3*g^3-3*a^2*b*f*g^2+3*a*b^2*f^2*g-b^3*f^3)/(c*g-d*f)/(c*g*(b*e/d+(a*d-b*c)*e/d

/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f)^3+e*(a*g-b*f)/(c*g-d*f)/(c*g*(b*e/d+(a*d-b*c)*e/d/(d*

x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-a*e*g+b*e*f))+1/4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*(b*e/d+(a*d-b*c)*e/d

/(d*x+c))*(c^3*g^3*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^3-3*c^2*d*f*g^2*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^3+3*c*d^2*f^2*g

*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^3-d^3*f^3*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^3-4*a*c^2*e*g^3*(b*e/d+(a*d-b*c)*e/d/(d

*x+c))^2+8*a*c*d*e*f*g^2*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2-4*a*d^2*e*f^2*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2+4*b*c

^2*e*f*g^2*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2-8*b*c*d*e*f^2*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2+4*b*d^2*e*f^3*(b*e/

d+(a*d-b*c)*e/d/(d*x+c))^2+6*a^2*c*e^2*g^3*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-6*a^2*d*e^2*f*g^2*(b*e/d+(a*d-b*c)*e/

d/(d*x+c))-12*a*b*c*e^2*f*g^2*(b*e/d+(a*d-b*c)*e/d/(d*x+c))+12*a*b*d*e^2*f^2*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))+6

*b^2*c*e^2*f^2*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-6*b^2*d*e^2*f^3*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-4*a^3*e^3*g^3+12*

a^2*b*e^3*f*g^2-12*a*b^2*e^3*f^2*g+4*b^3*e^3*f^3)/(c*g*(b*e/d+(a*d-b*c)*e/d/(d*x+c))-d*f*(b*e/d+(a*d-b*c)*e/d/

(d*x+c))-a*e*g+b*e*f)^4/(a*g-b*f)^2/(a^2*g^2-2*a*b*f*g+b^2*f^2)/e^4))

Fricas [F(-1)]

Timed out. \[ \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^5} \, dx=\text {Timed out} \]

integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(g*x+f)^5,x, algorithm="fricas")

Sympy [F(-1)]

Timed out. \[ \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^5} \, dx=\text {Timed out} \]

Maxima [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1757 vs. \(2 (365) = 730\).

Time = 0.33 (sec) , antiderivative size = 1757, normalized size of antiderivative = 4.64 \[ \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^5} \, dx=\text {Too large to display} \]

integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(g*x+f)^5,x, algorithm="maxima")

1/24*(6*b^4*log(b*x + a)/(b^4*f^4*g - 4*a*b^3*f^3*g^2 + 6*a^2*b^2*f^2*g^3 - 4*a^3*b*f*g^4 + a^4*g^5) - 6*d^4*l

og(d*x + c)/(d^4*f^4*g - 4*c*d^3*f^3*g^2 + 6*c^2*d^2*f^2*g^3 - 4*c^3*d*f*g^4 + c^4*g^5) + 6*(4*(b^4*c*d^3 - a*

b^3*d^4)*f^3 - 6*(b^4*c^2*d^2 - a^2*b^2*d^4)*f^2*g + 4*(b^4*c^3*d - a^3*b*d^4)*f*g^2 - (b^4*c^4 - a^4*d^4)*g^3

)*log(g*x + f)/(b^4*d^4*f^8 + a^4*c^4*g^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*f^7*g + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3

+ 3*a^2*b^2*d^4)*f^6*g^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*f^5*g^3 + (b^4*c^4 +

16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*f^4*g^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*

a^3*b*c^2*d^2 + a^4*c*d^3)*f^3*g^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f^2*g^6 - 4*(a^3*b*c^4

+ a^4*c^3*d)*f*g^7) - (26*(b^3*c*d^2 - a*b^2*d^3)*f^4 - 31*(b^3*c^2*d - a^2*b*d^3)*f^3*g + (11*b^3*c^3 + 15*a*

b^2*c^2*d - 15*a^2*b*c*d^2 - 11*a^3*d^3)*f^2*g^2 - 7*(a*b^2*c^3 - a^3*c*d^2)*f*g^3 + 2*(a^2*b*c^3 - a^3*c^2*d)

*g^4 + 6*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2*g^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g^3 + (b^3*c^3 - a^3*d^3)*g^4)*x^2 +

3*(14*(b^3*c*d^2 - a*b^2*d^3)*f^3*g - 15*(b^3*c^2*d - a^2*b*d^3)*f^2*g^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2

*b*c*d^2 - 5*a^3*d^3)*f*g^3 - (a*b^2*c^3 - a^3*c*d^2)*g^4)*x)/(b^3*d^3*f^9 + a^3*c^3*f^3*g^6 - 3*(b^3*c*d^2 +

a*b^2*d^3)*f^8*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^7*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^

2 + a^3*d^3)*f^6*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^5*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^4*g^5 +

(b^3*d^3*f^6*g^3 + a^3*c^3*g^9 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g^4 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3

)*f^4*g^5 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^6 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c

*d^2)*f^2*g^7 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^8)*x^3 + 3*(b^3*d^3*f^7*g^2 + a^3*c^3*f*g^8 - 3*(b^3*c*d^2 + a*b

^2*d^3)*f^6*g^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^5*g^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2

+ a^3*d^3)*f^4*g^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3*g^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^2*g^7)*x

^2 + 3*(b^3*d^3*f^8*g + a^3*c^3*f^2*g^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^7*g^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a

^2*b*d^3)*f^6*g^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^5*g^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d

+ a^3*c*d^2)*f^4*g^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^3*g^6)*x) - 6*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^5*x^

4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g))*B - 1/4*A/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 20791 vs. \(2 (365) = 730\).

Time = 0.99 (sec) , antiderivative size = 20791, normalized size of antiderivative = 54.86 \[ \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^5} \, dx=\text {Too large to display} \]

integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(g*x+f)^5,x, algorithm="giac")

1/24*(6*(4*B*b^5*c^2*d^3*e*f^3 - 8*B*a*b^4*c*d^4*e*f^3 + 4*B*a^2*b^3*d^5*e*f^3 - 6*B*b^5*c^3*d^2*e*f^2*g + 6*B

*a*b^4*c^2*d^3*e*f^2*g + 6*B*a^2*b^3*c*d^4*e*f^2*g - 6*B*a^3*b^2*d^5*e*f^2*g + 4*B*b^5*c^4*d*e*f*g^2 - 4*B*a*b

^4*c^3*d^2*e*f*g^2 - 4*B*a^3*b^2*c*d^4*e*f*g^2 + 4*B*a^4*b*d^5*e*f*g^2 - B*b^5*c^5*e*g^3 + B*a*b^4*c^4*d*e*g^3

+ B*a^4*b*c*d^4*e*g^3 - B*a^5*d^5*e*g^3)*log(-b*e*f + a*e*g + (b*e*x + a*e)*d*f/(d*x + c) - (b*e*x + a*e)*c*g

/(d*x + c))/(b^4*d^4*f^8 - 4*b^4*c*d^3*f^7*g - 4*a*b^3*d^4*f^7*g + 6*b^4*c^2*d^2*f^6*g^2 + 16*a*b^3*c*d^3*f^6*

g^2 + 6*a^2*b^2*d^4*f^6*g^2 - 4*b^4*c^3*d*f^5*g^3 - 24*a*b^3*c^2*d^2*f^5*g^3 - 24*a^2*b^2*c*d^3*f^5*g^3 - 4*a^

3*b*d^4*f^5*g^3 + b^4*c^4*f^4*g^4 + 16*a*b^3*c^3*d*f^4*g^4 + 36*a^2*b^2*c^2*d^2*f^4*g^4 + 16*a^3*b*c*d^3*f^4*g

^4 + a^4*d^4*f^4*g^4 - 4*a*b^3*c^4*f^3*g^5 - 24*a^2*b^2*c^3*d*f^3*g^5 - 24*a^3*b*c^2*d^2*f^3*g^5 - 4*a^4*c*d^3

*f^3*g^5 + 6*a^2*b^2*c^4*f^2*g^6 + 16*a^3*b*c^3*d*f^2*g^6 + 6*a^4*c^2*d^2*f^2*g^6 - 4*a^3*b*c^4*f*g^7 - 4*a^4*

c^3*d*f*g^7 + a^4*c^4*g^8) + 6*(4*B*b^5*c^2*d^3*e^5*f^3 - 8*B*a*b^4*c*d^4*e^5*f^3 + 4*B*a^2*b^3*d^5*e^5*f^3 -

6*B*b^5*c^3*d^2*e^5*f^2*g + 6*B*a*b^4*c^2*d^3*e^5*f^2*g + 6*B*a^2*b^3*c*d^4*e^5*f^2*g - 6*B*a^3*b^2*d^5*e^5*f^

2*g + 4*B*b^5*c^4*d*e^5*f*g^2 - 4*B*a*b^4*c^3*d^2*e^5*f*g^2 - 4*B*a^3*b^2*c*d^4*e^5*f*g^2 + 4*B*a^4*b*d^5*e^5*

f*g^2 - B*b^5*c^5*e^5*g^3 + B*a*b^4*c^4*d*e^5*g^3 + B*a^4*b*c*d^4*e^5*g^3 - B*a^5*d^5*e^5*g^3 - 12*(b*e*x + a*

e)*B*b^4*c^2*d^4*e^4*f^3/(d*x + c) + 24*(b*e*x + a*e)*B*a*b^3*c*d^5*e^4*f^3/(d*x + c) - 12*(b*e*x + a*e)*B*a^2

*b^2*d^6*e^4*f^3/(d*x + c) + 24*(b*e*x + a*e)*B*b^4*c^3*d^3*e^4*f^2*g/(d*x + c) - 36*(b*e*x + a*e)*B*a*b^3*c^2

*d^4*e^4*f^2*g/(d*x + c) + 12*(b*e*x + a*e)*B*a^3*b*d^6*e^4*f^2*g/(d*x + c) - 16*(b*e*x + a*e)*B*b^4*c^4*d^2*e

^4*f*g^2/(d*x + c) + 16*(b*e*x + a*e)*B*a*b^3*c^3*d^3*e^4*f*g^2/(d*x + c) + 12*(b*e*x + a*e)*B*a^2*b^2*c^2*d^4

*e^4*f*g^2/(d*x + c) - 8*(b*e*x + a*e)*B*a^3*b*c*d^5*e^4*f*g^2/(d*x + c) - 4*(b*e*x + a*e)*B*a^4*d^6*e^4*f*g^2

/(d*x + c) + 4*(b*e*x + a*e)*B*b^4*c^5*d*e^4*g^3/(d*x + c) - 4*(b*e*x + a*e)*B*a*b^3*c^4*d^2*e^4*g^3/(d*x + c)

- 4*(b*e*x + a*e)*B*a^3*b*c^2*d^4*e^4*g^3/(d*x + c) + 4*(b*e*x + a*e)*B*a^4*c*d^5*e^4*g^3/(d*x + c) + 12*(b*e

*x + a*e)^2*B*b^3*c^2*d^5*e^3*f^3/(d*x + c)^2 - 24*(b*e*x + a*e)^2*B*a*b^2*c*d^6*e^3*f^3/(d*x + c)^2 + 12*(b*e

*x + a*e)^2*B*a^2*b*d^7*e^3*f^3/(d*x + c)^2 - 30*(b*e*x + a*e)^2*B*b^3*c^3*d^4*e^3*f^2*g/(d*x + c)^2 + 54*(b*e

*x + a*e)^2*B*a*b^2*c^2*d^5*e^3*f^2*g/(d*x + c)^2 - 18*(b*e*x + a*e)^2*B*a^2*b*c*d^6*e^3*f^2*g/(d*x + c)^2 - 6

*(b*e*x + a*e)^2*B*a^3*d^7*e^3*f^2*g/(d*x + c)^2 + 24*(b*e*x + a*e)^2*B*b^3*c^4*d^3*e^3*f*g^2/(d*x + c)^2 - 36

*(b*e*x + a*e)^2*B*a*b^2*c^3*d^4*e^3*f*g^2/(d*x + c)^2 + 12*(b*e*x + a*e)^2*B*a^3*c*d^6*e^3*f*g^2/(d*x + c)^2

- 6*(b*e*x + a*e)^2*B*b^3*c^5*d^2*e^3*g^3/(d*x + c)^2 + 6*(b*e*x + a*e)^2*B*a*b^2*c^4*d^3*e^3*g^3/(d*x + c)^2

+ 6*(b*e*x + a*e)^2*B*a^2*b*c^3*d^4*e^3*g^3/(d*x + c)^2 - 6*(b*e*x + a*e)^2*B*a^3*c^2*d^5*e^3*g^3/(d*x + c)^2

- 4*(b*e*x + a*e)^3*B*b^2*c^2*d^6*e^2*f^3/(d*x + c)^3 + 8*(b*e*x + a*e)^3*B*a*b*c*d^7*e^2*f^3/(d*x + c)^3 - 4*

(b*e*x + a*e)^3*B*a^2*d^8*e^2*f^3/(d*x + c)^3 + 12*(b*e*x + a*e)^3*B*b^2*c^3*d^5*e^2*f^2*g/(d*x + c)^3 - 24*(b

*e*x + a*e)^3*B*a*b*c^2*d^6*e^2*f^2*g/(d*x + c)^3 + 12*(b*e*x + a*e)^3*B*a^2*c*d^7*e^2*f^2*g/(d*x + c)^3 - 12*

(b*e*x + a*e)^3*B*b^2*c^4*d^4*e^2*f*g^2/(d*x + c)^3 + 24*(b*e*x + a*e)^3*B*a*b*c^3*d^5*e^2*f*g^2/(d*x + c)^3 -

12*(b*e*x + a*e)^3*B*a^2*c^2*d^6*e^2*f*g^2/(d*x + c)^3 + 4*(b*e*x + a*e)^3*B*b^2*c^5*d^3*e^2*g^3/(d*x + c)^3

- 8*(b*e*x + a*e)^3*B*a*b*c^4*d^4*e^2*g^3/(d*x + c)^3 + 4*(b*e*x + a*e)^3*B*a^2*c^3*d^5*e^2*g^3/(d*x + c)^3)*l

og((b*e*x + a*e)/(d*x + c))/(b^4*d^4*e^4*f^8 - 4*b^4*c*d^3*e^4*f^7*g - 4*a*b^3*d^4*e^4*f^7*g + 6*b^4*c^2*d^2*e

^4*f^6*g^2 + 16*a*b^3*c*d^3*e^4*f^6*g^2 + 6*a^2*b^2*d^4*e^4*f^6*g^2 - 4*b^4*c^3*d*e^4*f^5*g^3 - 24*a*b^3*c^2*d

^2*e^4*f^5*g^3 - 24*a^2*b^2*c*d^3*e^4*f^5*g^3 - 4*a^3*b*d^4*e^4*f^5*g^3 + b^4*c^4*e^4*f^4*g^4 + 16*a*b^3*c^3*d

*e^4*f^4*g^4 + 36*a^2*b^2*c^2*d^2*e^4*f^4*g^4 + 16*a^3*b*c*d^3*e^4*f^4*g^4 + a^4*d^4*e^4*f^4*g^4 - 4*a*b^3*c^4

*e^4*f^3*g^5 - 24*a^2*b^2*c^3*d*e^4*f^3*g^5 - 24*a^3*b*c^2*d^2*e^4*f^3*g^5 - 4*a^4*c*d^3*e^4*f^3*g^5 + 6*a^2*b

^2*c^4*e^4*f^2*g^6 + 16*a^3*b*c^3*d*e^4*f^2*g^6 + 6*a^4*c^2*d^2*e^4*f^2*g^6 - 4*a^3*b*c^4*e^4*f*g^7 - 4*a^4*c^

3*d*e^4*f*g^7 + a^4*c^4*e^4*g^8 - 4*(b*e*x + a*e)*b^3*d^5*e^3*f^8/(d*x + c) + 20*(b*e*x + a*e)*b^3*c*d^4*e^3*f

^7*g/(d*x + c) + 12*(b*e*x + a*e)*a*b^2*d^5*e^3*f^7*g/(d*x + c) - 40*(b*e*x + a*e)*b^3*c^2*d^3*e^3*f^6*g^2/(d*

x + c) - 60*(b*e*x + a*e)*a*b^2*c*d^4*e^3*f^6*g^2/(d*x + c) - 12*(b*e*x + a*e)*a^2*b*d^5*e^3*f^6*g^2/(d*x + c)

+ 40*(b*e*x + a*e)*b^3*c^3*d^2*e^3*f^5*g^3/(d*x + c) + 120*(b*e*x + a*e)*a*b^2*c^2*d^3*e^3*f^5*g^3/(d*x + c)

+ 60*(b*e*x + a*e)*a^2*b*c*d^4*e^3*f^5*g^3/(d*x + c) + 4*(b*e*x + a*e)*a^3*d^5*e^3*f^5*g^3/(d*x + c) - 20*(b*e

*x + a*e)*b^3*c^4*d*e^3*f^4*g^4/(d*x + c) - 120*(b*e*x + a*e)*a*b^2*c^3*d^2*e^3*f^4*g^4/(d*x + c) - 120*(b*e*x

+ a*e)*a^2*b*c^2*d^3*e^3*f^4*g^4/(d*x + c) - 20*(b*e*x + a*e)*a^3*c*d^4*e^3*f^4*g^4/(d*x + c) + 4*(b*e*x + a*

e)*b^3*c^5*e^3*f^3*g^5/(d*x + c) + 60*(b*e*x + a*e)*a*b^2*c^4*d*e^3*f^3*g^5/(d*x + c) + 120*(b*e*x + a*e)*a^2*

b*c^3*d^2*e^3*f^3*g^5/(d*x + c) + 40*(b*e*x + a*e)*a^3*c^2*d^3*e^3*f^3*g^5/(d*x + c) - 12*(b*e*x + a*e)*a*b^2*

c^5*e^3*f^2*g^6/(d*x + c) - 60*(b*e*x + a*e)*a^2*b*c^4*d*e^3*f^2*g^6/(d*x + c) - 40*(b*e*x + a*e)*a^3*c^3*d^2*

e^3*f^2*g^6/(d*x + c) + 12*(b*e*x + a*e)*a^2*b*c^5*e^3*f*g^7/(d*x + c) + 20*(b*e*x + a*e)*a^3*c^4*d*e^3*f*g^7/

(d*x + c) - 4*(b*e*x + a*e)*a^3*c^5*e^3*g^8/(d*x + c) + 6*(b*e*x + a*e)^2*b^2*d^6*e^2*f^8/(d*x + c)^2 - 36*(b*

e*x + a*e)^2*b^2*c*d^5*e^2*f^7*g/(d*x + c)^2 - 12*(b*e*x + a*e)^2*a*b*d^6*e^2*f^7*g/(d*x + c)^2 + 90*(b*e*x +

a*e)^2*b^2*c^2*d^4*e^2*f^6*g^2/(d*x + c)^2 + 72*(b*e*x + a*e)^2*a*b*c*d^5*e^2*f^6*g^2/(d*x + c)^2 + 6*(b*e*x +

a*e)^2*a^2*d^6*e^2*f^6*g^2/(d*x + c)^2 - 120*(b*e*x + a*e)^2*b^2*c^3*d^3*e^2*f^5*g^3/(d*x + c)^2 - 180*(b*e*x

+ a*e)^2*a*b*c^2*d^4*e^2*f^5*g^3/(d*x + c)^2 - 36*(b*e*x + a*e)^2*a^2*c*d^5*e^2*f^5*g^3/(d*x + c)^2 + 90*(b*e

*x + a*e)^2*b^2*c^4*d^2*e^2*f^4*g^4/(d*x + c)^2 + 240*(b*e*x + a*e)^2*a*b*c^3*d^3*e^2*f^4*g^4/(d*x + c)^2 + 90

*(b*e*x + a*e)^2*a^2*c^2*d^4*e^2*f^4*g^4/(d*x + c)^2 - 36*(b*e*x + a*e)^2*b^2*c^5*d*e^2*f^3*g^5/(d*x + c)^2 -

180*(b*e*x + a*e)^2*a*b*c^4*d^2*e^2*f^3*g^5/(d*x + c)^2 - 120*(b*e*x + a*e)^2*a^2*c^3*d^3*e^2*f^3*g^5/(d*x + c

)^2 + 6*(b*e*x + a*e)^2*b^2*c^6*e^2*f^2*g^6/(d*x + c)^2 + 72*(b*e*x + a*e)^2*a*b*c^5*d*e^2*f^2*g^6/(d*x + c)^2

+ 90*(b*e*x + a*e)^2*a^2*c^4*d^2*e^2*f^2*g^6/(d*x + c)^2 - 12*(b*e*x + a*e)^2*a*b*c^6*e^2*f*g^7/(d*x + c)^2 -

36*(b*e*x + a*e)^2*a^2*c^5*d*e^2*f*g^7/(d*x + c)^2 + 6*(b*e*x + a*e)^2*a^2*c^6*e^2*g^8/(d*x + c)^2 - 4*(b*e*x

+ a*e)^3*b*d^7*e*f^8/(d*x + c)^3 + 28*(b*e*x + a*e)^3*b*c*d^6*e*f^7*g/(d*x + c)^3 + 4*(b*e*x + a*e)^3*a*d^7*e

*f^7*g/(d*x + c)^3 - 84*(b*e*x + a*e)^3*b*c^2*d^5*e*f^6*g^2/(d*x + c)^3 - 28*(b*e*x + a*e)^3*a*c*d^6*e*f^6*g^2

/(d*x + c)^3 + 140*(b*e*x + a*e)^3*b*c^3*d^4*e*f^5*g^3/(d*x + c)^3 + 84*(b*e*x + a*e)^3*a*c^2*d^5*e*f^5*g^3/(d

*x + c)^3 - 140*(b*e*x + a*e)^3*b*c^4*d^3*e*f^4*g^4/(d*x + c)^3 - 140*(b*e*x + a*e)^3*a*c^3*d^4*e*f^4*g^4/(d*x

+ c)^3 + 84*(b*e*x + a*e)^3*b*c^5*d^2*e*f^3*g^5/(d*x + c)^3 + 140*(b*e*x + a*e)^3*a*c^4*d^3*e*f^3*g^5/(d*x +

c)^3 - 28*(b*e*x + a*e)^3*b*c^6*d*e*f^2*g^6/(d*x + c)^3 - 84*(b*e*x + a*e)^3*a*c^5*d^2*e*f^2*g^6/(d*x + c)^3 +

4*(b*e*x + a*e)^3*b*c^7*e*f*g^7/(d*x + c)^3 + 28*(b*e*x + a*e)^3*a*c^6*d*e*f*g^7/(d*x + c)^3 - 4*(b*e*x + a*e

)^3*a*c^7*e*g^8/(d*x + c)^3 + (b*e*x + a*e)^4*d^8*f^8/(d*x + c)^4 - 8*(b*e*x + a*e)^4*c*d^7*f^7*g/(d*x + c)^4

+ 28*(b*e*x + a*e)^4*c^2*d^6*f^6*g^2/(d*x + c)^4 - 56*(b*e*x + a*e)^4*c^3*d^5*f^5*g^3/(d*x + c)^4 + 70*(b*e*x

+ a*e)^4*c^4*d^4*f^4*g^4/(d*x + c)^4 - 56*(b*e*x + a*e)^4*c^5*d^3*f^3*g^5/(d*x + c)^4 + 28*(b*e*x + a*e)^4*c^6

*d^2*f^2*g^6/(d*x + c)^4 - 8*(b*e*x + a*e)^4*c^7*d*f*g^7/(d*x + c)^4 + (b*e*x + a*e)^4*c^8*g^8/(d*x + c)^4) -

6*(4*B*b^5*c^2*d^3*e*f^3 - 8*B*a*b^4*c*d^4*e*f^3 + 4*B*a^2*b^3*d^5*e*f^3 - 6*B*b^5*c^3*d^2*e*f^2*g + 6*B*a*b^4

*c^2*d^3*e*f^2*g + 6*B*a^2*b^3*c*d^4*e*f^2*g - 6*B*a^3*b^2*d^5*e*f^2*g + 4*B*b^5*c^4*d*e*f*g^2 - 4*B*a*b^4*c^3

*d^2*e*f*g^2 - 4*B*a^3*b^2*c*d^4*e*f*g^2 + 4*B*a^4*b*d^5*e*f*g^2 - B*b^5*c^5*e*g^3 + B*a*b^4*c^4*d*e*g^3 + B*a

^4*b*c*d^4*e*g^3 - B*a^5*d^5*e*g^3)*log((b*e*x + a*e)/(d*x + c))/(b^4*d^4*f^8 - 4*b^4*c*d^3*f^7*g - 4*a*b^3*d^

4*f^7*g + 6*b^4*c^2*d^2*f^6*g^2 + 16*a*b^3*c*d^3*f^6*g^2 + 6*a^2*b^2*d^4*f^6*g^2 - 4*b^4*c^3*d*f^5*g^3 - 24*a*

b^3*c^2*d^2*f^5*g^3 - 24*a^2*b^2*c*d^3*f^5*g^3 - 4*a^3*b*d^4*f^5*g^3 + b^4*c^4*f^4*g^4 + 16*a*b^3*c^3*d*f^4*g^

4 + 36*a^2*b^2*c^2*d^2*f^4*g^4 + 16*a^3*b*c*d^3*f^4*g^4 + a^4*d^4*f^4*g^4 - 4*a*b^3*c^4*f^3*g^5 - 24*a^2*b^2*c

^3*d*f^3*g^5 - 24*a^3*b*c^2*d^2*f^3*g^5 - 4*a^4*c*d^3*f^3*g^5 + 6*a^2*b^2*c^4*f^2*g^6 + 16*a^3*b*c^3*d*f^2*g^6

+ 6*a^4*c^2*d^2*f^2*g^6 - 4*a^3*b*c^4*f*g^7 - 4*a^4*c^3*d*f*g^7 + a^4*c^4*g^8) + (24*A*b^8*c^2*d^3*e^5*f^6 -

48*A*a*b^7*c*d^4*e^5*f^6 + 24*A*a^2*b^6*d^5*e^5*f^6 - 36*A*b^8*c^3*d^2*e^5*f^5*g + 36*B*b^8*c^3*d^2*e^5*f^5*g

- 36*A*a*b^7*c^2*d^3*e^5*f^5*g - 108*B*a*b^7*c^2*d^3*e^5*f^5*g + 180*A*a^2*b^6*c*d^4*e^5*f^5*g + 108*B*a^2*b^6

*c*d^4*e^5*f^5*g - 108*A*a^3*b^5*d^5*e^5*f^5*g - 36*B*a^3*b^5*d^5*e^5*f^5*g + 24*A*b^8*c^4*d*e^5*f^4*g^2 - 36*

B*b^8*c^4*d*e^5*f^4*g^2 + 84*A*a*b^7*c^3*d^2*e^5*f^4*g^2 - 36*B*a*b^7*c^3*d^2*e^5*f^4*g^2 - 36*A*a^2*b^6*c^2*d

^3*e^5*f^4*g^2 + 324*B*a^2*b^6*c^2*d^3*e^5*f^4*g^2 - 276*A*a^3*b^5*c*d^4*e^5*f^4*g^2 - 396*B*a^3*b^5*c*d^4*e^5

*f^4*g^2 + 204*A*a^4*b^4*d^5*e^5*f^4*g^2 + 144*B*a^4*b^4*d^5*e^5*f^4*g^2 - 6*A*b^8*c^5*e^5*f^3*g^3 + 11*B*b^8*

c^5*e^5*f^3*g^3 - 66*A*a*b^7*c^4*d*e^5*f^3*g^3 + 89*B*a*b^7*c^4*d*e^5*f^3*g^3 - 36*A*a^2*b^6*c^3*d^2*e^5*f^3*g

^3 - 106*B*a^2*b^6*c^3*d^2*e^5*f^3*g^3 + 84*A*a^3*b^5*c^2*d^3*e^5*f^3*g^3 - 326*B*a^3*b^5*c^2*d^3*e^5*f^3*g^3

+ 234*A*a^4*b^4*c*d^4*e^5*f^3*g^3 + 559*B*a^4*b^4*c*d^4*e^5*f^3*g^3 - 210*A*a^5*b^3*d^5*e^5*f^3*g^3 - 227*B*a^

5*b^3*d^5*e^5*f^3*g^3 + 18*A*a*b^7*c^5*e^5*f^2*g^4 - 33*B*a*b^7*c^5*e^5*f^2*g^4 + 54*A*a^2*b^6*c^4*d*e^5*f^2*g

^4 - 51*B*a^2*b^6*c^4*d*e^5*f^2*g^4 - 36*A*a^3*b^5*c^3*d^2*e^5*f^2*g^4 + 174*B*a^3*b^5*c^3*d^2*e^5*f^2*g^4 - 3

6*A*a^4*b^4*c^2*d^3*e^5*f^2*g^4 + 114*B*a^4*b^4*c^2*d^3*e^5*f^2*g^4 - 126*A*a^5*b^3*c*d^4*e^5*f^2*g^4 - 381*B*

a^5*b^3*c*d^4*e^5*f^2*g^4 + 126*A*a^6*b^2*d^5*e^5*f^2*g^4 + 177*B*a^6*b^2*d^5*e^5*f^2*g^4 - 18*A*a^2*b^6*c^5*e

^5*f*g^5 + 33*B*a^2*b^6*c^5*e^5*f*g^5 - 6*A*a^3*b^5*c^4*d*e^5*f*g^5 - 21*B*a^3*b^5*c^4*d*e^5*f*g^5 + 24*A*a^4*

b^4*c^3*d^2*e^5*f*g^5 - 66*B*a^4*b^4*c^3*d^2*e^5*f*g^5 - 6*B*a^5*b^3*c^2*d^3*e^5*f*g^5 + 42*A*a^6*b^2*c*d^4*e^

5*f*g^5 + 129*B*a^6*b^2*c*d^4*e^5*f*g^5 - 42*A*a^7*b*d^5*e^5*f*g^5 - 69*B*a^7*b*d^5*e^5*f*g^5 + 6*A*a^3*b^5*c^

5*e^5*g^6 - 11*B*a^3*b^5*c^5*e^5*g^6 - 6*A*a^4*b^4*c^4*d*e^5*g^6 + 19*B*a^4*b^4*c^4*d*e^5*g^6 - 2*B*a^5*b^3*c^

3*d^2*e^5*g^6 + 2*B*a^6*b^2*c^2*d^3*e^5*g^6 - 6*A*a^7*b*c*d^4*e^5*g^6 - 19*B*a^7*b*c*d^4*e^5*g^6 + 6*A*a^8*d^5

*e^5*g^6 + 11*B*a^8*d^5*e^5*g^6 - 72*(b*e*x + a*e)*A*b^7*c^2*d^4*e^4*f^6/(d*x + c) + 144*(b*e*x + a*e)*A*a*b^6

*c*d^5*e^4*f^6/(d*x + c) - 72*(b*e*x + a*e)*A*a^2*b^5*d^6*e^4*f^6/(d*x + c) + 144*(b*e*x + a*e)*A*b^7*c^3*d^3*

e^4*f^5*g/(d*x + c) - 108*(b*e*x + a*e)*B*b^7*c^3*d^3*e^4*f^5*g/(d*x + c) + 324*(b*e*x + a*e)*B*a*b^6*c^2*d^4*

e^4*f^5*g/(d*x + c) - 432*(b*e*x + a*e)*A*a^2*b^5*c*d^5*e^4*f^5*g/(d*x + c) - 324*(b*e*x + a*e)*B*a^2*b^5*c*d^

5*e^4*f^5*g/(d*x + c) + 288*(b*e*x + a*e)*A*a^3*b^4*d^6*e^4*f^5*g/(d*x + c) + 108*(b*e*x + a*e)*B*a^3*b^4*d^6*

e^4*f^5*g/(d*x + c) - 96*(b*e*x + a*e)*A*b^7*c^4*d^2*e^4*f^4*g^2/(d*x + c) + 204*(b*e*x + a*e)*B*b^7*c^4*d^2*e

^4*f^4*g^2/(d*x + c) - 336*(b*e*x + a*e)*A*a*b^6*c^3*d^3*e^4*f^4*g^2/(d*x + c) - 276*(b*e*x + a*e)*B*a*b^6*c^3

*d^3*e^4*f^4*g^2/(d*x + c) + 504*(b*e*x + a*e)*A*a^2*b^5*c^2*d^4*e^4*f^4*g^2/(d*x + c) - 396*(b*e*x + a*e)*B*a

^2*b^5*c^2*d^4*e^4*f^4*g^2/(d*x + c) + 384*(b*e*x + a*e)*A*a^3*b^4*c*d^5*e^4*f^4*g^2/(d*x + c) + 804*(b*e*x +

a*e)*B*a^3*b^4*c*d^5*e^4*f^4*g^2/(d*x + c) - 456*(b*e*x + a*e)*A*a^4*b^3*d^6*e^4*f^4*g^2/(d*x + c) - 336*(b*e*

x + a*e)*B*a^4*b^3*d^6*e^4*f^4*g^2/(d*x + c) + 24*(b*e*x + a*e)*A*b^7*c^5*d*e^4*f^3*g^3/(d*x + c) - 122*(b*e*x

+ a*e)*B*b^7*c^5*d*e^4*f^3*g^3/(d*x + c) + 264*(b*e*x + a*e)*A*a*b^6*c^4*d^2*e^4*f^3*g^3/(d*x + c) - 206*(b*e

*x + a*e)*B*a*b^6*c^4*d^2*e^4*f^3*g^3/(d*x + c) + 144*(b*e*x + a*e)*A*a^2*b^5*c^3*d^3*e^4*f^3*g^3/(d*x + c) +

964*(b*e*x + a*e)*B*a^2*b^5*c^3*d^3*e^4*f^3*g^3/(d*x + c) - 816*(b*e*x + a*e)*A*a^3*b^4*c^2*d^4*e^4*f^3*g^3/(d

*x + c) - 436*(b*e*x + a*e)*B*a^3*b^4*c^2*d^4*e^4*f^3*g^3/(d*x + c) + 24*(b*e*x + a*e)*A*a^4*b^3*c*d^5*e^4*f^3

*g^3/(d*x + c) - 586*(b*e*x + a*e)*B*a^4*b^3*c*d^5*e^4*f^3*g^3/(d*x + c) + 360*(b*e*x + a*e)*A*a^5*b^2*d^6*e^4

*f^3*g^3/(d*x + c) + 386*(b*e*x + a*e)*B*a^5*b^2*d^6*e^4*f^3*g^3/(d*x + c) + 26*(b*e*x + a*e)*B*b^7*c^6*e^4*f^

2*g^4/(d*x + c) - 72*(b*e*x + a*e)*A*a*b^6*c^5*d*e^4*f^2*g^4/(d*x + c) + 210*(b*e*x + a*e)*B*a*b^6*c^5*d*e^4*f

^2*g^4/(d*x + c) - 216*(b*e*x + a*e)*A*a^2*b^5*c^4*d^2*e^4*f^2*g^4/(d*x + c) - 216*(b*e*x + a*e)*B*a^2*b^5*c^4

*d^2*e^4*f^2*g^4/(d*x + c) + 144*(b*e*x + a*e)*A*a^3*b^4*c^3*d^3*e^4*f^2*g^4/(d*x + c) - 676*(b*e*x + a*e)*B*a

^3*b^4*c^3*d^3*e^4*f^2*g^4/(d*x + c) + 504*(b*e*x + a*e)*A*a^4*b^3*c^2*d^4*e^4*f^2*g^4/(d*x + c) + 834*(b*e*x

+ a*e)*B*a^4*b^3*c^2*d^4*e^4*f^2*g^4/(d*x + c) - 216*(b*e*x + a*e)*A*a^5*b^2*c*d^5*e^4*f^2*g^4/(d*x + c) + 18*

(b*e*x + a*e)*B*a^5*b^2*c*d^5*e^4*f^2*g^4/(d*x + c) - 144*(b*e*x + a*e)*A*a^6*b*d^6*e^4*f^2*g^4/(d*x + c) - 19

6*(b*e*x + a*e)*B*a^6*b*d^6*e^4*f^2*g^4/(d*x + c) - 52*(b*e*x + a*e)*B*a*b^6*c^6*e^4*f*g^5/(d*x + c) + 72*(b*e

*x + a*e)*A*a^2*b^5*c^5*d*e^4*f*g^5/(d*x + c) - 54*(b*e*x + a*e)*B*a^2*b^5*c^5*d*e^4*f*g^5/(d*x + c) + 24*(b*e

*x + a*e)*A*a^3*b^4*c^4*d^2*e^4*f*g^5/(d*x + c) + 234*(b*e*x + a*e)*B*a^3*b^4*c^4*d^2*e^4*f*g^5/(d*x + c) - 96

*(b*e*x + a*e)*A*a^4*b^3*c^3*d^3*e^4*f*g^5/(d*x + c) + 104*(b*e*x + a*e)*B*a^4*b^3*c^3*d^3*e^4*f*g^5/(d*x + c)

- 144*(b*e*x + a*e)*A*a^5*b^2*c^2*d^4*e^4*f*g^5/(d*x + c) - 396*(b*e*x + a*e)*B*a^5*b^2*c^2*d^4*e^4*f*g^5/(d*

x + c) + 120*(b*e*x + a*e)*A*a^6*b*c*d^5*e^4*f*g^5/(d*x + c) + 126*(b*e*x + a*e)*B*a^6*b*c*d^5*e^4*f*g^5/(d*x

+ c) + 24*(b*e*x + a*e)*A*a^7*d^6*e^4*f*g^5/(d*x + c) + 38*(b*e*x + a*e)*B*a^7*d^6*e^4*f*g^5/(d*x + c) + 26*(b

*e*x + a*e)*B*a^2*b^5*c^6*e^4*g^6/(d*x + c) - 24*(b*e*x + a*e)*A*a^3*b^4*c^5*d*e^4*g^6/(d*x + c) - 34*(b*e*x +

a*e)*B*a^3*b^4*c^5*d*e^4*g^6/(d*x + c) + 24*(b*e*x + a*e)*A*a^4*b^3*c^4*d^2*e^4*g^6/(d*x + c) - 16*(b*e*x + a

*e)*B*a^4*b^3*c^4*d^2*e^4*g^6/(d*x + c) - 8*(b*e*x + a*e)*B*a^5*b^2*c^3*d^3*e^4*g^6/(d*x + c) + 24*(b*e*x + a*

e)*A*a^6*b*c^2*d^4*e^4*g^6/(d*x + c) + 70*(b*e*x + a*e)*B*a^6*b*c^2*d^4*e^4*g^6/(d*x + c) - 24*(b*e*x + a*e)*A

*a^7*c*d^5*e^4*g^6/(d*x + c) - 38*(b*e*x + a*e)*B*a^7*c*d^5*e^4*g^6/(d*x + c) + 72*(b*e*x + a*e)^2*A*b^6*c^2*d

^5*e^3*f^6/(d*x + c)^2 - 144*(b*e*x + a*e)^2*A*a*b^5*c*d^6*e^3*f^6/(d*x + c)^2 + 72*(b*e*x + a*e)^2*A*a^2*b^4*

d^7*e^3*f^6/(d*x + c)^2 - 180*(b*e*x + a*e)^2*A*b^6*c^3*d^4*e^3*f^5*g/(d*x + c)^2 + 108*(b*e*x + a*e)^2*B*b^6*

c^3*d^4*e^3*f^5*g/(d*x + c)^2 + 108*(b*e*x + a*e)^2*A*a*b^5*c^2*d^5*e^3*f^5*g/(d*x + c)^2 - 324*(b*e*x + a*e)^

2*B*a*b^5*c^2*d^5*e^3*f^5*g/(d*x + c)^2 + 324*(b*e*x + a*e)^2*A*a^2*b^4*c*d^6*e^3*f^5*g/(d*x + c)^2 + 324*(b*e

*x + a*e)^2*B*a^2*b^4*c*d^6*e^3*f^5*g/(d*x + c)^2 - 252*(b*e*x + a*e)^2*A*a^3*b^3*d^7*e^3*f^5*g/(d*x + c)^2 -

108*(b*e*x + a*e)^2*B*a^3*b^3*d^7*e^3*f^5*g/(d*x + c)^2 + 144*(b*e*x + a*e)^2*A*b^6*c^4*d^3*e^3*f^4*g^2/(d*x +

c)^2 - 300*(b*e*x + a*e)^2*B*b^6*c^4*d^3*e^3*f^4*g^2/(d*x + c)^2 + 324*(b*e*x + a*e)^2*A*a*b^5*c^3*d^4*e^3*f^

4*g^2/(d*x + c)^2 + 660*(b*e*x + a*e)^2*B*a*b^5*c^3*d^4*e^3*f^4*g^2/(d*x + c)^2 - 756*(b*e*x + a*e)^2*A*a^2*b^

4*c^2*d^5*e^3*f^4*g^2/(d*x + c)^2 - 180*(b*e*x + a*e)^2*B*a^2*b^4*c^2*d^5*e^3*f^4*g^2/(d*x + c)^2 - 36*(b*e*x

+ a*e)^2*A*a^3*b^3*c*d^6*e^3*f^4*g^2/(d*x + c)^2 - 420*(b*e*x + a*e)^2*B*a^3*b^3*c*d^6*e^3*f^4*g^2/(d*x + c)^2

+ 324*(b*e*x + a*e)^2*A*a^4*b^2*d^7*e^3*f^4*g^2/(d*x + c)^2 + 240*(b*e*x + a*e)^2*B*a^4*b^2*d^7*e^3*f^4*g^2/(

d*x + c)^2 - 36*(b*e*x + a*e)^2*A*b^6*c^5*d^2*e^3*f^3*g^3/(d*x + c)^2 + 297*(b*e*x + a*e)^2*B*b^6*c^5*d^2*e^3*

f^3*g^3/(d*x + c)^2 - 396*(b*e*x + a*e)^2*A*a*b^5*c^4*d^3*e^3*f^3*g^3/(d*x + c)^2 - 285*(b*e*x + a*e)^2*B*a*b^

5*c^4*d^3*e^3*f^3*g^3/(d*x + c)^2 + 144*(b*e*x + a*e)^2*A*a^2*b^4*c^3*d^4*e^3*f^3*g^3/(d*x + c)^2 - 750*(b*e*x

+ a*e)^2*B*a^2*b^4*c^3*d^4*e^3*f^3*g^3/(d*x + c)^2 + 864*(b*e*x + a*e)^2*A*a^3*b^3*c^2*d^5*e^3*f^3*g^3/(d*x +

c)^2 + 990*(b*e*x + a*e)^2*B*a^3*b^3*c^2*d^5*e^3*f^3*g^3/(d*x + c)^2 - 396*(b*e*x + a*e)^2*A*a^4*b^2*c*d^6*e^

3*f^3*g^3/(d*x + c)^2 - 75*(b*e*x + a*e)^2*B*a^4*b^2*c*d^6*e^3*f^3*g^3/(d*x + c)^2 - 180*(b*e*x + a*e)^2*A*a^5

*b*d^7*e^3*f^3*g^3/(d*x + c)^2 - 177*(b*e*x + a*e)^2*B*a^5*b*d^7*e^3*f^3*g^3/(d*x + c)^2 - 126*(b*e*x + a*e)^2

*B*b^6*c^6*d*e^3*f^2*g^4/(d*x + c)^2 + 108*(b*e*x + a*e)^2*A*a*b^5*c^5*d^2*e^3*f^2*g^4/(d*x + c)^2 - 135*(b*e*

x + a*e)^2*B*a*b^5*c^5*d^2*e^3*f^2*g^4/(d*x + c)^2 + 324*(b*e*x + a*e)^2*A*a^2*b^4*c^4*d^3*e^3*f^2*g^4/(d*x +

c)^2 + 765*(b*e*x + a*e)^2*B*a^2*b^4*c^4*d^3*e^3*f^2*g^4/(d*x + c)^2 - 576*(b*e*x + a*e)^2*A*a^3*b^3*c^3*d^4*e

^3*f^2*g^4/(d*x + c)^2 - 270*(b*e*x + a*e)^2*B*a^3*b^3*c^3*d^4*e^3*f^2*g^4/(d*x + c)^2 - 216*(b*e*x + a*e)^2*A

*a^4*b^2*c^2*d^5*e^3*f^2*g^4/(d*x + c)^2 - 540*(b*e*x + a*e)^2*B*a^4*b^2*c^2*d^5*e^3*f^2*g^4/(d*x + c)^2 + 324

*(b*e*x + a*e)^2*A*a^5*b*c*d^6*e^3*f^2*g^4/(d*x + c)^2 + 261*(b*e*x + a*e)^2*B*a^5*b*c*d^6*e^3*f^2*g^4/(d*x +

c)^2 + 36*(b*e*x + a*e)^2*A*a^6*d^7*e^3*f^2*g^4/(d*x + c)^2 + 45*(b*e*x + a*e)^2*B*a^6*d^7*e^3*f^2*g^4/(d*x +

c)^2 + 21*(b*e*x + a*e)^2*B*b^6*c^7*e^3*f*g^5/(d*x + c)^2 + 105*(b*e*x + a*e)^2*B*a*b^5*c^6*d*e^3*f*g^5/(d*x +

c)^2 - 108*(b*e*x + a*e)^2*A*a^2*b^4*c^5*d^2*e^3*f*g^5/(d*x + c)^2 - 180*(b*e*x + a*e)^2*B*a^2*b^4*c^5*d^2*e^

3*f*g^5/(d*x + c)^2 - 36*(b*e*x + a*e)^2*A*a^3*b^3*c^4*d^3*e^3*f*g^5/(d*x + c)^2 - 210*(b*e*x + a*e)^2*B*a^3*b

^3*c^4*d^3*e^3*f*g^5/(d*x + c)^2 + 324*(b*e*x + a*e)^2*A*a^4*b^2*c^3*d^4*e^3*f*g^5/(d*x + c)^2 + 345*(b*e*x +

a*e)^2*B*a^4*b^2*c^3*d^4*e^3*f*g^5/(d*x + c)^2 - 108*(b*e*x + a*e)^2*A*a^5*b*c^2*d^5*e^3*f*g^5/(d*x + c)^2 + 9

*(b*e*x + a*e)^2*B*a^5*b*c^2*d^5*e^3*f*g^5/(d*x + c)^2 - 72*(b*e*x + a*e)^2*A*a^6*c*d^6*e^3*f*g^5/(d*x + c)^2

- 90*(b*e*x + a*e)^2*B*a^6*c*d^6*e^3*f*g^5/(d*x + c)^2 - 21*(b*e*x + a*e)^2*B*a*b^5*c^7*e^3*g^6/(d*x + c)^2 +

21*(b*e*x + a*e)^2*B*a^2*b^4*c^6*d*e^3*g^6/(d*x + c)^2 + 36*(b*e*x + a*e)^2*A*a^3*b^3*c^5*d^2*e^3*g^6/(d*x + c

)^2 + 18*(b*e*x + a*e)^2*B*a^3*b^3*c^5*d^2*e^3*g^6/(d*x + c)^2 - 36*(b*e*x + a*e)^2*A*a^4*b^2*c^4*d^3*e^3*g^6/

(d*x + c)^2 + 30*(b*e*x + a*e)^2*B*a^4*b^2*c^4*d^3*e^3*g^6/(d*x + c)^2 - 36*(b*e*x + a*e)^2*A*a^5*b*c^3*d^4*e^

3*g^6/(d*x + c)^2 - 93*(b*e*x + a*e)^2*B*a^5*b*c^3*d^4*e^3*g^6/(d*x + c)^2 + 36*(b*e*x + a*e)^2*A*a^6*c^2*d^5*

e^3*g^6/(d*x + c)^2 + 45*(b*e*x + a*e)^2*B*a^6*c^2*d^5*e^3*g^6/(d*x + c)^2 - 24*(b*e*x + a*e)^3*A*b^5*c^2*d^6*

e^2*f^6/(d*x + c)^3 + 48*(b*e*x + a*e)^3*A*a*b^4*c*d^7*e^2*f^6/(d*x + c)^3 - 24*(b*e*x + a*e)^3*A*a^2*b^3*d^8*

e^2*f^6/(d*x + c)^3 + 72*(b*e*x + a*e)^3*A*b^5*c^3*d^5*e^2*f^5*g/(d*x + c)^3 - 36*(b*e*x + a*e)^3*B*b^5*c^3*d^

5*e^2*f^5*g/(d*x + c)^3 - 72*(b*e*x + a*e)^3*A*a*b^4*c^2*d^6*e^2*f^5*g/(d*x + c)^3 + 108*(b*e*x + a*e)^3*B*a*b

^4*c^2*d^6*e^2*f^5*g/(d*x + c)^3 - 72*(b*e*x + a*e)^3*A*a^2*b^3*c*d^7*e^2*f^5*g/(d*x + c)^3 - 108*(b*e*x + a*e

)^3*B*a^2*b^3*c*d^7*e^2*f^5*g/(d*x + c)^3 + 72*(b*e*x + a*e)^3*A*a^3*b^2*d^8*e^2*f^5*g/(d*x + c)^3 + 36*(b*e*x

+ a*e)^3*B*a^3*b^2*d^8*e^2*f^5*g/(d*x + c)^3 - 72*(b*e*x + a*e)^3*A*b^5*c^4*d^4*e^2*f^4*g^2/(d*x + c)^3 + 132

*(b*e*x + a*e)^3*B*b^5*c^4*d^4*e^2*f^4*g^2/(d*x + c)^3 - 72*(b*e*x + a*e)^3*A*a*b^4*c^3*d^5*e^2*f^4*g^2/(d*x +

c)^3 - 348*(b*e*x + a*e)^3*B*a*b^4*c^3*d^5*e^2*f^4*g^2/(d*x + c)^3 + 288*(b*e*x + a*e)^3*A*a^2*b^3*c^2*d^6*e^

2*f^4*g^2/(d*x + c)^3 + 252*(b*e*x + a*e)^3*B*a^2*b^3*c^2*d^6*e^2*f^4*g^2/(d*x + c)^3 - 72*(b*e*x + a*e)^3*A*a

^3*b^2*c*d^7*e^2*f^4*g^2/(d*x + c)^3 + 12*(b*e*x + a*e)^3*B*a^3*b^2*c*d^7*e^2*f^4*g^2/(d*x + c)^3 - 72*(b*e*x

+ a*e)^3*A*a^4*b*d^8*e^2*f^4*g^2/(d*x + c)^3 - 48*(b*e*x + a*e)^3*B*a^4*b*d^8*e^2*f^4*g^2/(d*x + c)^3 + 24*(b*

e*x + a*e)^3*A*b^5*c^5*d^3*e^2*f^3*g^3/(d*x + c)^3 - 186*(b*e*x + a*e)^3*B*b^5*c^5*d^3*e^2*f^3*g^3/(d*x + c)^3

+ 168*(b*e*x + a*e)^3*A*a*b^4*c^4*d^4*e^2*f^3*g^3/(d*x + c)^3 + 402*(b*e*x + a*e)^3*B*a*b^4*c^4*d^4*e^2*f^3*g

^3/(d*x + c)^3 - 192*(b*e*x + a*e)^3*A*a^2*b^3*c^3*d^5*e^2*f^3*g^3/(d*x + c)^3 - 108*(b*e*x + a*e)^3*B*a^2*b^3

*c^3*d^5*e^2*f^3*g^3/(d*x + c)^3 - 192*(b*e*x + a*e)^3*A*a^3*b^2*c^2*d^6*e^2*f^3*g^3/(d*x + c)^3 - 228*(b*e*x

+ a*e)^3*B*a^3*b^2*c^2*d^6*e^2*f^3*g^3/(d*x + c)^3 + 168*(b*e*x + a*e)^3*A*a^4*b*c*d^7*e^2*f^3*g^3/(d*x + c)^3

+ 102*(b*e*x + a*e)^3*B*a^4*b*c*d^7*e^2*f^3*g^3/(d*x + c)^3 + 24*(b*e*x + a*e)^3*A*a^5*d^8*e^2*f^3*g^3/(d*x +

c)^3 + 18*(b*e*x + a*e)^3*B*a^5*d^8*e^2*f^3*g^3/(d*x + c)^3 + 126*(b*e*x + a*e)^3*B*b^5*c^6*d^2*e^2*f^2*g^4/(

d*x + c)^3 - 72*(b*e*x + a*e)^3*A*a*b^4*c^5*d^3*e^2*f^2*g^4/(d*x + c)^3 - 198*(b*e*x + a*e)^3*B*a*b^4*c^5*d^3*

e^2*f^2*g^4/(d*x + c)^3 - 72*(b*e*x + a*e)^3*A*a^2*b^3*c^4*d^4*e^2*f^2*g^4/(d*x + c)^3 - 108*(b*e*x + a*e)^3*B

*a^2*b^3*c^4*d^4*e^2*f^2*g^4/(d*x + c)^3 + 288*(b*e*x + a*e)^3*A*a^3*b^2*c^3*d^5*e^2*f^2*g^4/(d*x + c)^3 + 252

*(b*e*x + a*e)^3*B*a^3*b^2*c^3*d^5*e^2*f^2*g^4/(d*x + c)^3 - 72*(b*e*x + a*e)^3*A*a^4*b*c^2*d^6*e^2*f^2*g^4/(d

*x + c)^3 - 18*(b*e*x + a*e)^3*B*a^4*b*c^2*d^6*e^2*f^2*g^4/(d*x + c)^3 - 72*(b*e*x + a*e)^3*A*a^5*c*d^7*e^2*f^

2*g^4/(d*x + c)^3 - 54*(b*e*x + a*e)^3*B*a^5*c*d^7*e^2*f^2*g^4/(d*x + c)^3 - 42*(b*e*x + a*e)^3*B*b^5*c^7*d*e^

2*f*g^5/(d*x + c)^3 + 42*(b*e*x + a*e)^3*B*a*b^4*c^6*d^2*e^2*f*g^5/(d*x + c)^3 + 72*(b*e*x + a*e)^3*A*a^2*b^3*

c^5*d^3*e^2*f*g^5/(d*x + c)^3 + 72*(b*e*x + a*e)^3*B*a^2*b^3*c^5*d^3*e^2*f*g^5/(d*x + c)^3 - 72*(b*e*x + a*e)^

3*A*a^3*b^2*c^4*d^4*e^2*f*g^5/(d*x + c)^3 - 48*(b*e*x + a*e)^3*B*a^3*b^2*c^4*d^4*e^2*f*g^5/(d*x + c)^3 - 72*(b

*e*x + a*e)^3*A*a^4*b*c^3*d^5*e^2*f*g^5/(d*x + c)^3 - 78*(b*e*x + a*e)^3*B*a^4*b*c^3*d^5*e^2*f*g^5/(d*x + c)^3

+ 72*(b*e*x + a*e)^3*A*a^5*c^2*d^6*e^2*f*g^5/(d*x + c)^3 + 54*(b*e*x + a*e)^3*B*a^5*c^2*d^6*e^2*f*g^5/(d*x +

c)^3 + 6*(b*e*x + a*e)^3*B*b^5*c^8*e^2*g^6/(d*x + c)^3 - 6*(b*e*x + a*e)^3*B*a*b^4*c^7*d*e^2*g^6/(d*x + c)^3 -

24*(b*e*x + a*e)^3*A*a^3*b^2*c^5*d^3*e^2*g^6/(d*x + c)^3 - 24*(b*e*x + a*e)^3*B*a^3*b^2*c^5*d^3*e^2*g^6/(d*x

+ c)^3 + 48*(b*e*x + a*e)^3*A*a^4*b*c^4*d^4*e^2*g^6/(d*x + c)^3 + 42*(b*e*x + a*e)^3*B*a^4*b*c^4*d^4*e^2*g^6/(

d*x + c)^3 - 24*(b*e*x + a*e)^3*A*a^5*c^3*d^5*e^2*g^6/(d*x + c)^3 - 18*(b*e*x + a*e)^3*B*a^5*c^3*d^5*e^2*g^6/(

d*x + c)^3)/(b^7*d^4*e^4*f^11 - 4*b^7*c*d^3*e^4*f^10*g - 7*a*b^6*d^4*e^4*f^10*g + 6*b^7*c^2*d^2*e^4*f^9*g^2 +

28*a*b^6*c*d^3*e^4*f^9*g^2 + 21*a^2*b^5*d^4*e^4*f^9*g^2 - 4*b^7*c^3*d*e^4*f^8*g^3 - 42*a*b^6*c^2*d^2*e^4*f^8*g

^3 - 84*a^2*b^5*c*d^3*e^4*f^8*g^3 - 35*a^3*b^4*d^4*e^4*f^8*g^3 + b^7*c^4*e^4*f^7*g^4 + 28*a*b^6*c^3*d*e^4*f^7*

g^4 + 126*a^2*b^5*c^2*d^2*e^4*f^7*g^4 + 140*a^3*b^4*c*d^3*e^4*f^7*g^4 + 35*a^4*b^3*d^4*e^4*f^7*g^4 - 7*a*b^6*c

^4*e^4*f^6*g^5 - 84*a^2*b^5*c^3*d*e^4*f^6*g^5 - 210*a^3*b^4*c^2*d^2*e^4*f^6*g^5 - 140*a^4*b^3*c*d^3*e^4*f^6*g^

5 - 21*a^5*b^2*d^4*e^4*f^6*g^5 + 21*a^2*b^5*c^4*e^4*f^5*g^6 + 140*a^3*b^4*c^3*d*e^4*f^5*g^6 + 210*a^4*b^3*c^2*

d^2*e^4*f^5*g^6 + 84*a^5*b^2*c*d^3*e^4*f^5*g^6 + 7*a^6*b*d^4*e^4*f^5*g^6 - 35*a^3*b^4*c^4*e^4*f^4*g^7 - 140*a^

4*b^3*c^3*d*e^4*f^4*g^7 - 126*a^5*b^2*c^2*d^2*e^4*f^4*g^7 - 28*a^6*b*c*d^3*e^4*f^4*g^7 - a^7*d^4*e^4*f^4*g^7 +

35*a^4*b^3*c^4*e^4*f^3*g^8 + 84*a^5*b^2*c^3*d*e^4*f^3*g^8 + 42*a^6*b*c^2*d^2*e^4*f^3*g^8 + 4*a^7*c*d^3*e^4*f^

3*g^8 - 21*a^5*b^2*c^4*e^4*f^2*g^9 - 28*a^6*b*c^3*d*e^4*f^2*g^9 - 6*a^7*c^2*d^2*e^4*f^2*g^9 + 7*a^6*b*c^4*e^4*

f*g^10 + 4*a^7*c^3*d*e^4*f*g^10 - a^7*c^4*e^4*g^11 - 4*(b*e*x + a*e)*b^6*d^5*e^3*f^11/(d*x + c) + 20*(b*e*x +

a*e)*b^6*c*d^4*e^3*f^10*g/(d*x + c) + 24*(b*e*x + a*e)*a*b^5*d^5*e^3*f^10*g/(d*x + c) - 40*(b*e*x + a*e)*b^6*c

^2*d^3*e^3*f^9*g^2/(d*x + c) - 120*(b*e*x + a*e)*a*b^5*c*d^4*e^3*f^9*g^2/(d*x + c) - 60*(b*e*x + a*e)*a^2*b^4*

d^5*e^3*f^9*g^2/(d*x + c) + 40*(b*e*x + a*e)*b^6*c^3*d^2*e^3*f^8*g^3/(d*x + c) + 240*(b*e*x + a*e)*a*b^5*c^2*d

^3*e^3*f^8*g^3/(d*x + c) + 300*(b*e*x + a*e)*a^2*b^4*c*d^4*e^3*f^8*g^3/(d*x + c) + 80*(b*e*x + a*e)*a^3*b^3*d^

5*e^3*f^8*g^3/(d*x + c) - 20*(b*e*x + a*e)*b^6*c^4*d*e^3*f^7*g^4/(d*x + c) - 240*(b*e*x + a*e)*a*b^5*c^3*d^2*e

^3*f^7*g^4/(d*x + c) - 600*(b*e*x + a*e)*a^2*b^4*c^2*d^3*e^3*f^7*g^4/(d*x + c) - 400*(b*e*x + a*e)*a^3*b^3*c*d

^4*e^3*f^7*g^4/(d*x + c) - 60*(b*e*x + a*e)*a^4*b^2*d^5*e^3*f^7*g^4/(d*x + c) + 4*(b*e*x + a*e)*b^6*c^5*e^3*f^

6*g^5/(d*x + c) + 120*(b*e*x + a*e)*a*b^5*c^4*d*e^3*f^6*g^5/(d*x + c) + 600*(b*e*x + a*e)*a^2*b^4*c^3*d^2*e^3*

f^6*g^5/(d*x + c) + 800*(b*e*x + a*e)*a^3*b^3*c^2*d^3*e^3*f^6*g^5/(d*x + c) + 300*(b*e*x + a*e)*a^4*b^2*c*d^4*

e^3*f^6*g^5/(d*x + c) + 24*(b*e*x + a*e)*a^5*b*d^5*e^3*f^6*g^5/(d*x + c) - 24*(b*e*x + a*e)*a*b^5*c^5*e^3*f^5*

g^6/(d*x + c) - 300*(b*e*x + a*e)*a^2*b^4*c^4*d*e^3*f^5*g^6/(d*x + c) - 800*(b*e*x + a*e)*a^3*b^3*c^3*d^2*e^3*

f^5*g^6/(d*x + c) - 600*(b*e*x + a*e)*a^4*b^2*c^2*d^3*e^3*f^5*g^6/(d*x + c) - 120*(b*e*x + a*e)*a^5*b*c*d^4*e^

3*f^5*g^6/(d*x + c) - 4*(b*e*x + a*e)*a^6*d^5*e^3*f^5*g^6/(d*x + c) + 60*(b*e*x + a*e)*a^2*b^4*c^5*e^3*f^4*g^7

/(d*x + c) + 400*(b*e*x + a*e)*a^3*b^3*c^4*d*e^3*f^4*g^7/(d*x + c) + 600*(b*e*x + a*e)*a^4*b^2*c^3*d^2*e^3*f^4

*g^7/(d*x + c) + 240*(b*e*x + a*e)*a^5*b*c^2*d^3*e^3*f^4*g^7/(d*x + c) + 20*(b*e*x + a*e)*a^6*c*d^4*e^3*f^4*g^

7/(d*x + c) - 80*(b*e*x + a*e)*a^3*b^3*c^5*e^3*f^3*g^8/(d*x + c) - 300*(b*e*x + a*e)*a^4*b^2*c^4*d*e^3*f^3*g^8

/(d*x + c) - 240*(b*e*x + a*e)*a^5*b*c^3*d^2*e^3*f^3*g^8/(d*x + c) - 40*(b*e*x + a*e)*a^6*c^2*d^3*e^3*f^3*g^8/

(d*x + c) + 60*(b*e*x + a*e)*a^4*b^2*c^5*e^3*f^2*g^9/(d*x + c) + 120*(b*e*x + a*e)*a^5*b*c^4*d*e^3*f^2*g^9/(d*

x + c) + 40*(b*e*x + a*e)*a^6*c^3*d^2*e^3*f^2*g^9/(d*x + c) - 24*(b*e*x + a*e)*a^5*b*c^5*e^3*f*g^10/(d*x + c)

- 20*(b*e*x + a*e)*a^6*c^4*d*e^3*f*g^10/(d*x + c) + 4*(b*e*x + a*e)*a^6*c^5*e^3*g^11/(d*x + c) + 6*(b*e*x + a*

e)^2*b^5*d^6*e^2*f^11/(d*x + c)^2 - 36*(b*e*x + a*e)^2*b^5*c*d^5*e^2*f^10*g/(d*x + c)^2 - 30*(b*e*x + a*e)^2*a

*b^4*d^6*e^2*f^10*g/(d*x + c)^2 + 90*(b*e*x + a*e)^2*b^5*c^2*d^4*e^2*f^9*g^2/(d*x + c)^2 + 180*(b*e*x + a*e)^2

*a*b^4*c*d^5*e^2*f^9*g^2/(d*x + c)^2 + 60*(b*e*x + a*e)^2*a^2*b^3*d^6*e^2*f^9*g^2/(d*x + c)^2 - 120*(b*e*x + a

*e)^2*b^5*c^3*d^3*e^2*f^8*g^3/(d*x + c)^2 - 450*(b*e*x + a*e)^2*a*b^4*c^2*d^4*e^2*f^8*g^3/(d*x + c)^2 - 360*(b

*e*x + a*e)^2*a^2*b^3*c*d^5*e^2*f^8*g^3/(d*x + c)^2 - 60*(b*e*x + a*e)^2*a^3*b^2*d^6*e^2*f^8*g^3/(d*x + c)^2 +

90*(b*e*x + a*e)^2*b^5*c^4*d^2*e^2*f^7*g^4/(d*x + c)^2 + 600*(b*e*x + a*e)^2*a*b^4*c^3*d^3*e^2*f^7*g^4/(d*x +

c)^2 + 900*(b*e*x + a*e)^2*a^2*b^3*c^2*d^4*e^2*f^7*g^4/(d*x + c)^2 + 360*(b*e*x + a*e)^2*a^3*b^2*c*d^5*e^2*f^

7*g^4/(d*x + c)^2 + 30*(b*e*x + a*e)^2*a^4*b*d^6*e^2*f^7*g^4/(d*x + c)^2 - 36*(b*e*x + a*e)^2*b^5*c^5*d*e^2*f^

6*g^5/(d*x + c)^2 - 450*(b*e*x + a*e)^2*a*b^4*c^4*d^2*e^2*f^6*g^5/(d*x + c)^2 - 1200*(b*e*x + a*e)^2*a^2*b^3*c

^3*d^3*e^2*f^6*g^5/(d*x + c)^2 - 900*(b*e*x + a*e)^2*a^3*b^2*c^2*d^4*e^2*f^6*g^5/(d*x + c)^2 - 180*(b*e*x + a*

e)^2*a^4*b*c*d^5*e^2*f^6*g^5/(d*x + c)^2 - 6*(b*e*x + a*e)^2*a^5*d^6*e^2*f^6*g^5/(d*x + c)^2 + 6*(b*e*x + a*e)

^2*b^5*c^6*e^2*f^5*g^6/(d*x + c)^2 + 180*(b*e*x + a*e)^2*a*b^4*c^5*d*e^2*f^5*g^6/(d*x + c)^2 + 900*(b*e*x + a*

e)^2*a^2*b^3*c^4*d^2*e^2*f^5*g^6/(d*x + c)^2 + 1200*(b*e*x + a*e)^2*a^3*b^2*c^3*d^3*e^2*f^5*g^6/(d*x + c)^2 +

450*(b*e*x + a*e)^2*a^4*b*c^2*d^4*e^2*f^5*g^6/(d*x + c)^2 + 36*(b*e*x + a*e)^2*a^5*c*d^5*e^2*f^5*g^6/(d*x + c)

^2 - 30*(b*e*x + a*e)^2*a*b^4*c^6*e^2*f^4*g^7/(d*x + c)^2 - 360*(b*e*x + a*e)^2*a^2*b^3*c^5*d*e^2*f^4*g^7/(d*x

+ c)^2 - 900*(b*e*x + a*e)^2*a^3*b^2*c^4*d^2*e^2*f^4*g^7/(d*x + c)^2 - 600*(b*e*x + a*e)^2*a^4*b*c^3*d^3*e^2*

f^4*g^7/(d*x + c)^2 - 90*(b*e*x + a*e)^2*a^5*c^2*d^4*e^2*f^4*g^7/(d*x + c)^2 + 60*(b*e*x + a*e)^2*a^2*b^3*c^6*

e^2*f^3*g^8/(d*x + c)^2 + 360*(b*e*x + a*e)^2*a^3*b^2*c^5*d*e^2*f^3*g^8/(d*x + c)^2 + 450*(b*e*x + a*e)^2*a^4*

b*c^4*d^2*e^2*f^3*g^8/(d*x + c)^2 + 120*(b*e*x + a*e)^2*a^5*c^3*d^3*e^2*f^3*g^8/(d*x + c)^2 - 60*(b*e*x + a*e)

^2*a^3*b^2*c^6*e^2*f^2*g^9/(d*x + c)^2 - 180*(b*e*x + a*e)^2*a^4*b*c^5*d*e^2*f^2*g^9/(d*x + c)^2 - 90*(b*e*x +

a*e)^2*a^5*c^4*d^2*e^2*f^2*g^9/(d*x + c)^2 + 30*(b*e*x + a*e)^2*a^4*b*c^6*e^2*f*g^10/(d*x + c)^2 + 36*(b*e*x

+ a*e)^2*a^5*c^5*d*e^2*f*g^10/(d*x + c)^2 - 6*(b*e*x + a*e)^2*a^5*c^6*e^2*g^11/(d*x + c)^2 - 4*(b*e*x + a*e)^3

*b^4*d^7*e*f^11/(d*x + c)^3 + 28*(b*e*x + a*e)^3*b^4*c*d^6*e*f^10*g/(d*x + c)^3 + 16*(b*e*x + a*e)^3*a*b^3*d^7

*e*f^10*g/(d*x + c)^3 - 84*(b*e*x + a*e)^3*b^4*c^2*d^5*e*f^9*g^2/(d*x + c)^3 - 112*(b*e*x + a*e)^3*a*b^3*c*d^6

*e*f^9*g^2/(d*x + c)^3 - 24*(b*e*x + a*e)^3*a^2*b^2*d^7*e*f^9*g^2/(d*x + c)^3 + 140*(b*e*x + a*e)^3*b^4*c^3*d^

4*e*f^8*g^3/(d*x + c)^3 + 336*(b*e*x + a*e)^3*a*b^3*c^2*d^5*e*f^8*g^3/(d*x + c)^3 + 168*(b*e*x + a*e)^3*a^2*b^

2*c*d^6*e*f^8*g^3/(d*x + c)^3 + 16*(b*e*x + a*e)^3*a^3*b*d^7*e*f^8*g^3/(d*x + c)^3 - 140*(b*e*x + a*e)^3*b^4*c

^4*d^3*e*f^7*g^4/(d*x + c)^3 - 560*(b*e*x + a*e)^3*a*b^3*c^3*d^4*e*f^7*g^4/(d*x + c)^3 - 504*(b*e*x + a*e)^3*a

^2*b^2*c^2*d^5*e*f^7*g^4/(d*x + c)^3 - 112*(b*e*x + a*e)^3*a^3*b*c*d^6*e*f^7*g^4/(d*x + c)^3 - 4*(b*e*x + a*e)

^3*a^4*d^7*e*f^7*g^4/(d*x + c)^3 + 84*(b*e*x + a*e)^3*b^4*c^5*d^2*e*f^6*g^5/(d*x + c)^3 + 560*(b*e*x + a*e)^3*

a*b^3*c^4*d^3*e*f^6*g^5/(d*x + c)^3 + 840*(b*e*x + a*e)^3*a^2*b^2*c^3*d^4*e*f^6*g^5/(d*x + c)^3 + 336*(b*e*x +

a*e)^3*a^3*b*c^2*d^5*e*f^6*g^5/(d*x + c)^3 + 28*(b*e*x + a*e)^3*a^4*c*d^6*e*f^6*g^5/(d*x + c)^3 - 28*(b*e*x +

a*e)^3*b^4*c^6*d*e*f^5*g^6/(d*x + c)^3 - 336*(b*e*x + a*e)^3*a*b^3*c^5*d^2*e*f^5*g^6/(d*x + c)^3 - 840*(b*e*x

+ a*e)^3*a^2*b^2*c^4*d^3*e*f^5*g^6/(d*x + c)^3 - 560*(b*e*x + a*e)^3*a^3*b*c^3*d^4*e*f^5*g^6/(d*x + c)^3 - 84

*(b*e*x + a*e)^3*a^4*c^2*d^5*e*f^5*g^6/(d*x + c)^3 + 4*(b*e*x + a*e)^3*b^4*c^7*e*f^4*g^7/(d*x + c)^3 + 112*(b*

e*x + a*e)^3*a*b^3*c^6*d*e*f^4*g^7/(d*x + c)^3 + 504*(b*e*x + a*e)^3*a^2*b^2*c^5*d^2*e*f^4*g^7/(d*x + c)^3 + 5

60*(b*e*x + a*e)^3*a^3*b*c^4*d^3*e*f^4*g^7/(d*x + c)^3 + 140*(b*e*x + a*e)^3*a^4*c^3*d^4*e*f^4*g^7/(d*x + c)^3

- 16*(b*e*x + a*e)^3*a*b^3*c^7*e*f^3*g^8/(d*x + c)^3 - 168*(b*e*x + a*e)^3*a^2*b^2*c^6*d*e*f^3*g^8/(d*x + c)^

3 - 336*(b*e*x + a*e)^3*a^3*b*c^5*d^2*e*f^3*g^8/(d*x + c)^3 - 140*(b*e*x + a*e)^3*a^4*c^4*d^3*e*f^3*g^8/(d*x +

c)^3 + 24*(b*e*x + a*e)^3*a^2*b^2*c^7*e*f^2*g^9/(d*x + c)^3 + 112*(b*e*x + a*e)^3*a^3*b*c^6*d*e*f^2*g^9/(d*x

+ c)^3 + 84*(b*e*x + a*e)^3*a^4*c^5*d^2*e*f^2*g^9/(d*x + c)^3 - 16*(b*e*x + a*e)^3*a^3*b*c^7*e*f*g^10/(d*x + c

)^3 - 28*(b*e*x + a*e)^3*a^4*c^6*d*e*f*g^10/(d*x + c)^3 + 4*(b*e*x + a*e)^3*a^4*c^7*e*g^11/(d*x + c)^3 + (b*e*

x + a*e)^4*b^3*d^8*f^11/(d*x + c)^4 - 8*(b*e*x + a*e)^4*b^3*c*d^7*f^10*g/(d*x + c)^4 - 3*(b*e*x + a*e)^4*a*b^2

*d^8*f^10*g/(d*x + c)^4 + 28*(b*e*x + a*e)^4*b^3*c^2*d^6*f^9*g^2/(d*x + c)^4 + 24*(b*e*x + a*e)^4*a*b^2*c*d^7*

f^9*g^2/(d*x + c)^4 + 3*(b*e*x + a*e)^4*a^2*b*d^8*f^9*g^2/(d*x + c)^4 - 56*(b*e*x + a*e)^4*b^3*c^3*d^5*f^8*g^3

/(d*x + c)^4 - 84*(b*e*x + a*e)^4*a*b^2*c^2*d^6*f^8*g^3/(d*x + c)^4 - 24*(b*e*x + a*e)^4*a^2*b*c*d^7*f^8*g^3/(

d*x + c)^4 - (b*e*x + a*e)^4*a^3*d^8*f^8*g^3/(d*x + c)^4 + 70*(b*e*x + a*e)^4*b^3*c^4*d^4*f^7*g^4/(d*x + c)^4

+ 168*(b*e*x + a*e)^4*a*b^2*c^3*d^5*f^7*g^4/(d*x + c)^4 + 84*(b*e*x + a*e)^4*a^2*b*c^2*d^6*f^7*g^4/(d*x + c)^4

+ 8*(b*e*x + a*e)^4*a^3*c*d^7*f^7*g^4/(d*x + c)^4 - 56*(b*e*x + a*e)^4*b^3*c^5*d^3*f^6*g^5/(d*x + c)^4 - 210*

(b*e*x + a*e)^4*a*b^2*c^4*d^4*f^6*g^5/(d*x + c)^4 - 168*(b*e*x + a*e)^4*a^2*b*c^3*d^5*f^6*g^5/(d*x + c)^4 - 28

*(b*e*x + a*e)^4*a^3*c^2*d^6*f^6*g^5/(d*x + c)^4 + 28*(b*e*x + a*e)^4*b^3*c^6*d^2*f^5*g^6/(d*x + c)^4 + 168*(b

*e*x + a*e)^4*a*b^2*c^5*d^3*f^5*g^6/(d*x + c)^4 + 210*(b*e*x + a*e)^4*a^2*b*c^4*d^4*f^5*g^6/(d*x + c)^4 + 56*(

b*e*x + a*e)^4*a^3*c^3*d^5*f^5*g^6/(d*x + c)^4 - 8*(b*e*x + a*e)^4*b^3*c^7*d*f^4*g^7/(d*x + c)^4 - 84*(b*e*x +

a*e)^4*a*b^2*c^6*d^2*f^4*g^7/(d*x + c)^4 - 168*(b*e*x + a*e)^4*a^2*b*c^5*d^3*f^4*g^7/(d*x + c)^4 - 70*(b*e*x

+ a*e)^4*a^3*c^4*d^4*f^4*g^7/(d*x + c)^4 + (b*e*x + a*e)^4*b^3*c^8*f^3*g^8/(d*x + c)^4 + 24*(b*e*x + a*e)^4*a*

b^2*c^7*d*f^3*g^8/(d*x + c)^4 + 84*(b*e*x + a*e)^4*a^2*b*c^6*d^2*f^3*g^8/(d*x + c)^4 + 56*(b*e*x + a*e)^4*a^3*

c^5*d^3*f^3*g^8/(d*x + c)^4 - 3*(b*e*x + a*e)^4*a*b^2*c^8*f^2*g^9/(d*x + c)^4 - 24*(b*e*x + a*e)^4*a^2*b*c^7*d

*f^2*g^9/(d*x + c)^4 - 28*(b*e*x + a*e)^4*a^3*c^6*d^2*f^2*g^9/(d*x + c)^4 + 3*(b*e*x + a*e)^4*a^2*b*c^8*f*g^10

/(d*x + c)^4 + 8*(b*e*x + a*e)^4*a^3*c^7*d*f*g^10/(d*x + c)^4 - (b*e*x + a*e)^4*a^3*c^8*g^11/(d*x + c)^4))*(b*

c/((b*c*e - a*d*e)*(b*c - a*d)) - a*d/((b*c*e - a*d*e)*(b*c - a*d)))

Mupad [B] (veriﬁcation not implemented)

Time = 12.46 (sec) , antiderivative size = 2518, normalized size of antiderivative = 6.64 \[ \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(f+g x)^5} \, dx=\text {Too large to display} \]

(log(f + g*x)*(g*(6*B*a^2*b^2*d^4*f^2 - 6*B*b^4*c^2*d^2*f^2) - g^2*(4*B*a^3*b*d^4*f - 4*B*b^4*c^3*d*f) + g^3*(

B*a^4*d^4 - B*b^4*c^4) - 4*B*a*b^3*d^4*f^3 + 4*B*b^4*c*d^3*f^3))/(4*a^4*c^4*g^8 + 4*b^4*d^4*f^8 + 4*a^4*d^4*f^

4*g^4 + 4*b^4*c^4*f^4*g^4 + 24*a^2*b^2*c^4*f^2*g^6 + 24*a^2*b^2*d^4*f^6*g^2 + 24*a^4*c^2*d^2*f^2*g^6 + 24*b^4*

c^2*d^2*f^6*g^2 - 16*a^3*b*c^4*f*g^7 - 16*a*b^3*d^4*f^7*g - 16*a^4*c^3*d*f*g^7 - 16*b^4*c*d^3*f^7*g - 16*a*b^3

*c^4*f^3*g^5 - 16*a^3*b*d^4*f^5*g^3 - 16*a^4*c*d^3*f^3*g^5 - 16*b^4*c^3*d*f^5*g^3 + 64*a*b^3*c*d^3*f^6*g^2 + 6

4*a*b^3*c^3*d*f^4*g^4 + 64*a^3*b*c*d^3*f^4*g^4 + 64*a^3*b*c^3*d*f^2*g^6 - 96*a*b^3*c^2*d^2*f^5*g^3 - 96*a^2*b^

2*c*d^3*f^5*g^3 - 96*a^2*b^2*c^3*d*f^3*g^5 - 96*a^3*b*c^2*d^2*f^3*g^5 + 144*a^2*b^2*c^2*d^2*f^4*g^4) - ((6*A*a

^3*c^3*g^6 + 6*A*b^3*d^3*f^6 - 6*A*a^3*d^3*f^3*g^3 - 6*A*b^3*c^3*f^3*g^3 - 11*B*a^3*d^3*f^3*g^3 + 11*B*b^3*c^3

*f^3*g^3 + 18*A*a*b^2*c^3*f^2*g^4 + 18*A*a^2*b*d^3*f^4*g^2 - 7*B*a*b^2*c^3*f^2*g^4 + 18*A*a^3*c*d^2*f^2*g^4 +

31*B*a^2*b*d^3*f^4*g^2 + 18*A*b^3*c^2*d*f^4*g^2 + 7*B*a^3*c*d^2*f^2*g^4 - 31*B*b^3*c^2*d*f^4*g^2 - 18*A*a^2*b*

c^3*f*g^5 - 18*A*a*b^2*d^3*f^5*g + 2*B*a^2*b*c^3*f*g^5 - 18*A*a^3*c^2*d*f*g^5 - 26*B*a*b^2*d^3*f^5*g - 18*A*b^

3*c*d^2*f^5*g - 2*B*a^3*c^2*d*f*g^5 + 26*B*b^3*c*d^2*f^5*g + 54*A*a*b^2*c*d^2*f^4*g^2 - 54*A*a*b^2*c^2*d*f^3*g

^3 - 54*A*a^2*b*c*d^2*f^3*g^3 + 54*A*a^2*b*c^2*d*f^2*g^4 + 15*B*a*b^2*c^2*d*f^3*g^3 - 15*B*a^2*b*c*d^2*f^3*g^3

)/(6*(a^3*c^3*g^6 + b^3*d^3*f^6 - a^3*d^3*f^3*g^3 - b^3*c^3*f^3*g^3 - 3*a^2*b*c^3*f*g^5 - 3*a*b^2*d^3*f^5*g -

3*a^3*c^2*d*f*g^5 - 3*b^3*c*d^2*f^5*g + 3*a*b^2*c^3*f^2*g^4 + 3*a^2*b*d^3*f^4*g^2 + 3*a^3*c*d^2*f^2*g^4 + 3*b^

3*c^2*d*f^4*g^2 + 9*a*b^2*c*d^2*f^4*g^2 - 9*a*b^2*c^2*d*f^3*g^3 - 9*a^2*b*c*d^2*f^3*g^3 + 9*a^2*b*c^2*d*f^2*g^

4)) - (x^2*(B*a*b^2*c^3*g^6 - B*a^3*c*d^2*g^6 + 7*B*a^3*d^3*f*g^5 - 7*B*b^3*c^3*f*g^5 + 20*B*a*b^2*d^3*f^3*g^3

- 21*B*a^2*b*d^3*f^2*g^4 - 20*B*b^3*c*d^2*f^3*g^3 + 21*B*b^3*c^2*d*f^2*g^4 - 3*B*a*b^2*c^2*d*f*g^5 + 3*B*a^2*

b*c*d^2*f*g^5))/(2*(a^3*c^3*g^6 + b^3*d^3*f^6 - a^3*d^3*f^3*g^3 - b^3*c^3*f^3*g^3 - 3*a^2*b*c^3*f*g^5 - 3*a*b^

2*d^3*f^5*g - 3*a^3*c^2*d*f*g^5 - 3*b^3*c*d^2*f^5*g + 3*a*b^2*c^3*f^2*g^4 + 3*a^2*b*d^3*f^4*g^2 + 3*a^3*c*d^2*

f^2*g^4 + 3*b^3*c^2*d*f^4*g^2 + 9*a*b^2*c*d^2*f^4*g^2 - 9*a*b^2*c^2*d*f^3*g^3 - 9*a^2*b*c*d^2*f^3*g^3 + 9*a^2*

b*c^2*d*f^2*g^4)) + (x*(B*a^2*b*c^3*g^6 - B*a^3*c^2*d*g^6 - 13*B*a^3*d^3*f^2*g^4 + 13*B*b^3*c^3*f^2*g^4 - 34*B

*a*b^2*d^3*f^4*g^2 + 38*B*a^2*b*d^3*f^3*g^3 + 34*B*b^3*c*d^2*f^4*g^2 - 38*B*b^3*c^2*d*f^3*g^3 - 5*B*a*b^2*c^3*

f*g^5 + 5*B*a^3*c*d^2*f*g^5 + 12*B*a*b^2*c^2*d*f^2*g^4 - 12*B*a^2*b*c*d^2*f^2*g^4))/(3*(a^3*c^3*g^6 + b^3*d^3*

f^6 - a^3*d^3*f^3*g^3 - b^3*c^3*f^3*g^3 - 3*a^2*b*c^3*f*g^5 - 3*a*b^2*d^3*f^5*g - 3*a^3*c^2*d*f*g^5 - 3*b^3*c*

d^2*f^5*g + 3*a*b^2*c^3*f^2*g^4 + 3*a^2*b*d^3*f^4*g^2 + 3*a^3*c*d^2*f^2*g^4 + 3*b^3*c^2*d*f^4*g^2 + 9*a*b^2*c*

d^2*f^4*g^2 - 9*a*b^2*c^2*d*f^3*g^3 - 9*a^2*b*c*d^2*f^3*g^3 + 9*a^2*b*c^2*d*f^2*g^4)) - (x^3*(B*a^3*d^3*g^6 -

B*b^3*c^3*g^6 + 3*B*a*b^2*d^3*f^2*g^4 - 3*B*b^3*c*d^2*f^2*g^4 - 3*B*a^2*b*d^3*f*g^5 + 3*B*b^3*c^2*d*f*g^5))/(a

^3*c^3*g^6 + b^3*d^3*f^6 - a^3*d^3*f^3*g^3 - b^3*c^3*f^3*g^3 - 3*a^2*b*c^3*f*g^5 - 3*a*b^2*d^3*f^5*g - 3*a^3*c

^2*d*f*g^5 - 3*b^3*c*d^2*f^5*g + 3*a*b^2*c^3*f^2*g^4 + 3*a^2*b*d^3*f^4*g^2 + 3*a^3*c*d^2*f^2*g^4 + 3*b^3*c^2*d

*f^4*g^2 + 9*a*b^2*c*d^2*f^4*g^2 - 9*a*b^2*c^2*d*f^3*g^3 - 9*a^2*b*c*d^2*f^3*g^3 + 9*a^2*b*c^2*d*f^2*g^4))/(4*

f^4*g + 4*g^5*x^4 + 16*f^3*g^2*x + 16*f*g^4*x^3 + 24*f^2*g^3*x^2) - (B*log((e*(a + b*x))/(c + d*x)))/(4*g*(f^4

+ g^4*x^4 + 4*f^3*g*x + 4*f*g^3*x^3 + 6*f^2*g^2*x^2)) + (B*b^4*log(a + b*x))/(4*a^4*g^5 + 4*b^4*f^4*g - 16*a*

b^3*f^3*g^2 + 24*a^2*b^2*f^2*g^3 - 16*a^3*b*f*g^4) - (B*d^4*log(c + d*x))/(4*c^4*g^5 + 4*d^4*f^4*g - 16*c*d^3*

\(\int \frac {A+B \log (\frac {e (a+b x)}{c+d x})}{(f+g x)^5} \, dx\) [239]

Optimal result