3.82 \(\int \frac{(c i+d i x)^3 (A+B \log (\frac{e (a+b x)}{c+d x}))^2}{(a g+b g x)^6} \, dx\)

Optimal. Leaf size=299 \[ -\frac{b i^3 (c+d x)^5 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{5 g^6 (a+b x)^5 (b c-a d)^2}-\frac{2 b B i^3 (c+d x)^5 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{25 g^6 (a+b x)^5 (b c-a d)^2}+\frac{d i^3 (c+d x)^4 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{4 g^6 (a+b x)^4 (b c-a d)^2}+\frac{B d i^3 (c+d x)^4 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{8 g^6 (a+b x)^4 (b c-a d)^2}-\frac{2 b B^2 i^3 (c+d x)^5}{125 g^6 (a+b x)^5 (b c-a d)^2}+\frac{B^2 d i^3 (c+d x)^4}{32 g^6 (a+b x)^4 (b c-a d)^2} \]

[Out]

(B^2*d*i^3*(c + d*x)^4)/(32*(b*c - a*d)^2*g^6*(a + b*x)^4) - (2*b*B^2*i^3*(c + d*x)^5)/(125*(b*c - a*d)^2*g^6*
(a + b*x)^5) + (B*d*i^3*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(8*(b*c - a*d)^2*g^6*(a + b*x)^4) -
(2*b*B*i^3*(c + d*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(25*(b*c - a*d)^2*g^6*(a + b*x)^5) + (d*i^3*(c +
d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(4*(b*c - a*d)^2*g^6*(a + b*x)^4) - (b*i^3*(c + d*x)^5*(A + B*L
og[(e*(a + b*x))/(c + d*x)])^2)/(5*(b*c - a*d)^2*g^6*(a + b*x)^5)

________________________________________________________________________________________

Rubi [C]  time = 5.19533, antiderivative size = 1061, normalized size of antiderivative = 3.55, number of steps used = 146, number of rules used = 11, integrand size = 42, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.262, Rules used = {2528, 2525, 12, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391} \[ -\frac{B^2 i^3 \log ^2(a+b x) d^5}{20 b^4 (b c-a d)^2 g^6}-\frac{B^2 i^3 \log ^2(c+d x) d^5}{20 b^4 (b c-a d)^2 g^6}+\frac{9 B^2 i^3 \log (a+b x) d^5}{200 b^4 (b c-a d)^2 g^6}+\frac{B i^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^5}{10 b^4 (b c-a d)^2 g^6}-\frac{9 B^2 i^3 \log (c+d x) d^5}{200 b^4 (b c-a d)^2 g^6}+\frac{B^2 i^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) d^5}{10 b^4 (b c-a d)^2 g^6}-\frac{B i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x) d^5}{10 b^4 (b c-a d)^2 g^6}+\frac{B^2 i^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right ) d^5}{10 b^4 (b c-a d)^2 g^6}+\frac{B^2 i^3 \text{PolyLog}\left (2,-\frac{d (a+b x)}{b c-a d}\right ) d^5}{10 b^4 (b c-a d)^2 g^6}+\frac{B^2 i^3 \text{PolyLog}\left (2,\frac{b (c+d x)}{b c-a d}\right ) d^5}{10 b^4 (b c-a d)^2 g^6}+\frac{B i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^4}{10 b^4 (b c-a d) g^6 (a+b x)}+\frac{9 B^2 i^3 d^4}{200 b^4 (b c-a d) g^6 (a+b x)}-\frac{i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 d^3}{2 b^4 g^6 (a+b x)^2}-\frac{B i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^3}{20 b^4 g^6 (a+b x)^2}+\frac{11 B^2 i^3 d^3}{400 b^4 g^6 (a+b x)^2}-\frac{(b c-a d) i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 d^2}{b^4 g^6 (a+b x)^3}-\frac{3 B (b c-a d) i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^2}{10 b^4 g^6 (a+b x)^3}-\frac{7 B^2 (b c-a d) i^3 d^2}{200 b^4 g^6 (a+b x)^3}-\frac{3 (b c-a d)^2 i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 d}{4 b^4 g^6 (a+b x)^4}-\frac{11 B (b c-a d)^2 i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d}{40 b^4 g^6 (a+b x)^4}-\frac{39 B^2 (b c-a d)^2 i^3 d}{800 b^4 g^6 (a+b x)^4}-\frac{(b c-a d)^3 i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{2 B (b c-a d)^3 i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac{2 B^2 (b c-a d)^3 i^3}{125 b^4 g^6 (a+b x)^5} \]

Antiderivative was successfully verified.

[In]

Int[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^6,x]

[Out]

(-2*B^2*(b*c - a*d)^3*i^3)/(125*b^4*g^6*(a + b*x)^5) - (39*B^2*d*(b*c - a*d)^2*i^3)/(800*b^4*g^6*(a + b*x)^4)
- (7*B^2*d^2*(b*c - a*d)*i^3)/(200*b^4*g^6*(a + b*x)^3) + (11*B^2*d^3*i^3)/(400*b^4*g^6*(a + b*x)^2) + (9*B^2*
d^4*i^3)/(200*b^4*(b*c - a*d)*g^6*(a + b*x)) + (9*B^2*d^5*i^3*Log[a + b*x])/(200*b^4*(b*c - a*d)^2*g^6) - (B^2
*d^5*i^3*Log[a + b*x]^2)/(20*b^4*(b*c - a*d)^2*g^6) - (2*B*(b*c - a*d)^3*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x
)]))/(25*b^4*g^6*(a + b*x)^5) - (11*B*d*(b*c - a*d)^2*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(40*b^4*g^6*(a
+ b*x)^4) - (3*B*d^2*(b*c - a*d)*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(10*b^4*g^6*(a + b*x)^3) - (B*d^3*
i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(20*b^4*g^6*(a + b*x)^2) + (B*d^4*i^3*(A + B*Log[(e*(a + b*x))/(c +
d*x)]))/(10*b^4*(b*c - a*d)*g^6*(a + b*x)) + (B*d^5*i^3*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(10
*b^4*(b*c - a*d)^2*g^6) - ((b*c - a*d)^3*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(5*b^4*g^6*(a + b*x)^5) -
(3*d*(b*c - a*d)^2*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(4*b^4*g^6*(a + b*x)^4) - (d^2*(b*c - a*d)*i^3
*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(b^4*g^6*(a + b*x)^3) - (d^3*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])
^2)/(2*b^4*g^6*(a + b*x)^2) - (9*B^2*d^5*i^3*Log[c + d*x])/(200*b^4*(b*c - a*d)^2*g^6) + (B^2*d^5*i^3*Log[-((d
*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(10*b^4*(b*c - a*d)^2*g^6) - (B*d^5*i^3*(A + B*Log[(e*(a + b*x))/(c +
d*x)])*Log[c + d*x])/(10*b^4*(b*c - a*d)^2*g^6) - (B^2*d^5*i^3*Log[c + d*x]^2)/(20*b^4*(b*c - a*d)^2*g^6) + (B
^2*d^5*i^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(10*b^4*(b*c - a*d)^2*g^6) + (B^2*d^5*i^3*PolyLog[2, -
((d*(a + b*x))/(b*c - a*d))])/(10*b^4*(b*c - a*d)^2*g^6) + (B^2*d^5*i^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])
/(10*b^4*(b*c - a*d)^2*g^6)

Rule 2528

Int[((a_.) + Log[(c_.)*(RFx_)^(p_.)]*(b_.))^(n_.)*(RGx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*
RFx^p])^n, RGx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, p}, x] && RationalFunctionQ[RFx, x] && RationalF
unctionQ[RGx, x] && IGtQ[n, 0]

Rule 2525

Int[((a_.) + Log[(c_.)*(RFx_)^(p_.)]*(b_.))^(n_.)*((d_.) + (e_.)*(x_))^(m_.), x_Symbol] :> Simp[((d + e*x)^(m
+ 1)*(a + b*Log[c*RFx^p])^n)/(e*(m + 1)), x] - Dist[(b*n*p)/(e*(m + 1)), Int[SimplifyIntegrand[((d + e*x)^(m +
1)*(a + b*Log[c*RFx^p])^(n - 1)*D[RFx, x])/RFx, x], x], x] /; FreeQ[{a, b, c, d, e, m, p}, x] && RationalFunc
tionQ[RFx, x] && IGtQ[n, 0] && (EqQ[n, 1] || IntegerQ[m]) && NeQ[m, -1]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 44

Int[((a_) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*
x)^n, x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0] && ILtQ[m, 0] && IntegerQ[n] &&  !(IGtQ[n, 0] && L
tQ[m + n + 2, 0])

Rule 2524

Int[((a_.) + Log[(c_.)*(RFx_)^(p_.)]*(b_.))^(n_.)/((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[(Log[d + e*x]*(a + b
*Log[c*RFx^p])^n)/e, x] - Dist[(b*n*p)/e, Int[(Log[d + e*x]*(a + b*Log[c*RFx^p])^(n - 1)*D[RFx, x])/RFx, x], x
] /; FreeQ[{a, b, c, d, e, p}, x] && RationalFunctionQ[RFx, x] && IGtQ[n, 0]

Rule 2418

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[
(a + b*Log[c*(d + e*x)^n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, d, e, n}, x] && RationalFunct
ionQ[RFx, x] && IntegerQ[p]

Rule 2390

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_) + (g_.)*(x_))^(q_.), x_Symbol] :> Dist[1/
e, Subst[Int[((f*x)/d)^q*(a + b*Log[c*x^n])^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, n, p, q}, x]
&& EqQ[e*f - d*g, 0]

Rule 2301

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

Rule 2394

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))/((f_.) + (g_.)*(x_)), x_Symbol] :> Simp[(Log[(e*(f +
g*x))/(e*f - d*g)]*(a + b*Log[c*(d + e*x)^n]))/g, x] - Dist[(b*e*n)/g, Int[Log[(e*(f + g*x))/(e*f - d*g)]/(d +
e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n}, x] && NeQ[e*f - d*g, 0]

Rule 2393

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))]*(b_.))/((f_.) + (g_.)*(x_)), x_Symbol] :> Dist[1/g, Subst[Int[(a +
b*Log[1 + (c*e*x)/g])/x, x], x, f + g*x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[e*f - d*g, 0] && EqQ[g
+ c*(e*f - d*g), 0]

Rule 2391

Int[Log[(c_.)*((d_) + (e_.)*(x_)^(n_.))]/(x_), x_Symbol] :> -Simp[PolyLog[2, -(c*e*x^n)]/n, x] /; FreeQ[{c, d,
e, n}, x] && EqQ[c*d, 1]

Rubi steps

\begin{align*} \int \frac{(82 c+82 d x)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a g+b g x)^6} \, dx &=\int \left (\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^6 (a+b x)^6}+\frac{1654104 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^6 (a+b x)^5}+\frac{1654104 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^6 (a+b x)^4}+\frac{551368 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^6 (a+b x)^3}\right ) \, dx\\ &=\frac{\left (551368 d^3\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^3} \, dx}{b^3 g^6}+\frac{\left (1654104 d^2 (b c-a d)\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^4} \, dx}{b^3 g^6}+\frac{\left (1654104 d (b c-a d)^2\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^5} \, dx}{b^3 g^6}+\frac{\left (551368 (b c-a d)^3\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^6} \, dx}{b^3 g^6}\\ &=-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}+\frac{\left (551368 B d^3\right ) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B d^2 (b c-a d)\right ) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (827052 B d (b c-a d)^2\right ) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x)^5 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B (b c-a d)^3\right ) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x)^6 (c+d x)} \, dx}{5 b^4 g^6}\\ &=-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}+\frac{\left (551368 B d^3 (b c-a d)\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B d^2 (b c-a d)^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (827052 B d (b c-a d)^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^5 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B (b c-a d)^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^6 (c+d x)} \, dx}{5 b^4 g^6}\\ &=-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}+\frac{\left (551368 B d^3 (b c-a d)\right ) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^3}-\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac{\left (1102736 B d^2 (b c-a d)^2\right ) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^4}-\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^3}+\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^2}-\frac{b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)}+\frac{d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac{\left (827052 B d (b c-a d)^3\right ) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^5}-\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^4}+\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^3}-\frac{b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)^2}+\frac{b d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (a+b x)}-\frac{d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac{\left (1102736 B (b c-a d)^4\right ) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^6}-\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^5}+\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^4}-\frac{b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)^3}+\frac{b d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (a+b x)^2}-\frac{b d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^6 (a+b x)}+\frac{d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^6 (c+d x)}\right ) \, dx}{5 b^4 g^6}\\ &=-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac{\left (1102736 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{5 b^3 g^6}+\frac{\left (551368 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{b^3 g^6}+\frac{\left (827052 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{b^3 g^6}-\frac{\left (1102736 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{b^3 g^6}-\frac{\left (1102736 B d^5\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{5 b^3 (b c-a d)^2 g^6}+\frac{\left (551368 B d^5\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac{\left (827052 B d^5\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac{\left (1102736 B d^5\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac{\left (1102736 B d^6\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{5 b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B d^6\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac{\left (827052 B d^6\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B d^6\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{5 b^3 (b c-a d) g^6}-\frac{\left (551368 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^3 (b c-a d) g^6}-\frac{\left (827052 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^3 (b c-a d) g^6}+\frac{\left (1102736 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^3 (b c-a d) g^6}+\frac{\left (1102736 B d^2 (b c-a d)\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{5 b^3 g^6}-\frac{\left (827052 B d^2 (b c-a d)\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{b^3 g^6}+\frac{\left (1102736 B d^2 (b c-a d)\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{b^3 g^6}-\frac{\left (1102736 B d (b c-a d)^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^5} \, dx}{5 b^3 g^6}+\frac{\left (827052 B d (b c-a d)^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^5} \, dx}{b^3 g^6}+\frac{\left (1102736 B (b c-a d)^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^6} \, dx}{5 b^3 g^6}\\ &=-\frac{1102736 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac{758131 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac{827052 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac{137842 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac{275684 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac{275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac{275684 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{5 b^4 g^6}+\frac{\left (275684 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (413526 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}-\frac{\left (551368 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{5 b^4 (b c-a d)^2 g^6}-\frac{\left (1102736 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (c+d x)}{e (a+b x)} \, dx}{5 b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (551368 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (c+d x)}{e (a+b x)} \, dx}{b^4 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (827052 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (c+d x)}{e (a+b x)} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{b^4 (b c-a d)^2 g^6}-\frac{\left (1102736 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (c+d x)}{e (a+b x)} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^4\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{5 b^4 (b c-a d) g^6}-\frac{\left (551368 B^2 d^4\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 (b c-a d) g^6}-\frac{\left (827052 B^2 d^4\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 (b c-a d) g^6}+\frac{\left (1102736 B^2 d^4\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 (b c-a d) g^6}+\frac{\left (1102736 B^2 d^2 (b c-a d)\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{15 b^4 g^6}-\frac{\left (275684 B^2 d^2 (b c-a d)\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 d^2 (b c-a d)\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{3 b^4 g^6}-\frac{\left (275684 B^2 d (b c-a d)^2\right ) \int \frac{b c-a d}{(a+b x)^5 (c+d x)} \, dx}{5 b^4 g^6}+\frac{\left (206763 B^2 d (b c-a d)^2\right ) \int \frac{b c-a d}{(a+b x)^5 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 (b c-a d)^3\right ) \int \frac{b c-a d}{(a+b x)^6 (c+d x)} \, dx}{25 b^4 g^6}\\ &=-\frac{1102736 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac{758131 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac{827052 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac{137842 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac{275684 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac{275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac{275684 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^4\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{5 b^4 g^6}-\frac{\left (551368 B^2 d^4\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^6}-\frac{\left (827052 B^2 d^4\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 d^4\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^6}-\frac{\left (551368 B^2 d^3 (b c-a d)\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{5 b^4 g^6}+\frac{\left (275684 B^2 d^3 (b c-a d)\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (413526 B^2 d^3 (b c-a d)\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}-\frac{\left (551368 B^2 d^3 (b c-a d)\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 d^2 (b c-a d)^2\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{15 b^4 g^6}-\frac{\left (275684 B^2 d^2 (b c-a d)^2\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 d^2 (b c-a d)^2\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{3 b^4 g^6}-\frac{\left (275684 B^2 d (b c-a d)^3\right ) \int \frac{1}{(a+b x)^5 (c+d x)} \, dx}{5 b^4 g^6}+\frac{\left (206763 B^2 d (b c-a d)^3\right ) \int \frac{1}{(a+b x)^5 (c+d x)} \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 (b c-a d)^4\right ) \int \frac{1}{(a+b x)^6 (c+d x)} \, dx}{25 b^4 g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{5 b^4 (b c-a d)^2 e g^6}-\frac{\left (1102736 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{5 b^4 (b c-a d)^2 e g^6}-\frac{\left (551368 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^4 (b c-a d)^2 e g^6}+\frac{\left (551368 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{b^4 (b c-a d)^2 e g^6}-\frac{\left (827052 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^4 (b c-a d)^2 e g^6}+\frac{\left (827052 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{b^4 (b c-a d)^2 e g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^4 (b c-a d)^2 e g^6}-\frac{\left (1102736 B^2 d^5\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{b^4 (b c-a d)^2 e g^6}\\ &=-\frac{1102736 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac{758131 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac{827052 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac{137842 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac{275684 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac{275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac{275684 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^4\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^2}-\frac{b d}{(b c-a d)^2 (a+b x)}+\frac{d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{5 b^4 g^6}-\frac{\left (551368 B^2 d^4\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^2}-\frac{b d}{(b c-a d)^2 (a+b x)}+\frac{d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{b^4 g^6}-\frac{\left (827052 B^2 d^4\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^2}-\frac{b d}{(b c-a d)^2 (a+b x)}+\frac{d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 d^4\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^2}-\frac{b d}{(b c-a d)^2 (a+b x)}+\frac{d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{b^4 g^6}-\frac{\left (551368 B^2 d^3 (b c-a d)\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{5 b^4 g^6}+\frac{\left (275684 B^2 d^3 (b c-a d)\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac{\left (413526 B^2 d^3 (b c-a d)\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{b^4 g^6}-\frac{\left (551368 B^2 d^3 (b c-a d)\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 d^2 (b c-a d)^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^4}-\frac{b d}{(b c-a d)^2 (a+b x)^3}+\frac{b d^2}{(b c-a d)^3 (a+b x)^2}-\frac{b d^3}{(b c-a d)^4 (a+b x)}+\frac{d^4}{(b c-a d)^4 (c+d x)}\right ) \, dx}{15 b^4 g^6}-\frac{\left (275684 B^2 d^2 (b c-a d)^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^4}-\frac{b d}{(b c-a d)^2 (a+b x)^3}+\frac{b d^2}{(b c-a d)^3 (a+b x)^2}-\frac{b d^3}{(b c-a d)^4 (a+b x)}+\frac{d^4}{(b c-a d)^4 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 d^2 (b c-a d)^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^4}-\frac{b d}{(b c-a d)^2 (a+b x)^3}+\frac{b d^2}{(b c-a d)^3 (a+b x)^2}-\frac{b d^3}{(b c-a d)^4 (a+b x)}+\frac{d^4}{(b c-a d)^4 (c+d x)}\right ) \, dx}{3 b^4 g^6}-\frac{\left (275684 B^2 d (b c-a d)^3\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^5}-\frac{b d}{(b c-a d)^2 (a+b x)^4}+\frac{b d^2}{(b c-a d)^3 (a+b x)^3}-\frac{b d^3}{(b c-a d)^4 (a+b x)^2}+\frac{b d^4}{(b c-a d)^5 (a+b x)}-\frac{d^5}{(b c-a d)^5 (c+d x)}\right ) \, dx}{5 b^4 g^6}+\frac{\left (206763 B^2 d (b c-a d)^3\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^5}-\frac{b d}{(b c-a d)^2 (a+b x)^4}+\frac{b d^2}{(b c-a d)^3 (a+b x)^3}-\frac{b d^3}{(b c-a d)^4 (a+b x)^2}+\frac{b d^4}{(b c-a d)^5 (a+b x)}-\frac{d^5}{(b c-a d)^5 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac{\left (1102736 B^2 (b c-a d)^4\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^6}-\frac{b d}{(b c-a d)^2 (a+b x)^5}+\frac{b d^2}{(b c-a d)^3 (a+b x)^4}-\frac{b d^3}{(b c-a d)^4 (a+b x)^3}+\frac{b d^4}{(b c-a d)^5 (a+b x)^2}-\frac{b d^5}{(b c-a d)^6 (a+b x)}+\frac{d^6}{(b c-a d)^6 (c+d x)}\right ) \, dx}{25 b^4 g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \left (\frac{b e \log (a+b x)}{a+b x}-\frac{d e \log (a+b x)}{c+d x}\right ) \, dx}{5 b^4 (b c-a d)^2 e g^6}-\frac{\left (1102736 B^2 d^5\right ) \int \left (\frac{b e \log (c+d x)}{a+b x}-\frac{d e \log (c+d x)}{c+d x}\right ) \, dx}{5 b^4 (b c-a d)^2 e g^6}-\frac{\left (551368 B^2 d^5\right ) \int \left (\frac{b e \log (a+b x)}{a+b x}-\frac{d e \log (a+b x)}{c+d x}\right ) \, dx}{b^4 (b c-a d)^2 e g^6}+\frac{\left (551368 B^2 d^5\right ) \int \left (\frac{b e \log (c+d x)}{a+b x}-\frac{d e \log (c+d x)}{c+d x}\right ) \, dx}{b^4 (b c-a d)^2 e g^6}-\frac{\left (827052 B^2 d^5\right ) \int \left (\frac{b e \log (a+b x)}{a+b x}-\frac{d e \log (a+b x)}{c+d x}\right ) \, dx}{b^4 (b c-a d)^2 e g^6}+\frac{\left (827052 B^2 d^5\right ) \int \left (\frac{b e \log (c+d x)}{a+b x}-\frac{d e \log (c+d x)}{c+d x}\right ) \, dx}{b^4 (b c-a d)^2 e g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \left (\frac{b e \log (a+b x)}{a+b x}-\frac{d e \log (a+b x)}{c+d x}\right ) \, dx}{b^4 (b c-a d)^2 e g^6}-\frac{\left (1102736 B^2 d^5\right ) \int \left (\frac{b e \log (c+d x)}{a+b x}-\frac{d e \log (c+d x)}{c+d x}\right ) \, dx}{b^4 (b c-a d)^2 e g^6}\\ &=-\frac{1102736 B^2 (b c-a d)^3}{125 b^4 g^6 (a+b x)^5}-\frac{2687919 B^2 d (b c-a d)^2}{100 b^4 g^6 (a+b x)^4}-\frac{482447 B^2 d^2 (b c-a d)}{25 b^4 g^6 (a+b x)^3}+\frac{758131 B^2 d^3}{50 b^4 g^6 (a+b x)^2}+\frac{620289 B^2 d^4}{25 b^4 (b c-a d) g^6 (a+b x)}+\frac{620289 B^2 d^5 \log (a+b x)}{25 b^4 (b c-a d)^2 g^6}-\frac{1102736 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac{758131 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac{827052 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac{137842 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac{275684 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac{275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac{620289 B^2 d^5 \log (c+d x)}{25 b^4 (b c-a d)^2 g^6}-\frac{275684 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{5 b^3 (b c-a d)^2 g^6}-\frac{\left (1102736 B^2 d^5\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{5 b^3 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^5\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac{\left (551368 B^2 d^5\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^5\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac{\left (827052 B^2 d^5\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac{\left (1102736 B^2 d^5\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac{\left (1102736 B^2 d^6\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^6\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (551368 B^2 d^6\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^6\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (827052 B^2 d^6\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^6\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac{\left (1102736 B^2 d^6\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^6\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}\\ &=-\frac{1102736 B^2 (b c-a d)^3}{125 b^4 g^6 (a+b x)^5}-\frac{2687919 B^2 d (b c-a d)^2}{100 b^4 g^6 (a+b x)^4}-\frac{482447 B^2 d^2 (b c-a d)}{25 b^4 g^6 (a+b x)^3}+\frac{758131 B^2 d^3}{50 b^4 g^6 (a+b x)^2}+\frac{620289 B^2 d^4}{25 b^4 (b c-a d) g^6 (a+b x)}+\frac{620289 B^2 d^5 \log (a+b x)}{25 b^4 (b c-a d)^2 g^6}-\frac{1102736 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac{758131 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac{827052 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac{137842 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac{275684 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac{275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac{620289 B^2 d^5 \log (c+d x)}{25 b^4 (b c-a d)^2 g^6}+\frac{275684 B^2 d^5 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac{275684 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac{275684 B^2 d^5 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{5 b^3 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^5\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^5\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^6\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{5 b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^6\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^6\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^6\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}\\ &=-\frac{1102736 B^2 (b c-a d)^3}{125 b^4 g^6 (a+b x)^5}-\frac{2687919 B^2 d (b c-a d)^2}{100 b^4 g^6 (a+b x)^4}-\frac{482447 B^2 d^2 (b c-a d)}{25 b^4 g^6 (a+b x)^3}+\frac{758131 B^2 d^3}{50 b^4 g^6 (a+b x)^2}+\frac{620289 B^2 d^4}{25 b^4 (b c-a d) g^6 (a+b x)}+\frac{620289 B^2 d^5 \log (a+b x)}{25 b^4 (b c-a d)^2 g^6}-\frac{137842 B^2 d^5 \log ^2(a+b x)}{5 b^4 (b c-a d)^2 g^6}-\frac{1102736 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac{758131 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac{827052 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac{137842 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac{275684 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac{275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac{620289 B^2 d^5 \log (c+d x)}{25 b^4 (b c-a d)^2 g^6}+\frac{275684 B^2 d^5 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac{275684 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac{137842 B^2 d^5 \log ^2(c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac{275684 B^2 d^5 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{5 b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}-\frac{\left (551368 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}-\frac{\left (827052 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}+\frac{\left (1102736 B^2 d^5\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}\\ &=-\frac{1102736 B^2 (b c-a d)^3}{125 b^4 g^6 (a+b x)^5}-\frac{2687919 B^2 d (b c-a d)^2}{100 b^4 g^6 (a+b x)^4}-\frac{482447 B^2 d^2 (b c-a d)}{25 b^4 g^6 (a+b x)^3}+\frac{758131 B^2 d^3}{50 b^4 g^6 (a+b x)^2}+\frac{620289 B^2 d^4}{25 b^4 (b c-a d) g^6 (a+b x)}+\frac{620289 B^2 d^5 \log (a+b x)}{25 b^4 (b c-a d)^2 g^6}-\frac{137842 B^2 d^5 \log ^2(a+b x)}{5 b^4 (b c-a d)^2 g^6}-\frac{1102736 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac{758131 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac{827052 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac{137842 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac{275684 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac{275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac{551368 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac{413526 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac{551368 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac{275684 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac{620289 B^2 d^5 \log (c+d x)}{25 b^4 (b c-a d)^2 g^6}+\frac{275684 B^2 d^5 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac{275684 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac{137842 B^2 d^5 \log ^2(c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac{275684 B^2 d^5 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}+\frac{275684 B^2 d^5 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}+\frac{275684 B^2 d^5 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}\\ \end{align*}

Mathematica [C]  time = 4.47046, size = 2289, normalized size = 7.66 \[ \text{Result too large to show} \]

Antiderivative was successfully verified.

[In]

Integrate[((c*i + d*i*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(a*g + b*g*x)^6,x]

[Out]

(i^3*(2000*a^2*B^2*d^2*(b*c - a*d)^3 - 825*a*B^2*d*(b*c - a*d)^4 - 192*B^2*(b*c - a*d)^5 + 4000*a*b*B^2*d^2*(b
*c - a*d)^3*x - 825*b*B^2*d*(b*c - a*d)^4*x + 2000*b^2*B^2*d^2*(b*c - a*d)^3*x^2 - 3000*a^2*B^2*d^3*(b*c - a*d
)^2*(a + b*x) + 1100*a*B^2*d^2*(b*c - a*d)^3*(a + b*x) + 240*B^2*d*(b*c - a*d)^4*(a + b*x) - 6000*a*b*B^2*d^3*
(b*c - a*d)^2*x*(a + b*x) + 1100*b*B^2*d^2*(b*c - a*d)^3*x*(a + b*x) - 3000*b^2*B^2*d^3*(b*c - a*d)^2*x^2*(a +
b*x) + 6000*a^2*B^2*d^4*(b*c - a*d)*(a + b*x)^2 - 6150*a*B^2*d^3*(b*c - a*d)^2*(a + b*x)^2 + 3520*B^2*d^2*(-(
b*c) + a*d)^3*(a + b*x)^2 + 12000*a*b*B^2*d^4*(b*c - a*d)*x*(a + b*x)^2 - 6150*b*B^2*d^3*(b*c - a*d)^2*x*(a +
b*x)^2 + 6000*b^2*B^2*d^4*(b*c - a*d)*x^2*(a + b*x)^2 + 18000*a*b*B^2*c*d^4*(a + b*x)^3 - 18000*a^2*B^2*d^5*(a
+ b*x)^3 + 12300*a*B^2*d^4*(b*c - a*d)*(a + b*x)^3 + 9480*B^2*d^3*(b*c - a*d)^2*(a + b*x)^3 + 18000*b^2*B^2*c
*d^4*x*(a + b*x)^3 - 18000*a*b*B^2*d^5*x*(a + b*x)^3 + 12300*b*B^2*d^4*(b*c - a*d)*x*(a + b*x)^3 - 16800*b*B^2
*c*d^4*(a + b*x)^4 + 16800*a*B^2*d^5*(a + b*x)^4 + 18960*B^2*d^4*(-(b*c) + a*d)*(a + b*x)^4 + 6000*a^2*B^2*d^5
*(a + b*x)^3*Log[a + b*x] + 12000*a*b*B^2*d^5*x*(a + b*x)^3*Log[a + b*x] + 6000*b^2*B^2*d^5*x^2*(a + b*x)^3*Lo
g[a + b*x] + 30300*a*B^2*d^5*(a + b*x)^4*Log[a + b*x] + 30300*b*B^2*d^5*x*(a + b*x)^4*Log[a + b*x] - 35760*B^2
*d^5*(a + b*x)^5*Log[a + b*x] - 4500*a*B*d*(b*c - a*d)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 960*B*(b*c - a
*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 4500*b*B*d*(b*c - a*d)^4*x*(A + B*Log[(e*(a + b*x))/(c + d*x)]) +
6000*a*B*d^2*(b*c - a*d)^3*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 1200*B*d*(b*c - a*d)^4*(a + b*x)*
(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 6000*b*B*d^2*(b*c - a*d)^3*x*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*
x)]) - 9000*a*B*d^3*(b*c - a*d)^2*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 9600*B*d^2*(-(b*c) + a*d)
^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 9000*b*B*d^3*(b*c - a*d)^2*x*(a + b*x)^2*(A + B*Log[(e*(
a + b*x))/(c + d*x)]) + 18000*a*B*d^4*(b*c - a*d)*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 8400*B*d^
3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 18000*b*B*d^4*(b*c - a*d)*x*(a + b*x)^3*(A
+ B*Log[(e*(a + b*x))/(c + d*x)]) + 16800*B*d^4*(-(b*c) + a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]
) + 18000*a*B*d^5*(a + b*x)^4*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 18000*b*B*d^5*x*(a + b*x)^4*
Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 16800*B*d^5*(a + b*x)^5*Log[a + b*x]*(A + B*Log[(e*(a + b*
x))/(c + d*x)]) - 2400*(b*c - a*d)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 9000*d*(b*c - a*d)^4*(a + b*x)*(
A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 12000*d^2*(-(b*c) + a*d)^3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d
*x)])^2 - 6000*d^3*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 6000*a^2*B^2*d^5*(a + b*
x)^3*Log[c + d*x] - 12000*a*b*B^2*d^5*x*(a + b*x)^3*Log[c + d*x] - 6000*b^2*B^2*d^5*x^2*(a + b*x)^3*Log[c + d*
x] - 30300*a*B^2*d^5*(a + b*x)^4*Log[c + d*x] - 30300*b*B^2*d^5*x*(a + b*x)^4*Log[c + d*x] + 35760*B^2*d^5*(a
+ b*x)^5*Log[c + d*x] - 18000*a*B*d^5*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 18000*b*
B*d^5*x*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 16800*B*d^5*(a + b*x)^5*(A + B*Log[(e*
(a + b*x))/(c + d*x)])*Log[c + d*x] - 9000*a*B^2*d^5*(a + b*x)^4*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d
*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 9000*b*B^2*d^5*x*(a + b*x)^4*(Log[a + b*x]*
(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) + 8400*B^2*d^5
*(a + b*x)^5*(Log[a + b*x]*(Log[a + b*x] - 2*Log[(b*(c + d*x))/(b*c - a*d)]) - 2*PolyLog[2, (d*(a + b*x))/(-(b
*c) + a*d)]) + 9000*a*B^2*d^5*(a + b*x)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] +
2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 9000*b*B^2*d^5*x*(a + b*x)^4*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)]
- Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) - 8400*B^2*d^5*(a + b*x)^5*((2*Log[(d
*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])))/(12000*b
^4*(b*c - a*d)^2*g^6*(a + b*x)^5)

________________________________________________________________________________________

Maple [B]  time = 0.055, size = 1814, normalized size = 6.1 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*i*x+c*i)^3*(A+B*ln(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^6,x)

[Out]

1/4*e^4*d^2*i^3/(a*d-b*c)^3/g^6*A^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*a-1/4*e^4*d*i^3/(a*d-b*c)^3/g^6*A^2/
(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*b*c-1/5*e^5*d*i^3/(a*d-b*c)^3/g^6*A^2*b/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b
*c)^5*a+1/5*e^5*i^3/(a*d-b*c)^3/g^6*A^2*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*c+1/2*e^4*d^2*i^3/(a*d-b*c)^
3/g^6*A*B/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*a-1/2*e^4*d*i^3/(a*d-b*c)^3/g^
6*A*B/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*b*c+1/8*e^4*d^2*i^3/(a*d-b*c)^3/g^
6*A*B/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*a-1/8*e^4*d*i^3/(a*d-b*c)^3/g^6*A*B/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)
*b*c)^4*b*c-2/5*e^5*d*i^3/(a*d-b*c)^3/g^6*A*B*b/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*ln(b*e/d+(a*d-b*c)*e/d/(
d*x+c))*a+2/5*e^5*i^3/(a*d-b*c)^3/g^6*A*B*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*ln(b*e/d+(a*d-b*c)*e/d/(d*
x+c))*c-2/25*e^5*d*i^3/(a*d-b*c)^3/g^6*A*B*b/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*a+2/25*e^5*i^3/(a*d-b*c)^3/
g^6*A*B*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*c+1/4*e^4*d^2*i^3/(a*d-b*c)^3/g^6*B^2/(b*e/d+e/(d*x+c)*a-e/d
/(d*x+c)*b*c)^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2*a-1/4*e^4*d*i^3/(a*d-b*c)^3/g^6*B^2/(b*e/d+e/(d*x+c)*a-e/d/(
d*x+c)*b*c)^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2*b*c+1/8*e^4*d^2*i^3/(a*d-b*c)^3/g^6*B^2/(b*e/d+e/(d*x+c)*a-e/d
/(d*x+c)*b*c)^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*a-1/8*e^4*d*i^3/(a*d-b*c)^3/g^6*B^2/(b*e/d+e/(d*x+c)*a-e/d/(d*
x+c)*b*c)^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*b*c+1/32*e^4*d^2*i^3/(a*d-b*c)^3/g^6*B^2/(b*e/d+e/(d*x+c)*a-e/d/(d
*x+c)*b*c)^4*a-1/32*e^4*d*i^3/(a*d-b*c)^3/g^6*B^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*b*c-1/5*e^5*d*i^3/(a*d
-b*c)^3/g^6*B^2*b/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2*a+1/5*e^5*i^3/(a*d-b
*c)^3/g^6*B^2*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2*c-2/25*e^5*d*i^3/(a*
d-b*c)^3/g^6*B^2*b/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*a+2/25*e^5*i^3/(a*d-b
*c)^3/g^6*B^2*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*c-2/125*e^5*d*i^3/(a*d
-b*c)^3/g^6*B^2*b/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*a+2/125*e^5*i^3/(a*d-b*c)^3/g^6*B^2*b^2/(b*e/d+e/(d*x+
c)*a-e/d/(d*x+c)*b*c)^5*c

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Maxima [B]  time = 9.61578, size = 21283, normalized size = 71.18 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^6,x, algorithm="maxima")

[Out]

-3/20*(5*b*x + a)*B^2*c^2*d*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2
*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/10*(10*b^2*x^2 + 5*a*b*x + a^2)*B^2*c*d
^2*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5
*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/20*(10*b^3*x^3 + 10*a*b^2*x^2 + 5*a^2*b*x + a^3)*B^2*d^3*i^3*log
(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^9*g^6*x^5 + 5*a*b^8*g^6*x^4 + 10*a^2*b^7*g^6*x^3 + 10*a^3*b^6*g^6*x^2 +
5*a^4*b^5*g^6*x + a^5*b^4*g^6) - 1/9000*(60*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*
d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 +
47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a
*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a
^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^
2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4
*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b
^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*d^
5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d
^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2
*c*d^4 - a^5*b*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (144*b^5*c^5 - 1125*a*b^4*c^4*d + 4000*a^2*b^
3*c^3*d^2 - 9000*a^3*b^2*c^2*d^3 + 18000*a^4*b*c*d^4 - 12019*a^5*d^5 + 8220*(b^5*c*d^4 - a*b^4*d^5)*x^4 - 30*(
77*b^5*c^2*d^3 - 1250*a*b^4*c*d^4 + 1173*a^2*b^3*d^5)*x^3 + 10*(94*b^5*c^3*d^2 - 975*a*b^4*c^2*d^3 + 6600*a^2*
b^3*c*d^4 - 5719*a^3*b^2*d^5)*x^2 - 1800*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*
x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a)^2 - 1800*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*
a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(d*x + c)^2 - 5*(81*b^5*c^4*d - 700*a*b^4*c^3*d^2 + 3000*a^2*b^3
*c^2*d^3 - 10800*a^3*b^2*c*d^4 + 8419*a^4*b*d^5)*x + 8220*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3
+ 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a) - 60*(137*b^5*d^5*x^5 + 685*a*b^4*d^5*x^4 + 1370*
a^2*b^3*d^5*x^3 + 1370*a^3*b^2*d^5*x^2 + 685*a^4*b*d^5*x + 137*a^5*d^5 - 60*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 1
0*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a))*log(d*x + c))/(a^5*b^6*c^5*g^6
- 5*a^6*b^5*c^4*d*g^6 + 10*a^7*b^4*c^3*d^2*g^6 - 10*a^8*b^3*c^2*d^3*g^6 + 5*a^9*b^2*c*d^4*g^6 - a^10*b*d^5*g^
6 + (b^11*c^5*g^6 - 5*a*b^10*c^4*d*g^6 + 10*a^2*b^9*c^3*d^2*g^6 - 10*a^3*b^8*c^2*d^3*g^6 + 5*a^4*b^7*c*d^4*g^6
- a^5*b^6*d^5*g^6)*x^5 + 5*(a*b^10*c^5*g^6 - 5*a^2*b^9*c^4*d*g^6 + 10*a^3*b^8*c^3*d^2*g^6 - 10*a^4*b^7*c^2*d^
3*g^6 + 5*a^5*b^6*c*d^4*g^6 - a^6*b^5*d^5*g^6)*x^4 + 10*(a^2*b^9*c^5*g^6 - 5*a^3*b^8*c^4*d*g^6 + 10*a^4*b^7*c^
3*d^2*g^6 - 10*a^5*b^6*c^2*d^3*g^6 + 5*a^6*b^5*c*d^4*g^6 - a^7*b^4*d^5*g^6)*x^3 + 10*(a^3*b^8*c^5*g^6 - 5*a^4*
b^7*c^4*d*g^6 + 10*a^5*b^6*c^3*d^2*g^6 - 10*a^6*b^5*c^2*d^3*g^6 + 5*a^7*b^4*c*d^4*g^6 - a^8*b^3*d^5*g^6)*x^2 +
5*(a^4*b^7*c^5*g^6 - 5*a^5*b^6*c^4*d*g^6 + 10*a^6*b^5*c^3*d^2*g^6 - 10*a^7*b^4*c^2*d^3*g^6 + 5*a^8*b^3*c*d^4*
g^6 - a^9*b^2*d^5*g^6)*x))*B^2*c^3*i^3 - 1/12000*(60*((27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2
- 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2
*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4
- 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*
a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2
- 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*
c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b
^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x
+ (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a
*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5
*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b
^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (549*a*b^5*c^5 - 4625
*a^2*b^4*c^4*d + 19000*a^3*b^3*c^3*d^2 - 63000*a^4*b^2*c^2*d^3 + 51875*a^5*b*c*d^4 - 3799*a^6*d^5 - 60*(625*b^
6*c^2*d^3 - 702*a*b^5*c*d^4 + 77*a^2*b^4*d^5)*x^4 + 30*(325*b^6*c^3*d^2 - 5667*a*b^5*c^2*d^3 + 5975*a^2*b^4*c*
d^4 - 633*a^3*b^3*d^5)*x^3 - 10*(350*b^6*c^4*d - 3949*a*b^5*c^3*d^2 + 29475*a^2*b^4*c^2*d^3 - 28775*a^3*b^3*c*
d^4 + 2899*a^4*b^2*d^5)*x^2 + 1800*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4
- a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a
^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(b*x + a)^2 + 1800*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 +
5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d
^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(d*x + c)^2 + 5*(225*b^6*c^5 - 2201*a*b^5*c^4*d + 10900*a^2*b^
4*c^3*d^2 - 46200*a^3*b^3*c^2*d^3 + 41075*a^4*b^2*c*d^4 - 3799*a^5*b*d^5)*x - 60*(625*a^5*b*c*d^4 - 77*a^6*d^5
+ (625*b^6*c*d^4 - 77*a*b^5*d^5)*x^5 + 5*(625*a*b^5*c*d^4 - 77*a^2*b^4*d^5)*x^4 + 10*(625*a^2*b^4*c*d^4 - 77*
a^3*b^3*d^5)*x^3 + 10*(625*a^3*b^3*c*d^4 - 77*a^4*b^2*d^5)*x^2 + 5*(625*a^4*b^2*c*d^4 - 77*a^5*b*d^5)*x)*log(b
*x + a) + 60*(625*a^5*b*c*d^4 - 77*a^6*d^5 + (625*b^6*c*d^4 - 77*a*b^5*d^5)*x^5 + 5*(625*a*b^5*c*d^4 - 77*a^2*
b^4*d^5)*x^4 + 10*(625*a^2*b^4*c*d^4 - 77*a^3*b^3*d^5)*x^3 + 10*(625*a^3*b^3*c*d^4 - 77*a^4*b^2*d^5)*x^2 + 5*(
625*a^4*b^2*c*d^4 - 77*a^5*b*d^5)*x - 60*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5
*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 +
5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(b*x + a))*log(d*x + c))/(a^5*b^7*c^5*g^6 - 5*a^6*b^6*c^4*d*g^6 + 10*a^7
*b^5*c^3*d^2*g^6 - 10*a^8*b^4*c^2*d^3*g^6 + 5*a^9*b^3*c*d^4*g^6 - a^10*b^2*d^5*g^6 + (b^12*c^5*g^6 - 5*a*b^11*
c^4*d*g^6 + 10*a^2*b^10*c^3*d^2*g^6 - 10*a^3*b^9*c^2*d^3*g^6 + 5*a^4*b^8*c*d^4*g^6 - a^5*b^7*d^5*g^6)*x^5 + 5*
(a*b^11*c^5*g^6 - 5*a^2*b^10*c^4*d*g^6 + 10*a^3*b^9*c^3*d^2*g^6 - 10*a^4*b^8*c^2*d^3*g^6 + 5*a^5*b^7*c*d^4*g^6
- a^6*b^6*d^5*g^6)*x^4 + 10*(a^2*b^10*c^5*g^6 - 5*a^3*b^9*c^4*d*g^6 + 10*a^4*b^8*c^3*d^2*g^6 - 10*a^5*b^7*c^2
*d^3*g^6 + 5*a^6*b^6*c*d^4*g^6 - a^7*b^5*d^5*g^6)*x^3 + 10*(a^3*b^9*c^5*g^6 - 5*a^4*b^8*c^4*d*g^6 + 10*a^5*b^7
*c^3*d^2*g^6 - 10*a^6*b^6*c^2*d^3*g^6 + 5*a^7*b^5*c*d^4*g^6 - a^8*b^4*d^5*g^6)*x^2 + 5*(a^4*b^8*c^5*g^6 - 5*a^
5*b^7*c^4*d*g^6 + 10*a^6*b^6*c^3*d^2*g^6 - 10*a^7*b^5*c^2*d^3*g^6 + 5*a^8*b^4*c*d^4*g^6 - a^9*b^3*d^5*g^6)*x))
*B^2*c^2*d*i^3 - 1/18000*(60*((47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47
*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^
2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3
+ 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5
*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^
11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*
a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d
+ 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c
^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4
*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*
d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b
*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4
*c*d^4 - a^5*b^3*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (1489*a^2*b^5*c^5 - 14375*a^3*b^4*c^4*d + 8
5000*a^4*b^3*c^3*d^2 - 85000*a^5*b^2*c^2*d^3 + 14375*a^6*b*c*d^4 - 1489*a^7*d^5 + 60*(1100*b^7*c^3*d^2 - 1425*
a*b^6*c^2*d^3 + 372*a^2*b^5*c*d^4 - 47*a^3*b^4*d^5)*x^4 - 30*(500*b^7*c^4*d - 9825*a*b^6*c^3*d^2 + 11937*a^2*b
^5*c^2*d^3 - 2975*a^3*b^4*c*d^4 + 363*a^4*b^3*d^5)*x^3 + 10*(400*b^7*c^5 - 5450*a*b^6*c^4*d + 49189*a^2*b^5*c^
3*d^2 - 55525*a^3*b^4*c^2*d^3 + 12875*a^4*b^3*c*d^4 - 1489*a^5*b^2*d^5)*x^2 - 1800*(10*a^5*b^2*c^2*d^3 - 5*a^6
*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^
4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 -
5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(b*x + a)^2 -
1800*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(1
0*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)
*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 +
a^6*b*d^5)*x)*log(d*x + c)^2 + 5*(925*a*b^6*c^5 - 9911*a^2*b^5*c^4*d + 67900*a^3*b^4*c^3*d^2 - 71800*a^4*b^3*
c^2*d^3 + 14375*a^5*b^2*c*d^4 - 1489*a^6*b*d^5)*x + 60*(1100*a^5*b^2*c^2*d^3 - 325*a^6*b*c*d^4 + 47*a^7*d^5 +
(1100*b^7*c^2*d^3 - 325*a*b^6*c*d^4 + 47*a^2*b^5*d^5)*x^5 + 5*(1100*a*b^6*c^2*d^3 - 325*a^2*b^5*c*d^4 + 47*a^3
*b^4*d^5)*x^4 + 10*(1100*a^2*b^5*c^2*d^3 - 325*a^3*b^4*c*d^4 + 47*a^4*b^3*d^5)*x^3 + 10*(1100*a^3*b^4*c^2*d^3
- 325*a^4*b^3*c*d^4 + 47*a^5*b^2*d^5)*x^2 + 5*(1100*a^4*b^3*c^2*d^3 - 325*a^5*b^2*c*d^4 + 47*a^6*b*d^5)*x)*log
(b*x + a) - 60*(1100*a^5*b^2*c^2*d^3 - 325*a^6*b*c*d^4 + 47*a^7*d^5 + (1100*b^7*c^2*d^3 - 325*a*b^6*c*d^4 + 47
*a^2*b^5*d^5)*x^5 + 5*(1100*a*b^6*c^2*d^3 - 325*a^2*b^5*c*d^4 + 47*a^3*b^4*d^5)*x^4 + 10*(1100*a^2*b^5*c^2*d^3
- 325*a^3*b^4*c*d^4 + 47*a^4*b^3*d^5)*x^3 + 10*(1100*a^3*b^4*c^2*d^3 - 325*a^4*b^3*c*d^4 + 47*a^5*b^2*d^5)*x^
2 + 5*(1100*a^4*b^3*c^2*d^3 - 325*a^5*b^2*c*d^4 + 47*a^6*b*d^5)*x - 60*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a
^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*
d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*
d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(b*x + a))*log(d*x + c))/(
a^5*b^8*c^5*g^6 - 5*a^6*b^7*c^4*d*g^6 + 10*a^7*b^6*c^3*d^2*g^6 - 10*a^8*b^5*c^2*d^3*g^6 + 5*a^9*b^4*c*d^4*g^6
- a^10*b^3*d^5*g^6 + (b^13*c^5*g^6 - 5*a*b^12*c^4*d*g^6 + 10*a^2*b^11*c^3*d^2*g^6 - 10*a^3*b^10*c^2*d^3*g^6 +
5*a^4*b^9*c*d^4*g^6 - a^5*b^8*d^5*g^6)*x^5 + 5*(a*b^12*c^5*g^6 - 5*a^2*b^11*c^4*d*g^6 + 10*a^3*b^10*c^3*d^2*g^
6 - 10*a^4*b^9*c^2*d^3*g^6 + 5*a^5*b^8*c*d^4*g^6 - a^6*b^7*d^5*g^6)*x^4 + 10*(a^2*b^11*c^5*g^6 - 5*a^3*b^10*c^
4*d*g^6 + 10*a^4*b^9*c^3*d^2*g^6 - 10*a^5*b^8*c^2*d^3*g^6 + 5*a^6*b^7*c*d^4*g^6 - a^7*b^6*d^5*g^6)*x^3 + 10*(a
^3*b^10*c^5*g^6 - 5*a^4*b^9*c^4*d*g^6 + 10*a^5*b^8*c^3*d^2*g^6 - 10*a^6*b^7*c^2*d^3*g^6 + 5*a^7*b^6*c*d^4*g^6
- a^8*b^5*d^5*g^6)*x^2 + 5*(a^4*b^9*c^5*g^6 - 5*a^5*b^8*c^4*d*g^6 + 10*a^6*b^7*c^3*d^2*g^6 - 10*a^7*b^6*c^2*d^
3*g^6 + 5*a^8*b^5*c*d^4*g^6 - a^9*b^4*d^5*g^6)*x))*B^2*c*d^2*i^3 - 1/36000*(60*((77*a^3*b^4*c^4 - 548*a^4*b^3*
c^3*d + 352*a^5*b^2*c^2*d^2 - 148*a^6*b*c*d^3 + 27*a^7*d^4 - 60*(10*b^7*c^3*d - 10*a*b^6*c^2*d^2 + 5*a^2*b^5*c
*d^3 - a^3*b^4*d^4)*x^4 + 30*(10*b^7*c^4 - 100*a*b^6*c^3*d + 95*a^2*b^5*c^2*d^2 - 46*a^3*b^4*c*d^3 + 9*a^4*b^3
*d^4)*x^3 + 10*(50*a*b^6*c^4 - 410*a^2*b^5*c^3*d + 337*a^3*b^4*c^2*d^2 - 148*a^4*b^3*c*d^3 + 27*a^5*b^2*d^4)*x
^2 + 5*(65*a^2*b^5*c^4 - 488*a^3*b^4*c^3*d + 352*a^4*b^3*c^2*d^2 - 148*a^5*b^2*c*d^3 + 27*a^6*b*d^4)*x)/((b^13
*c^4 - 4*a*b^12*c^3*d + 6*a^2*b^11*c^2*d^2 - 4*a^3*b^10*c*d^3 + a^4*b^9*d^4)*g^6*x^5 + 5*(a*b^12*c^4 - 4*a^2*b
^11*c^3*d + 6*a^3*b^10*c^2*d^2 - 4*a^4*b^9*c*d^3 + a^5*b^8*d^4)*g^6*x^4 + 10*(a^2*b^11*c^4 - 4*a^3*b^10*c^3*d
+ 6*a^4*b^9*c^2*d^2 - 4*a^5*b^8*c*d^3 + a^6*b^7*d^4)*g^6*x^3 + 10*(a^3*b^10*c^4 - 4*a^4*b^9*c^3*d + 6*a^5*b^8*
c^2*d^2 - 4*a^6*b^7*c*d^3 + a^7*b^6*d^4)*g^6*x^2 + 5*(a^4*b^9*c^4 - 4*a^5*b^8*c^3*d + 6*a^6*b^7*c^2*d^2 - 4*a^
7*b^6*c*d^3 + a^8*b^5*d^4)*g^6*x + (a^5*b^8*c^4 - 4*a^6*b^7*c^3*d + 6*a^7*b^6*c^2*d^2 - 4*a^8*b^5*c*d^3 + a^9*
b^4*d^4)*g^6) - 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(b*x + a)/((b^9*c^5 - 5*a*
b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6) + 60*(10*b^3*c^3*d^2
- 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(d*x + c)/((b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 1
0*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (3799*a^3*b^5*
c^5 - 51875*a^4*b^4*c^4*d + 63000*a^5*b^3*c^3*d^2 - 19000*a^6*b^2*c^2*d^3 + 4625*a^7*b*c*d^4 - 549*a^8*d^5 - 6
0*(900*b^8*c^4*d - 1400*a*b^7*c^3*d^2 + 675*a^2*b^6*c^2*d^3 - 202*a^3*b^5*c*d^4 + 27*a^4*b^4*d^5)*x^4 + 30*(30
0*b^8*c^5 - 7700*a*b^7*c^4*d + 11175*a^2*b^6*c^3*d^2 - 5017*a^3*b^5*c^2*d^3 + 1425*a^4*b^4*c*d^4 - 183*a^5*b^3
*d^5)*x^3 + 10*(1900*a*b^7*c^5 - 33950*a^2*b^6*c^4*d + 45999*a^3*b^5*c^3*d^2 - 18025*a^4*b^4*c^2*d^3 + 4625*a^
5*b^3*c*d^4 - 549*a^6*b^2*d^5)*x^2 + 1800*(10*a^5*b^3*c^3*d^2 - 10*a^6*b^2*c^2*d^3 + 5*a^7*b*c*d^4 - a^8*d^5 +
(10*b^8*c^3*d^2 - 10*a*b^7*c^2*d^3 + 5*a^2*b^6*c*d^4 - a^3*b^5*d^5)*x^5 + 5*(10*a*b^7*c^3*d^2 - 10*a^2*b^6*c^
2*d^3 + 5*a^3*b^5*c*d^4 - a^4*b^4*d^5)*x^4 + 10*(10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a
^5*b^3*d^5)*x^3 + 10*(10*a^3*b^5*c^3*d^2 - 10*a^4*b^4*c^2*d^3 + 5*a^5*b^3*c*d^4 - a^6*b^2*d^5)*x^2 + 5*(10*a^4
*b^4*c^3*d^2 - 10*a^5*b^3*c^2*d^3 + 5*a^6*b^2*c*d^4 - a^7*b*d^5)*x)*log(b*x + a)^2 + 1800*(10*a^5*b^3*c^3*d^2
- 10*a^6*b^2*c^2*d^3 + 5*a^7*b*c*d^4 - a^8*d^5 + (10*b^8*c^3*d^2 - 10*a*b^7*c^2*d^3 + 5*a^2*b^6*c*d^4 - a^3*b^
5*d^5)*x^5 + 5*(10*a*b^7*c^3*d^2 - 10*a^2*b^6*c^2*d^3 + 5*a^3*b^5*c*d^4 - a^4*b^4*d^5)*x^4 + 10*(10*a^2*b^6*c^
3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*x^3 + 10*(10*a^3*b^5*c^3*d^2 - 10*a^4*b^4*c^2*d^3
+ 5*a^5*b^3*c*d^4 - a^6*b^2*d^5)*x^2 + 5*(10*a^4*b^4*c^3*d^2 - 10*a^5*b^3*c^2*d^3 + 5*a^6*b^2*c*d^4 - a^7*b*d^
5)*x)*log(d*x + c)^2 + 5*(2875*a^2*b^6*c^5 - 43451*a^3*b^5*c^4*d + 55500*a^4*b^4*c^3*d^2 - 19000*a^5*b^3*c^2*d
^3 + 4625*a^6*b^2*c*d^4 - 549*a^7*b*d^5)*x - 60*(900*a^5*b^3*c^3*d^2 - 500*a^6*b^2*c^2*d^3 + 175*a^7*b*c*d^4 -
27*a^8*d^5 + (900*b^8*c^3*d^2 - 500*a*b^7*c^2*d^3 + 175*a^2*b^6*c*d^4 - 27*a^3*b^5*d^5)*x^5 + 5*(900*a*b^7*c^
3*d^2 - 500*a^2*b^6*c^2*d^3 + 175*a^3*b^5*c*d^4 - 27*a^4*b^4*d^5)*x^4 + 10*(900*a^2*b^6*c^3*d^2 - 500*a^3*b^5*
c^2*d^3 + 175*a^4*b^4*c*d^4 - 27*a^5*b^3*d^5)*x^3 + 10*(900*a^3*b^5*c^3*d^2 - 500*a^4*b^4*c^2*d^3 + 175*a^5*b^
3*c*d^4 - 27*a^6*b^2*d^5)*x^2 + 5*(900*a^4*b^4*c^3*d^2 - 500*a^5*b^3*c^2*d^3 + 175*a^6*b^2*c*d^4 - 27*a^7*b*d^
5)*x)*log(b*x + a) + 60*(900*a^5*b^3*c^3*d^2 - 500*a^6*b^2*c^2*d^3 + 175*a^7*b*c*d^4 - 27*a^8*d^5 + (900*b^8*c
^3*d^2 - 500*a*b^7*c^2*d^3 + 175*a^2*b^6*c*d^4 - 27*a^3*b^5*d^5)*x^5 + 5*(900*a*b^7*c^3*d^2 - 500*a^2*b^6*c^2*
d^3 + 175*a^3*b^5*c*d^4 - 27*a^4*b^4*d^5)*x^4 + 10*(900*a^2*b^6*c^3*d^2 - 500*a^3*b^5*c^2*d^3 + 175*a^4*b^4*c*
d^4 - 27*a^5*b^3*d^5)*x^3 + 10*(900*a^3*b^5*c^3*d^2 - 500*a^4*b^4*c^2*d^3 + 175*a^5*b^3*c*d^4 - 27*a^6*b^2*d^5
)*x^2 + 5*(900*a^4*b^4*c^3*d^2 - 500*a^5*b^3*c^2*d^3 + 175*a^6*b^2*c*d^4 - 27*a^7*b*d^5)*x - 60*(10*a^5*b^3*c^
3*d^2 - 10*a^6*b^2*c^2*d^3 + 5*a^7*b*c*d^4 - a^8*d^5 + (10*b^8*c^3*d^2 - 10*a*b^7*c^2*d^3 + 5*a^2*b^6*c*d^4 -
a^3*b^5*d^5)*x^5 + 5*(10*a*b^7*c^3*d^2 - 10*a^2*b^6*c^2*d^3 + 5*a^3*b^5*c*d^4 - a^4*b^4*d^5)*x^4 + 10*(10*a^2*
b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*x^3 + 10*(10*a^3*b^5*c^3*d^2 - 10*a^4*b^4*c^
2*d^3 + 5*a^5*b^3*c*d^4 - a^6*b^2*d^5)*x^2 + 5*(10*a^4*b^4*c^3*d^2 - 10*a^5*b^3*c^2*d^3 + 5*a^6*b^2*c*d^4 - a^
7*b*d^5)*x)*log(b*x + a))*log(d*x + c))/(a^5*b^9*c^5*g^6 - 5*a^6*b^8*c^4*d*g^6 + 10*a^7*b^7*c^3*d^2*g^6 - 10*a
^8*b^6*c^2*d^3*g^6 + 5*a^9*b^5*c*d^4*g^6 - a^10*b^4*d^5*g^6 + (b^14*c^5*g^6 - 5*a*b^13*c^4*d*g^6 + 10*a^2*b^12
*c^3*d^2*g^6 - 10*a^3*b^11*c^2*d^3*g^6 + 5*a^4*b^10*c*d^4*g^6 - a^5*b^9*d^5*g^6)*x^5 + 5*(a*b^13*c^5*g^6 - 5*a
^2*b^12*c^4*d*g^6 + 10*a^3*b^11*c^3*d^2*g^6 - 10*a^4*b^10*c^2*d^3*g^6 + 5*a^5*b^9*c*d^4*g^6 - a^6*b^8*d^5*g^6)
*x^4 + 10*(a^2*b^12*c^5*g^6 - 5*a^3*b^11*c^4*d*g^6 + 10*a^4*b^10*c^3*d^2*g^6 - 10*a^5*b^9*c^2*d^3*g^6 + 5*a^6*
b^8*c*d^4*g^6 - a^7*b^7*d^5*g^6)*x^3 + 10*(a^3*b^11*c^5*g^6 - 5*a^4*b^10*c^4*d*g^6 + 10*a^5*b^9*c^3*d^2*g^6 -
10*a^6*b^8*c^2*d^3*g^6 + 5*a^7*b^7*c*d^4*g^6 - a^8*b^6*d^5*g^6)*x^2 + 5*(a^4*b^10*c^5*g^6 - 5*a^5*b^9*c^4*d*g^
6 + 10*a^6*b^8*c^3*d^2*g^6 - 10*a^7*b^7*c^2*d^3*g^6 + 5*a^8*b^6*c*d^4*g^6 - a^9*b^5*d^5*g^6)*x))*B^2*d^3*i^3 -
1/600*A*B*d^3*i^3*(60*(10*b^3*x^3 + 10*a*b^2*x^2 + 5*a^2*b*x + a^3)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^9
*g^6*x^5 + 5*a*b^8*g^6*x^4 + 10*a^2*b^7*g^6*x^3 + 10*a^3*b^6*g^6*x^2 + 5*a^4*b^5*g^6*x + a^5*b^4*g^6) + (77*a^
3*b^4*c^4 - 548*a^4*b^3*c^3*d + 352*a^5*b^2*c^2*d^2 - 148*a^6*b*c*d^3 + 27*a^7*d^4 - 60*(10*b^7*c^3*d - 10*a*b
^6*c^2*d^2 + 5*a^2*b^5*c*d^3 - a^3*b^4*d^4)*x^4 + 30*(10*b^7*c^4 - 100*a*b^6*c^3*d + 95*a^2*b^5*c^2*d^2 - 46*a
^3*b^4*c*d^3 + 9*a^4*b^3*d^4)*x^3 + 10*(50*a*b^6*c^4 - 410*a^2*b^5*c^3*d + 337*a^3*b^4*c^2*d^2 - 148*a^4*b^3*c
*d^3 + 27*a^5*b^2*d^4)*x^2 + 5*(65*a^2*b^5*c^4 - 488*a^3*b^4*c^3*d + 352*a^4*b^3*c^2*d^2 - 148*a^5*b^2*c*d^3 +
27*a^6*b*d^4)*x)/((b^13*c^4 - 4*a*b^12*c^3*d + 6*a^2*b^11*c^2*d^2 - 4*a^3*b^10*c*d^3 + a^4*b^9*d^4)*g^6*x^5 +
5*(a*b^12*c^4 - 4*a^2*b^11*c^3*d + 6*a^3*b^10*c^2*d^2 - 4*a^4*b^9*c*d^3 + a^5*b^8*d^4)*g^6*x^4 + 10*(a^2*b^11
*c^4 - 4*a^3*b^10*c^3*d + 6*a^4*b^9*c^2*d^2 - 4*a^5*b^8*c*d^3 + a^6*b^7*d^4)*g^6*x^3 + 10*(a^3*b^10*c^4 - 4*a^
4*b^9*c^3*d + 6*a^5*b^8*c^2*d^2 - 4*a^6*b^7*c*d^3 + a^7*b^6*d^4)*g^6*x^2 + 5*(a^4*b^9*c^4 - 4*a^5*b^8*c^3*d +
6*a^6*b^7*c^2*d^2 - 4*a^7*b^6*c*d^3 + a^8*b^5*d^4)*g^6*x + (a^5*b^8*c^4 - 4*a^6*b^7*c^3*d + 6*a^7*b^6*c^2*d^2
- 4*a^8*b^5*c*d^3 + a^9*b^4*d^4)*g^6) - 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(b
*x + a)/((b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g
^6) + 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(d*x + c)/((b^9*c^5 - 5*a*b^8*c^4*d
+ 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6)) - 1/300*A*B*c*d^2*i^3*(60*(10
*b^2*x^2 + 5*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6
*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) + (47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2
*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c
^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b
^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d
^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 +
a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*
g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10
*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4
- 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d
+ 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*
x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^
6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 -
10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6)) - 1/200*A*B*c^2*d*i^3*(60*(5*b*x + a)*log(b*e*x/(d*
x + c) + a*e/(d*x + c))/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g
^6*x + a^5*b^2*g^6) + (27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 -
60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d
- 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c
^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^
3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4
)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 1
0*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4
- 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d
+ 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5
*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 -
a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a
^5*b^2*d^5)*g^6)) - 1/150*A*B*c^3*i^3*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 1
63*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*
b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^
3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*
c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a
^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3
+ a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)
*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*log(b*e*x
/(d*x + c) + a*e/(d*x + c))/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b
^2*g^6*x + a^5*b*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^
3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 1
0*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6)) - 1/5*B^2*c^3*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^
2/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) - 3/
20*(5*b*x + a)*A^2*c^2*d*i^3/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*
b^3*g^6*x + a^5*b^2*g^6) - 1/10*(10*b^2*x^2 + 5*a*b*x + a^2)*A^2*c*d^2*i^3/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10
*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/20*(10*b^3*x^3 + 10*a*b^2*x^2 + 5*a
^2*b*x + a^3)*A^2*d^3*i^3/(b^9*g^6*x^5 + 5*a*b^8*g^6*x^4 + 10*a^2*b^7*g^6*x^3 + 10*a^3*b^6*g^6*x^2 + 5*a^4*b^5
*g^6*x + a^5*b^4*g^6) - 1/5*A^2*c^3*i^3/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x
^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6)

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Fricas [B]  time = 0.623722, size = 2209, normalized size = 7.39 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^6,x, algorithm="fricas")

[Out]

1/4000*(20*((20*A*B + 9*B^2)*b^5*c*d^4 - (20*A*B + 9*B^2)*a*b^4*d^5)*i^3*x^4 - 10*((200*A^2 + 20*A*B - 11*B^2)
*b^5*c^2*d^3 - 50*(8*A^2 + 4*A*B + B^2)*a*b^4*c*d^4 + (200*A^2 + 180*A*B + 61*B^2)*a^2*b^3*d^5)*i^3*x^3 - 10*(
2*(200*A^2 + 60*A*B + 7*B^2)*b^5*c^3*d^2 - 75*(8*A^2 + 4*A*B + B^2)*a*b^4*c^2*d^3 + (200*A^2 + 180*A*B + 61*B^
2)*a^3*b^2*d^5)*i^3*x^2 - 5*((600*A^2 + 220*A*B + 39*B^2)*b^5*c^4*d - 100*(8*A^2 + 4*A*B + B^2)*a*b^4*c^3*d^2
+ (200*A^2 + 180*A*B + 61*B^2)*a^4*b*d^5)*i^3*x - (32*(25*A^2 + 10*A*B + 2*B^2)*b^5*c^5 - 125*(8*A^2 + 4*A*B +
B^2)*a*b^4*c^4*d + (200*A^2 + 180*A*B + 61*B^2)*a^5*d^5)*i^3 + 200*(B^2*b^5*d^5*i^3*x^5 + 5*B^2*a*b^4*d^5*i^3
*x^4 - 10*(B^2*b^5*c^2*d^3 - 2*B^2*a*b^4*c*d^4)*i^3*x^3 - 10*(2*B^2*b^5*c^3*d^2 - 3*B^2*a*b^4*c^2*d^3)*i^3*x^2
- 5*(3*B^2*b^5*c^4*d - 4*B^2*a*b^4*c^3*d^2)*i^3*x - (4*B^2*b^5*c^5 - 5*B^2*a*b^4*c^4*d)*i^3)*log((b*e*x + a*e
)/(d*x + c))^2 + 20*((20*A*B + 9*B^2)*b^5*d^5*i^3*x^5 + 5*(4*B^2*b^5*c*d^4 + 5*(4*A*B + B^2)*a*b^4*d^5)*i^3*x^
4 - 10*((20*A*B + B^2)*b^5*c^2*d^3 - 10*(4*A*B + B^2)*a*b^4*c*d^4)*i^3*x^3 - 10*(2*(20*A*B + 3*B^2)*b^5*c^3*d^
2 - 15*(4*A*B + B^2)*a*b^4*c^2*d^3)*i^3*x^2 - 5*((60*A*B + 11*B^2)*b^5*c^4*d - 20*(4*A*B + B^2)*a*b^4*c^3*d^2)
*i^3*x - (16*(5*A*B + B^2)*b^5*c^5 - 25*(4*A*B + B^2)*a*b^4*c^4*d)*i^3)*log((b*e*x + a*e)/(d*x + c)))/((b^11*c
^2 - 2*a*b^10*c*d + a^2*b^9*d^2)*g^6*x^5 + 5*(a*b^10*c^2 - 2*a^2*b^9*c*d + a^3*b^8*d^2)*g^6*x^4 + 10*(a^2*b^9*
c^2 - 2*a^3*b^8*c*d + a^4*b^7*d^2)*g^6*x^3 + 10*(a^3*b^8*c^2 - 2*a^4*b^7*c*d + a^5*b^6*d^2)*g^6*x^2 + 5*(a^4*b
^7*c^2 - 2*a^5*b^6*c*d + a^6*b^5*d^2)*g^6*x + (a^5*b^6*c^2 - 2*a^6*b^5*c*d + a^7*b^4*d^2)*g^6)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*i*x+c*i)**3*(A+B*ln(e*(b*x+a)/(d*x+c)))**2/(b*g*x+a*g)**6,x)

[Out]

Timed out

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Giac [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (d i x + c i\right )}^{3}{\left (B \log \left (\frac{{\left (b x + a\right )} e}{d x + c}\right ) + A\right )}^{2}}{{\left (b g x + a g\right )}^{6}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^6,x, algorithm="giac")

[Out]

integrate((d*i*x + c*i)^3*(B*log((b*x + a)*e/(d*x + c)) + A)^2/(b*g*x + a*g)^6, x)