3.83 \(\int \frac{(c i+d i x)^3 (A+B \log (\frac{e (a+b x)}{c+d x}))^2}{(a g+b g x)^7} \, dx\)

Optimal. Leaf size=463 \[ -\frac{b^2 i^3 (c+d x)^6 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{6 g^7 (a+b x)^6 (b c-a d)^3}-\frac{b^2 B i^3 (c+d x)^6 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{18 g^7 (a+b x)^6 (b c-a d)^3}-\frac{d^2 i^3 (c+d x)^4 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{4 g^7 (a+b x)^4 (b c-a d)^3}-\frac{B d^2 i^3 (c+d x)^4 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{8 g^7 (a+b x)^4 (b c-a d)^3}+\frac{2 b d i^3 (c+d x)^5 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{5 g^7 (a+b x)^5 (b c-a d)^3}+\frac{4 b B d i^3 (c+d x)^5 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{25 g^7 (a+b x)^5 (b c-a d)^3}-\frac{b^2 B^2 i^3 (c+d x)^6}{108 g^7 (a+b x)^6 (b c-a d)^3}-\frac{B^2 d^2 i^3 (c+d x)^4}{32 g^7 (a+b x)^4 (b c-a d)^3}+\frac{4 b B^2 d i^3 (c+d x)^5}{125 g^7 (a+b x)^5 (b c-a d)^3} \]

[Out]

-(B^2*d^2*i^3*(c + d*x)^4)/(32*(b*c - a*d)^3*g^7*(a + b*x)^4) + (4*b*B^2*d*i^3*(c + d*x)^5)/(125*(b*c - a*d)^3
*g^7*(a + b*x)^5) - (b^2*B^2*i^3*(c + d*x)^6)/(108*(b*c - a*d)^3*g^7*(a + b*x)^6) - (B*d^2*i^3*(c + d*x)^4*(A
+ B*Log[(e*(a + b*x))/(c + d*x)]))/(8*(b*c - a*d)^3*g^7*(a + b*x)^4) + (4*b*B*d*i^3*(c + d*x)^5*(A + B*Log[(e*
(a + b*x))/(c + d*x)]))/(25*(b*c - a*d)^3*g^7*(a + b*x)^5) - (b^2*B*i^3*(c + d*x)^6*(A + B*Log[(e*(a + b*x))/(
c + d*x)]))/(18*(b*c - a*d)^3*g^7*(a + b*x)^6) - (d^2*i^3*(c + d*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/
(4*(b*c - a*d)^3*g^7*(a + b*x)^4) + (2*b*d*i^3*(c + d*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(5*(b*c - a
*d)^3*g^7*(a + b*x)^5) - (b^2*i^3*(c + d*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(6*(b*c - a*d)^3*g^7*(a
+ b*x)^6)

________________________________________________________________________________________

Rubi [C]  time = 6.0774, antiderivative size = 1152, normalized size of antiderivative = 2.49, number of steps used = 162, 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^6}{60 b^4 (b c-a d)^3 g^7}+\frac{B^2 i^3 \log ^2(c+d x) d^6}{60 b^4 (b c-a d)^3 g^7}-\frac{37 B^2 i^3 \log (a+b x) d^6}{1800 b^4 (b c-a d)^3 g^7}-\frac{B i^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^6}{30 b^4 (b c-a d)^3 g^7}+\frac{37 B^2 i^3 \log (c+d x) d^6}{1800 b^4 (b c-a d)^3 g^7}-\frac{B^2 i^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) d^6}{30 b^4 (b c-a d)^3 g^7}+\frac{B i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x) d^6}{30 b^4 (b c-a d)^3 g^7}-\frac{B^2 i^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right ) d^6}{30 b^4 (b c-a d)^3 g^7}-\frac{B^2 i^3 \text{PolyLog}\left (2,-\frac{d (a+b x)}{b c-a d}\right ) d^6}{30 b^4 (b c-a d)^3 g^7}-\frac{B^2 i^3 \text{PolyLog}\left (2,\frac{b (c+d x)}{b c-a d}\right ) d^6}{30 b^4 (b c-a d)^3 g^7}-\frac{B i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^5}{30 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{37 B^2 i^3 d^5}{1800 b^4 (b c-a d)^2 g^7 (a+b x)}+\frac{B i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^4}{60 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{23 B^2 i^3 d^4}{3600 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 d^3}{3 b^4 g^7 (a+b x)^3}-\frac{B i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^3}{90 b^4 g^7 (a+b x)^3}+\frac{53 B^2 i^3 d^3}{5400 b^4 g^7 (a+b x)^3}-\frac{3 (b c-a d) i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 d^2}{4 b^4 g^7 (a+b x)^4}-\frac{19 B (b c-a d) i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d^2}{120 b^4 g^7 (a+b x)^4}-\frac{73 B^2 (b c-a d) i^3 d^2}{7200 b^4 g^7 (a+b x)^4}-\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}{5 b^4 g^7 (a+b x)^5}-\frac{13 B (b c-a d)^2 i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) d}{75 b^4 g^7 (a+b x)^5}-\frac{53 B^2 (b c-a d)^2 i^3 d}{2250 b^4 g^7 (a+b x)^5}-\frac{(b c-a d)^3 i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{B (b c-a d)^3 i^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{18 b^4 g^7 (a+b x)^6}-\frac{B^2 (b c-a d)^3 i^3}{108 b^4 g^7 (a+b x)^6} \]

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)^7,x]

[Out]

-(B^2*(b*c - a*d)^3*i^3)/(108*b^4*g^7*(a + b*x)^6) - (53*B^2*d*(b*c - a*d)^2*i^3)/(2250*b^4*g^7*(a + b*x)^5) -
(73*B^2*d^2*(b*c - a*d)*i^3)/(7200*b^4*g^7*(a + b*x)^4) + (53*B^2*d^3*i^3)/(5400*b^4*g^7*(a + b*x)^3) - (23*B
^2*d^4*i^3)/(3600*b^4*(b*c - a*d)*g^7*(a + b*x)^2) - (37*B^2*d^5*i^3)/(1800*b^4*(b*c - a*d)^2*g^7*(a + b*x)) -
(37*B^2*d^6*i^3*Log[a + b*x])/(1800*b^4*(b*c - a*d)^3*g^7) + (B^2*d^6*i^3*Log[a + b*x]^2)/(60*b^4*(b*c - a*d)
^3*g^7) - (B*(b*c - a*d)^3*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(18*b^4*g^7*(a + b*x)^6) - (13*B*d*(b*c -
a*d)^2*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(75*b^4*g^7*(a + b*x)^5) - (19*B*d^2*(b*c - a*d)*i^3*(A + B*
Log[(e*(a + b*x))/(c + d*x)]))/(120*b^4*g^7*(a + b*x)^4) - (B*d^3*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(9
0*b^4*g^7*(a + b*x)^3) + (B*d^4*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(60*b^4*(b*c - a*d)*g^7*(a + b*x)^2)
- (B*d^5*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(30*b^4*(b*c - a*d)^2*g^7*(a + b*x)) - (B*d^6*i^3*Log[a +
b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(30*b^4*(b*c - a*d)^3*g^7) - ((b*c - a*d)^3*i^3*(A + B*Log[(e*(a +
b*x))/(c + d*x)])^2)/(6*b^4*g^7*(a + b*x)^6) - (3*d*(b*c - a*d)^2*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/
(5*b^4*g^7*(a + b*x)^5) - (3*d^2*(b*c - a*d)*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(4*b^4*g^7*(a + b*x)^
4) - (d^3*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(3*b^4*g^7*(a + b*x)^3) + (37*B^2*d^6*i^3*Log[c + d*x])/
(1800*b^4*(b*c - a*d)^3*g^7) - (B^2*d^6*i^3*Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/(30*b^4*(b*c - a*d
)^3*g^7) + (B*d^6*i^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x])/(30*b^4*(b*c - a*d)^3*g^7) + (B^2*d^6
*i^3*Log[c + d*x]^2)/(60*b^4*(b*c - a*d)^3*g^7) - (B^2*d^6*i^3*Log[a + b*x]*Log[(b*(c + d*x))/(b*c - a*d)])/(3
0*b^4*(b*c - a*d)^3*g^7) - (B^2*d^6*i^3*PolyLog[2, -((d*(a + b*x))/(b*c - a*d))])/(30*b^4*(b*c - a*d)^3*g^7) -
(B^2*d^6*i^3*PolyLog[2, (b*(c + d*x))/(b*c - a*d)])/(30*b^4*(b*c - a*d)^3*g^7)

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{(83 c+83 d x)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a g+b g x)^7} \, dx &=\int \left (\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^7 (a+b x)^7}+\frac{1715361 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^7 (a+b x)^6}+\frac{1715361 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^7 (a+b x)^5}+\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^7 (a+b x)^4}\right ) \, dx\\ &=\frac{\left (571787 d^3\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^7}+\frac{\left (1715361 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)^5} \, dx}{b^3 g^7}+\frac{\left (1715361 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)^6} \, dx}{b^3 g^7}+\frac{\left (571787 (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)^7} \, dx}{b^3 g^7}\\ &=-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{\left (1143574 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)^4 (c+d x)} \, dx}{3 b^4 g^7}+\frac{\left (1715361 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)^5 (c+d x)} \, dx}{2 b^4 g^7}+\frac{\left (3430722 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)^6 (c+d x)} \, dx}{5 b^4 g^7}+\frac{\left (571787 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)^7 (c+d x)} \, dx}{3 b^4 g^7}\\ &=-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{\left (1143574 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)^4 (c+d x)} \, dx}{3 b^4 g^7}+\frac{\left (1715361 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)^5 (c+d x)} \, dx}{2 b^4 g^7}+\frac{\left (3430722 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)^6 (c+d x)} \, dx}{5 b^4 g^7}+\frac{\left (571787 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)^7 (c+d x)} \, dx}{3 b^4 g^7}\\ &=-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{\left (1143574 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)^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}{3 b^4 g^7}+\frac{\left (1715361 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)^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}{2 b^4 g^7}+\frac{\left (3430722 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)^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^7}+\frac{\left (571787 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)^7}-\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)^6}+\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)^5}-\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)^4}+\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)^3}-\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)^2}+\frac{b d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^7 (a+b x)}-\frac{d^7 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^7 (c+d x)}\right ) \, dx}{3 b^4 g^7}\\ &=-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}-\frac{\left (571787 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{3 b^3 g^7}+\frac{\left (1143574 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{3 b^3 g^7}+\frac{\left (3430722 B d^3\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^7}-\frac{\left (1715361 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{2 b^3 g^7}+\frac{\left (571787 B d^6\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{3 b^3 (b c-a d)^3 g^7}-\frac{\left (1143574 B d^6\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{3 b^3 (b c-a d)^3 g^7}-\frac{\left (3430722 B d^6\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)^3 g^7}+\frac{\left (1715361 B d^6\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{2 b^3 (b c-a d)^3 g^7}-\frac{\left (571787 B d^7\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (1143574 B d^7\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (3430722 B d^7\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)^3 g^7}-\frac{\left (1715361 B d^7\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{2 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B d^5\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{3 b^3 (b c-a d)^2 g^7}+\frac{\left (1143574 B d^5\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{3 b^3 (b c-a d)^2 g^7}+\frac{\left (3430722 B d^5\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)^2 g^7}-\frac{\left (1715361 B d^5\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{2 b^3 (b c-a d)^2 g^7}+\frac{\left (571787 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{3 b^3 (b c-a d) g^7}-\frac{\left (1143574 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{3 b^3 (b c-a d) g^7}-\frac{\left (3430722 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{5 b^3 (b c-a d) g^7}+\frac{\left (1715361 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{2 b^3 (b c-a d) g^7}+\frac{\left (571787 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)^5} \, dx}{3 b^3 g^7}-\frac{\left (3430722 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)^5} \, dx}{5 b^3 g^7}+\frac{\left (1715361 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)^5} \, dx}{2 b^3 g^7}-\frac{\left (571787 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)^6} \, dx}{3 b^3 g^7}+\frac{\left (3430722 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)^6} \, dx}{5 b^3 g^7}+\frac{\left (571787 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)^7} \, dx}{3 b^3 g^7}\\ &=-\frac{571787 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{18 b^4 g^7 (a+b x)^6}-\frac{7433231 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{75 b^4 g^7 (a+b x)^5}-\frac{10863953 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{120 b^4 g^7 (a+b x)^4}-\frac{571787 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{90 b^4 g^7 (a+b x)^3}+\frac{571787 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{60 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{571787 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{571787 B d^6 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{571787 B d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{9 b^4 g^7}+\frac{\left (1143574 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{9 b^4 g^7}+\frac{\left (1143574 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{5 b^4 g^7}-\frac{\left (571787 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{2 b^4 g^7}-\frac{\left (571787 B^2 d^6\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}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (571787 B^2 d^6\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}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^6\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}{3 b^4 (b c-a d)^3 g^7}-\frac{\left (1143574 B^2 d^6\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}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (3430722 B^2 d^6\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)^3 g^7}-\frac{\left (3430722 B^2 d^6\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)^3 g^7}-\frac{\left (1715361 B^2 d^6\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}{2 b^4 (b c-a d)^3 g^7}+\frac{\left (1715361 B^2 d^6\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}{2 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^5\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{3 b^4 (b c-a d)^2 g^7}+\frac{\left (1143574 B^2 d^5\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{3 b^4 (b c-a d)^2 g^7}+\frac{\left (3430722 B^2 d^5\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{5 b^4 (b c-a d)^2 g^7}-\frac{\left (1715361 B^2 d^5\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{2 b^4 (b c-a d)^2 g^7}+\frac{\left (571787 B^2 d^4\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{6 b^4 (b c-a d) g^7}-\frac{\left (571787 B^2 d^4\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{3 b^4 (b c-a d) g^7}-\frac{\left (1715361 B^2 d^4\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{5 b^4 (b c-a d) g^7}+\frac{\left (1715361 B^2 d^4\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{4 b^4 (b c-a d) g^7}+\frac{\left (571787 B^2 d^2 (b c-a d)\right ) \int \frac{b c-a d}{(a+b x)^5 (c+d x)} \, dx}{12 b^4 g^7}-\frac{\left (1715361 B^2 d^2 (b c-a d)\right ) \int \frac{b c-a d}{(a+b x)^5 (c+d x)} \, dx}{10 b^4 g^7}+\frac{\left (1715361 B^2 d^2 (b c-a d)\right ) \int \frac{b c-a d}{(a+b x)^5 (c+d x)} \, dx}{8 b^4 g^7}-\frac{\left (571787 B^2 d (b c-a d)^2\right ) \int \frac{b c-a d}{(a+b x)^6 (c+d x)} \, dx}{15 b^4 g^7}+\frac{\left (3430722 B^2 d (b c-a d)^2\right ) \int \frac{b c-a d}{(a+b x)^6 (c+d x)} \, dx}{25 b^4 g^7}+\frac{\left (571787 B^2 (b c-a d)^3\right ) \int \frac{b c-a d}{(a+b x)^7 (c+d x)} \, dx}{18 b^4 g^7}\\ &=-\frac{571787 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{18 b^4 g^7 (a+b x)^6}-\frac{7433231 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{75 b^4 g^7 (a+b x)^5}-\frac{10863953 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{120 b^4 g^7 (a+b x)^4}-\frac{571787 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{90 b^4 g^7 (a+b x)^3}+\frac{571787 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{60 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{571787 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{571787 B d^6 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{571787 B d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}+\frac{\left (571787 B^2 d^4\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{6 b^4 g^7}-\frac{\left (571787 B^2 d^4\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{3 b^4 g^7}-\frac{\left (1715361 B^2 d^4\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{5 b^4 g^7}+\frac{\left (1715361 B^2 d^4\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{4 b^4 g^7}-\frac{\left (571787 B^2 d^5\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{3 b^4 (b c-a d) g^7}+\frac{\left (1143574 B^2 d^5\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{3 b^4 (b c-a d) g^7}+\frac{\left (3430722 B^2 d^5\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{5 b^4 (b c-a d) g^7}-\frac{\left (1715361 B^2 d^5\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{2 b^4 (b c-a d) g^7}-\frac{\left (571787 B^2 d^3 (b c-a d)\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{9 b^4 g^7}+\frac{\left (1143574 B^2 d^3 (b c-a d)\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{9 b^4 g^7}+\frac{\left (1143574 B^2 d^3 (b c-a d)\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{5 b^4 g^7}-\frac{\left (571787 B^2 d^3 (b c-a d)\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{2 b^4 g^7}+\frac{\left (571787 B^2 d^2 (b c-a d)^2\right ) \int \frac{1}{(a+b x)^5 (c+d x)} \, dx}{12 b^4 g^7}-\frac{\left (1715361 B^2 d^2 (b c-a d)^2\right ) \int \frac{1}{(a+b x)^5 (c+d x)} \, dx}{10 b^4 g^7}+\frac{\left (1715361 B^2 d^2 (b c-a d)^2\right ) \int \frac{1}{(a+b x)^5 (c+d x)} \, dx}{8 b^4 g^7}-\frac{\left (571787 B^2 d (b c-a d)^3\right ) \int \frac{1}{(a+b x)^6 (c+d x)} \, dx}{15 b^4 g^7}+\frac{\left (3430722 B^2 d (b c-a d)^3\right ) \int \frac{1}{(a+b x)^6 (c+d x)} \, dx}{25 b^4 g^7}+\frac{\left (571787 B^2 (b c-a d)^4\right ) \int \frac{1}{(a+b x)^7 (c+d x)} \, dx}{18 b^4 g^7}-\frac{\left (571787 B^2 d^6\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}{3 b^4 (b c-a d)^3 e g^7}+\frac{\left (571787 B^2 d^6\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}{3 b^4 (b c-a d)^3 e g^7}+\frac{\left (1143574 B^2 d^6\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}{3 b^4 (b c-a d)^3 e g^7}-\frac{\left (1143574 B^2 d^6\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}{3 b^4 (b c-a d)^3 e g^7}+\frac{\left (3430722 B^2 d^6\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)^3 e g^7}-\frac{\left (3430722 B^2 d^6\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)^3 e g^7}-\frac{\left (1715361 B^2 d^6\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}{2 b^4 (b c-a d)^3 e g^7}+\frac{\left (1715361 B^2 d^6\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}{2 b^4 (b c-a d)^3 e g^7}\\ &=-\frac{571787 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{18 b^4 g^7 (a+b x)^6}-\frac{7433231 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{75 b^4 g^7 (a+b x)^5}-\frac{10863953 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{120 b^4 g^7 (a+b x)^4}-\frac{571787 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{90 b^4 g^7 (a+b x)^3}+\frac{571787 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{60 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{571787 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{571787 B d^6 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{571787 B d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}+\frac{\left (571787 B^2 d^4\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}{6 b^4 g^7}-\frac{\left (571787 B^2 d^4\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}{3 b^4 g^7}-\frac{\left (1715361 B^2 d^4\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^7}+\frac{\left (1715361 B^2 d^4\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}{4 b^4 g^7}-\frac{\left (571787 B^2 d^5\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}{3 b^4 (b c-a d) g^7}+\frac{\left (1143574 B^2 d^5\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}{3 b^4 (b c-a d) g^7}+\frac{\left (3430722 B^2 d^5\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 (b c-a d) g^7}-\frac{\left (1715361 B^2 d^5\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}{2 b^4 (b c-a d) g^7}-\frac{\left (571787 B^2 d^3 (b c-a d)\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}{9 b^4 g^7}+\frac{\left (1143574 B^2 d^3 (b c-a d)\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}{9 b^4 g^7}+\frac{\left (1143574 B^2 d^3 (b c-a d)\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}{5 b^4 g^7}-\frac{\left (571787 B^2 d^3 (b c-a d)\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}{2 b^4 g^7}+\frac{\left (571787 B^2 d^2 (b c-a d)^2\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}{12 b^4 g^7}-\frac{\left (1715361 B^2 d^2 (b c-a d)^2\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}{10 b^4 g^7}+\frac{\left (1715361 B^2 d^2 (b c-a d)^2\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}{8 b^4 g^7}-\frac{\left (571787 B^2 d (b c-a d)^3\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}{15 b^4 g^7}+\frac{\left (3430722 B^2 d (b c-a d)^3\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^7}+\frac{\left (571787 B^2 (b c-a d)^4\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^7}-\frac{b d}{(b c-a d)^2 (a+b x)^6}+\frac{b d^2}{(b c-a d)^3 (a+b x)^5}-\frac{b d^3}{(b c-a d)^4 (a+b x)^4}+\frac{b d^4}{(b c-a d)^5 (a+b x)^3}-\frac{b d^5}{(b c-a d)^6 (a+b x)^2}+\frac{b d^6}{(b c-a d)^7 (a+b x)}-\frac{d^7}{(b c-a d)^7 (c+d x)}\right ) \, dx}{18 b^4 g^7}-\frac{\left (571787 B^2 d^6\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}{3 b^4 (b c-a d)^3 e g^7}+\frac{\left (571787 B^2 d^6\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}{3 b^4 (b c-a d)^3 e g^7}+\frac{\left (1143574 B^2 d^6\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}{3 b^4 (b c-a d)^3 e g^7}-\frac{\left (1143574 B^2 d^6\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}{3 b^4 (b c-a d)^3 e g^7}+\frac{\left (3430722 B^2 d^6\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)^3 e g^7}-\frac{\left (3430722 B^2 d^6\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)^3 e g^7}-\frac{\left (1715361 B^2 d^6\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}{2 b^4 (b c-a d)^3 e g^7}+\frac{\left (1715361 B^2 d^6\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}{2 b^4 (b c-a d)^3 e g^7}\\ &=-\frac{571787 B^2 (b c-a d)^3}{108 b^4 g^7 (a+b x)^6}-\frac{30304711 B^2 d (b c-a d)^2}{2250 b^4 g^7 (a+b x)^5}-\frac{41740451 B^2 d^2 (b c-a d)}{7200 b^4 g^7 (a+b x)^4}+\frac{30304711 B^2 d^3}{5400 b^4 g^7 (a+b x)^3}-\frac{13151101 B^2 d^4}{3600 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{21156119 B^2 d^5}{1800 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{21156119 B^2 d^6 \log (a+b x)}{1800 b^4 (b c-a d)^3 g^7}-\frac{571787 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{18 b^4 g^7 (a+b x)^6}-\frac{7433231 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{75 b^4 g^7 (a+b x)^5}-\frac{10863953 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{120 b^4 g^7 (a+b x)^4}-\frac{571787 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{90 b^4 g^7 (a+b x)^3}+\frac{571787 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{60 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{571787 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{571787 B d^6 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{21156119 B^2 d^6 \log (c+d x)}{1800 b^4 (b c-a d)^3 g^7}+\frac{571787 B d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^6\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{3 b^3 (b c-a d)^3 g^7}+\frac{\left (571787 B^2 d^6\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{3 b^3 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^6\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{3 b^3 (b c-a d)^3 g^7}-\frac{\left (1143574 B^2 d^6\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{3 b^3 (b c-a d)^3 g^7}+\frac{\left (3430722 B^2 d^6\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{5 b^3 (b c-a d)^3 g^7}-\frac{\left (3430722 B^2 d^6\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{5 b^3 (b c-a d)^3 g^7}-\frac{\left (1715361 B^2 d^6\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{2 b^3 (b c-a d)^3 g^7}+\frac{\left (1715361 B^2 d^6\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{2 b^3 (b c-a d)^3 g^7}+\frac{\left (571787 B^2 d^7\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{3 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^7\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{3 b^4 (b c-a d)^3 g^7}-\frac{\left (1143574 B^2 d^7\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^7\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{3 b^4 (b c-a d)^3 g^7}-\frac{\left (3430722 B^2 d^7\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{5 b^4 (b c-a d)^3 g^7}+\frac{\left (3430722 B^2 d^7\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{5 b^4 (b c-a d)^3 g^7}+\frac{\left (1715361 B^2 d^7\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{2 b^4 (b c-a d)^3 g^7}-\frac{\left (1715361 B^2 d^7\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{2 b^4 (b c-a d)^3 g^7}\\ &=-\frac{571787 B^2 (b c-a d)^3}{108 b^4 g^7 (a+b x)^6}-\frac{30304711 B^2 d (b c-a d)^2}{2250 b^4 g^7 (a+b x)^5}-\frac{41740451 B^2 d^2 (b c-a d)}{7200 b^4 g^7 (a+b x)^4}+\frac{30304711 B^2 d^3}{5400 b^4 g^7 (a+b x)^3}-\frac{13151101 B^2 d^4}{3600 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{21156119 B^2 d^5}{1800 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{21156119 B^2 d^6 \log (a+b x)}{1800 b^4 (b c-a d)^3 g^7}-\frac{571787 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{18 b^4 g^7 (a+b x)^6}-\frac{7433231 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{75 b^4 g^7 (a+b x)^5}-\frac{10863953 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{120 b^4 g^7 (a+b x)^4}-\frac{571787 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{90 b^4 g^7 (a+b x)^3}+\frac{571787 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{60 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{571787 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{571787 B d^6 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{21156119 B^2 d^6 \log (c+d x)}{1800 b^4 (b c-a d)^3 g^7}-\frac{571787 B^2 d^6 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}+\frac{571787 B d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 B^2 d^6 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{3 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (3430722 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{5 b^4 (b c-a d)^3 g^7}+\frac{\left (3430722 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{5 b^4 (b c-a d)^3 g^7}-\frac{\left (1715361 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{2 b^4 (b c-a d)^3 g^7}-\frac{\left (1715361 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{2 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^6\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{3 b^3 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^6\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{3 b^3 (b c-a d)^3 g^7}+\frac{\left (3430722 B^2 d^6\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)^3 g^7}-\frac{\left (1715361 B^2 d^6\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{2 b^3 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^7\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^7\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (3430722 B^2 d^7\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)^3 g^7}-\frac{\left (1715361 B^2 d^7\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{2 b^4 (b c-a d)^3 g^7}\\ &=-\frac{571787 B^2 (b c-a d)^3}{108 b^4 g^7 (a+b x)^6}-\frac{30304711 B^2 d (b c-a d)^2}{2250 b^4 g^7 (a+b x)^5}-\frac{41740451 B^2 d^2 (b c-a d)}{7200 b^4 g^7 (a+b x)^4}+\frac{30304711 B^2 d^3}{5400 b^4 g^7 (a+b x)^3}-\frac{13151101 B^2 d^4}{3600 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{21156119 B^2 d^5}{1800 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{21156119 B^2 d^6 \log (a+b x)}{1800 b^4 (b c-a d)^3 g^7}+\frac{571787 B^2 d^6 \log ^2(a+b x)}{60 b^4 (b c-a d)^3 g^7}-\frac{571787 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{18 b^4 g^7 (a+b x)^6}-\frac{7433231 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{75 b^4 g^7 (a+b x)^5}-\frac{10863953 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{120 b^4 g^7 (a+b x)^4}-\frac{571787 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{90 b^4 g^7 (a+b x)^3}+\frac{571787 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{60 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{571787 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{571787 B d^6 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{21156119 B^2 d^6 \log (c+d x)}{1800 b^4 (b c-a d)^3 g^7}-\frac{571787 B^2 d^6 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}+\frac{571787 B d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}+\frac{571787 B^2 d^6 \log ^2(c+d x)}{60 b^4 (b c-a d)^3 g^7}-\frac{571787 B^2 d^6 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{3 b^4 (b c-a d)^3 g^7}-\frac{\left (571787 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (1143574 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{3 b^4 (b c-a d)^3 g^7}+\frac{\left (3430722 B^2 d^6\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)^3 g^7}+\frac{\left (3430722 B^2 d^6\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)^3 g^7}-\frac{\left (1715361 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{2 b^4 (b c-a d)^3 g^7}-\frac{\left (1715361 B^2 d^6\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{2 b^4 (b c-a d)^3 g^7}\\ &=-\frac{571787 B^2 (b c-a d)^3}{108 b^4 g^7 (a+b x)^6}-\frac{30304711 B^2 d (b c-a d)^2}{2250 b^4 g^7 (a+b x)^5}-\frac{41740451 B^2 d^2 (b c-a d)}{7200 b^4 g^7 (a+b x)^4}+\frac{30304711 B^2 d^3}{5400 b^4 g^7 (a+b x)^3}-\frac{13151101 B^2 d^4}{3600 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{21156119 B^2 d^5}{1800 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{21156119 B^2 d^6 \log (a+b x)}{1800 b^4 (b c-a d)^3 g^7}+\frac{571787 B^2 d^6 \log ^2(a+b x)}{60 b^4 (b c-a d)^3 g^7}-\frac{571787 B (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{18 b^4 g^7 (a+b x)^6}-\frac{7433231 B d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{75 b^4 g^7 (a+b x)^5}-\frac{10863953 B d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{120 b^4 g^7 (a+b x)^4}-\frac{571787 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{90 b^4 g^7 (a+b x)^3}+\frac{571787 B d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{60 b^4 (b c-a d) g^7 (a+b x)^2}-\frac{571787 B d^5 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^2 g^7 (a+b x)}-\frac{571787 B d^6 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 (b c-a d)^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{6 b^4 g^7 (a+b x)^6}-\frac{1715361 d (b c-a d)^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^7 (a+b x)^5}-\frac{1715361 d^2 (b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^7 (a+b x)^4}-\frac{571787 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3 b^4 g^7 (a+b x)^3}+\frac{21156119 B^2 d^6 \log (c+d x)}{1800 b^4 (b c-a d)^3 g^7}-\frac{571787 B^2 d^6 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}+\frac{571787 B d^6 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{30 b^4 (b c-a d)^3 g^7}+\frac{571787 B^2 d^6 \log ^2(c+d x)}{60 b^4 (b c-a d)^3 g^7}-\frac{571787 B^2 d^6 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 B^2 d^6 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{30 b^4 (b c-a d)^3 g^7}-\frac{571787 B^2 d^6 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{30 b^4 (b c-a d)^3 g^7}\\ \end{align*}

Mathematica [C]  time = 5.9321, size = 2583, normalized size = 5.58 \[ \text{Result too large to show} \]

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)^7,x]

[Out]

(i^3*(8100*a^2*B^2*d^2*(b*c - a*d)^4 - 1000*B^2*(b*c - a*d)^6 + 3744*a*B^2*d*(-(b*c) + a*d)^5 + 16200*a*b*B^2*
d^2*(b*c - a*d)^4*x - 3744*b*B^2*d*(b*c - a*d)^5*x + 8100*b^2*B^2*d^2*(b*c - a*d)^4*x^2 + 4680*a*B^2*d^2*(b*c
- a*d)^4*(a + b*x) + 1200*B^2*d*(b*c - a*d)^5*(a + b*x) + 10800*a^2*B^2*d^3*(-(b*c) + a*d)^3*(a + b*x) + 4680*
b*B^2*d^2*(b*c - a*d)^4*x*(a + b*x) + 21600*a*b*B^2*d^3*(-(b*c) + a*d)^3*x*(a + b*x) - 10800*b^2*B^2*d^3*(b*c
- a*d)^3*x^2*(a + b*x) + 16200*a^2*B^2*d^4*(b*c - a*d)^2*(a + b*x)^2 - 13875*B^2*d^2*(b*c - a*d)^4*(a + b*x)^2
+ 20640*a*B^2*d^3*(-(b*c) + a*d)^3*(a + b*x)^2 + 32400*a*b*B^2*d^4*(b*c - a*d)^2*x*(a + b*x)^2 - 20640*b*B^2*
d^3*(b*c - a*d)^3*x*(a + b*x)^2 + 16200*b^2*B^2*d^4*(b*c - a*d)^2*x^2*(a + b*x)^2 + 63360*a*B^2*d^4*(b*c - a*d
)^2*(a + b*x)^3 + 32500*B^2*d^3*(b*c - a*d)^3*(a + b*x)^3 + 32400*a^2*B^2*d^5*(-(b*c) + a*d)*(a + b*x)^3 + 633
60*b*B^2*d^4*(b*c - a*d)^2*x*(a + b*x)^3 + 64800*a*b*B^2*d^5*(-(b*c) + a*d)*x*(a + b*x)^3 - 32400*b^2*B^2*d^5*
(b*c - a*d)*x^2*(a + b*x)^3 - 129600*a*b*B^2*c*d^5*(a + b*x)^4 + 129600*a^2*B^2*d^6*(a + b*x)^4 - 80250*B^2*d^
4*(b*c - a*d)^2*(a + b*x)^4 + 126720*a*B^2*d^5*(-(b*c) + a*d)*(a + b*x)^4 - 129600*b^2*B^2*c*d^5*x*(a + b*x)^4
+ 129600*a*b*B^2*d^6*x*(a + b*x)^4 - 126720*b*B^2*d^5*(b*c - a*d)*x*(a + b*x)^4 + 126000*b*B^2*c*d^5*(a + b*x
)^5 - 126000*a*B^2*d^6*(a + b*x)^5 + 160500*B^2*d^5*(b*c - a*d)*(a + b*x)^5 - 32400*a^2*B^2*d^6*(a + b*x)^4*Lo
g[a + b*x] - 64800*a*b*B^2*d^6*x*(a + b*x)^4*Log[a + b*x] - 32400*b^2*B^2*d^6*x^2*(a + b*x)^4*Log[a + b*x] - 2
56320*a*B^2*d^6*(a + b*x)^5*Log[a + b*x] - 256320*b*B^2*d^6*x*(a + b*x)^5*Log[a + b*x] + 286500*B^2*d^6*(a + b
*x)^6*Log[a + b*x] - 6000*B*(b*c - a*d)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 25920*a*B*d*(-(b*c) + a*d)^5*
(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 25920*b*B*d*(b*c - a*d)^5*x*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 3240
0*a*B*d^2*(b*c - a*d)^4*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 7200*B*d*(b*c - a*d)^5*(a + b*x)*(A +
B*Log[(e*(a + b*x))/(c + d*x)]) + 32400*b*B*d^2*(b*c - a*d)^4*x*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]
) - 49500*B*d^2*(b*c - a*d)^4*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 43200*a*B*d^3*(-(b*c) + a*d)^
3*(a + b*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 43200*b*B*d^3*(b*c - a*d)^3*x*(a + b*x)^2*(A + B*Log[(e*(
a + b*x))/(c + d*x)]) + 64800*a*B*d^4*(b*c - a*d)^2*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 42000*B
*d^3*(b*c - a*d)^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 64800*b*B*d^4*(b*c - a*d)^2*x*(a + b*x)^
3*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 63000*B*d^4*(b*c - a*d)^2*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d
*x)]) + 129600*a*B*d^5*(-(b*c) + a*d)*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 129600*b*B*d^5*(b*c -
a*d)*x*(a + b*x)^4*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 126000*B*d^5*(b*c - a*d)*(a + b*x)^5*(A + B*Log[(e*
(a + b*x))/(c + d*x)]) - 129600*a*B*d^6*(a + b*x)^5*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 129600
*b*B*d^6*x*(a + b*x)^5*Log[a + b*x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) + 126000*B*d^6*(a + b*x)^6*Log[a + b*
x]*(A + B*Log[(e*(a + b*x))/(c + d*x)]) - 18000*(b*c - a*d)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 + 64800*d
*(-(b*c) + a*d)^5*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2 - 81000*d^2*(b*c - a*d)^4*(a + b*x)^2*(A +
B*Log[(e*(a + b*x))/(c + d*x)])^2 + 36000*d^3*(-(b*c) + a*d)^3*(a + b*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)]
)^2 + 32400*a^2*B^2*d^6*(a + b*x)^4*Log[c + d*x] + 64800*a*b*B^2*d^6*x*(a + b*x)^4*Log[c + d*x] + 32400*b^2*B^
2*d^6*x^2*(a + b*x)^4*Log[c + d*x] + 256320*a*B^2*d^6*(a + b*x)^5*Log[c + d*x] + 256320*b*B^2*d^6*x*(a + b*x)^
5*Log[c + d*x] - 286500*B^2*d^6*(a + b*x)^6*Log[c + d*x] + 129600*a*B*d^6*(a + b*x)^5*(A + B*Log[(e*(a + b*x))
/(c + d*x)])*Log[c + d*x] + 129600*b*B*d^6*x*(a + b*x)^5*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] - 1
26000*B*d^6*(a + b*x)^6*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[c + d*x] + 64800*a*B^2*d^6*(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)]) + 6480
0*b*B^2*d^6*x*(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)]) - 63000*B^2*d^6*(a + b*x)^6*(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)]) - 64800*a*B^2*d^6*(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)]) - 64800*b*B^2*d^6*x*(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)]) + 63000*B^2*d^6*(a + b*x)^6*((2*Log[(d*(a + b*x))/(-(b*c) + a*d)] - Log[c + d*x])*Log[c + d*x] + 2*PolyL
og[2, (b*(c + d*x))/(b*c - a*d)])))/(108000*b^4*(b*c - a*d)^3*g^7*(a + b*x)^6)

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Maple [B]  time = 0.053, size = 2762, normalized size = 6. \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)^7,x)

[Out]

1/18*e^6*d*i^3/(a*d-b*c)^4/g^7*A*B*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*a-1/3*e^6*i^3/(a*d-b*c)^4/g^7*A*B
*b^3/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*c-1/4*e^4*d^2*i^3/(a*d-b*c)^4/g^7*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+1/18*e^6*d*i^3/(a*d-b*c)^4/g^7*
B^2*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*a-1/8*e^4*d^2*i^3/(a*d-b*c)^4/g^
7*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+1/2*e^4*d^3*i^3/(a*d-b*c)^4/g^
7*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-2/5*e^5*d^2*i^3/(a*d-b*c)^4/g^7*
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+2/5*e^5*d*i^3/(a*d-b*c)^4/g^7*
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+4/25*e^5*d*i^3/(a*d-b*c)^4/g
^7*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+1/6*e^6*d*i^3/(a*d-b*c)^4/g
^7*B^2*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2*a-1/8*e^4*d^2*i^3/(a*d-b*c)
^4/g^7*A*B/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*b*c-4/25*e^5*d^2*i^3/(a*d-b*c)^4/g^7*A*B*b/(b*e/d+e/(d*x+c)*a
-e/d/(d*x+c)*b*c)^5*a+4/25*e^5*d*i^3/(a*d-b*c)^4/g^7*A*B*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*c-4/25*e^5*
d^2*i^3/(a*d-b*c)^4/g^7*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-4/125*e^
5*d^2*i^3/(a*d-b*c)^4/g^7*B^2*b/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*a+4/125*e^5*d*i^3/(a*d-b*c)^4/g^7*B^2*b^
2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^5*c+1/108*e^6*d*i^3/(a*d-b*c)^4/g^7*B^2*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+
c)*b*c)^6*a-1/18*e^6*i^3/(a*d-b*c)^4/g^7*B^2*b^3/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*ln(b*e/d+(a*d-b*c)*e/d/
(d*x+c))*c+1/4*e^4*d^3*i^3/(a*d-b*c)^4/g^7*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+1/8*e^4*d^3*i^3/(a*d-b*c)^4/g^7*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-1/6*e^6*i^3/(a*d-b*c)^4/g^7*B^2*b^3/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*ln(b*e/d+(a*d-b*c)*e/d/(d*x
+c))^2*c+1/4*e^4*d^3*i^3/(a*d-b*c)^4/g^7*A^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*a+1/6*e^6*d*i^3/(a*d-b*c)^4
/g^7*A^2*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*a+1/8*e^4*d^3*i^3/(a*d-b*c)^4/g^7*A*B/(b*e/d+e/(d*x+c)*a-e/
d/(d*x+c)*b*c)^4*a-1/32*e^4*d^2*i^3/(a*d-b*c)^4/g^7*B^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*b*c+1/32*e^4*d^3
*i^3/(a*d-b*c)^4/g^7*B^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*a-1/6*e^6*i^3/(a*d-b*c)^4/g^7*A^2*b^3/(b*e/d+e/
(d*x+c)*a-e/d/(d*x+c)*b*c)^6*c-1/108*e^6*i^3/(a*d-b*c)^4/g^7*B^2*b^3/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*c+1
/3*e^6*d*i^3/(a*d-b*c)^4/g^7*A*B*b^2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))*a-1
/2*e^4*d^2*i^3/(a*d-b*c)^4/g^7*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-4
/5*e^5*d^2*i^3/(a*d-b*c)^4/g^7*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+4
/5*e^5*d*i^3/(a*d-b*c)^4/g^7*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-1
/18*e^6*i^3/(a*d-b*c)^4/g^7*A*B*b^3/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^6*c-1/4*e^4*d^2*i^3/(a*d-b*c)^4/g^7*A^
2/(b*e/d+e/(d*x+c)*a-e/d/(d*x+c)*b*c)^4*b*c-2/5*e^5*d^2*i^3/(a*d-b*c)^4/g^7*A^2*b/(b*e/d+e/(d*x+c)*a-e/d/(d*x+
c)*b*c)^5*a+2/5*e^5*d*i^3/(a*d-b*c)^4/g^7*A^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 [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*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^7,x, algorithm="maxima")

[Out]

Timed out

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Fricas [B]  time = 0.703528, size = 3443, normalized size = 7.44 \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)^7,x, algorithm="fricas")

[Out]

-1/108000*(60*((60*A*B + 37*B^2)*b^6*c*d^5 - (60*A*B + 37*B^2)*a*b^5*d^6)*i^3*x^5 - 30*((60*A*B - 23*B^2)*b^6*
c^2*d^4 - 36*(20*A*B + 9*B^2)*a*b^5*c*d^5 + (660*A*B + 347*B^2)*a^2*b^4*d^6)*i^3*x^4 + 20*((1800*A^2 + 60*A*B
- 53*B^2)*b^6*c^3*d^3 - 27*(200*A^2 + 20*A*B - 11*B^2)*a*b^5*c^2*d^4 + 675*(8*A^2 + 4*A*B + B^2)*a^2*b^4*c*d^5
- (1800*A^2 + 2220*A*B + 919*B^2)*a^3*b^3*d^6)*i^3*x^3 + 15*((5400*A^2 + 1140*A*B + 73*B^2)*b^6*c^4*d^2 - 72*
(200*A^2 + 60*A*B + 7*B^2)*a*b^5*c^3*d^3 + 1350*(8*A^2 + 4*A*B + B^2)*a^2*b^4*c^2*d^4 - (1800*A^2 + 2220*A*B +
919*B^2)*a^4*b^2*d^6)*i^3*x^2 + 6*(8*(1350*A^2 + 390*A*B + 53*B^2)*b^6*c^5*d - 45*(600*A^2 + 220*A*B + 39*B^2
)*a*b^5*c^4*d^2 + 2250*(8*A^2 + 4*A*B + B^2)*a^2*b^4*c^3*d^3 - (1800*A^2 + 2220*A*B + 919*B^2)*a^5*b*d^6)*i^3*
x + (1000*(18*A^2 + 6*A*B + B^2)*b^6*c^6 - 1728*(25*A^2 + 10*A*B + 2*B^2)*a*b^5*c^5*d + 3375*(8*A^2 + 4*A*B +
B^2)*a^2*b^4*c^4*d^2 - (1800*A^2 + 2220*A*B + 919*B^2)*a^6*d^6)*i^3 + 1800*(B^2*b^6*d^6*i^3*x^6 + 6*B^2*a*b^5*
d^6*i^3*x^5 + 15*B^2*a^2*b^4*d^6*i^3*x^4 + 20*(B^2*b^6*c^3*d^3 - 3*B^2*a*b^5*c^2*d^4 + 3*B^2*a^2*b^4*c*d^5)*i^
3*x^3 + 15*(3*B^2*b^6*c^4*d^2 - 8*B^2*a*b^5*c^3*d^3 + 6*B^2*a^2*b^4*c^2*d^4)*i^3*x^2 + 6*(6*B^2*b^6*c^5*d - 15
*B^2*a*b^5*c^4*d^2 + 10*B^2*a^2*b^4*c^3*d^3)*i^3*x + (10*B^2*b^6*c^6 - 24*B^2*a*b^5*c^5*d + 15*B^2*a^2*b^4*c^4
*d^2)*i^3)*log((b*e*x + a*e)/(d*x + c))^2 + 60*((60*A*B + 37*B^2)*b^6*d^6*i^3*x^6 + 6*(10*B^2*b^6*c*d^5 + 3*(2
0*A*B + 9*B^2)*a*b^5*d^6)*i^3*x^5 - 15*(2*B^2*b^6*c^2*d^4 - 24*B^2*a*b^5*c*d^5 - 15*(4*A*B + B^2)*a^2*b^4*d^6)
*i^3*x^4 + 20*((60*A*B + B^2)*b^6*c^3*d^3 - 9*(20*A*B + B^2)*a*b^5*c^2*d^4 + 45*(4*A*B + B^2)*a^2*b^4*c*d^5)*i
^3*x^3 + 15*((180*A*B + 19*B^2)*b^6*c^4*d^2 - 24*(20*A*B + 3*B^2)*a*b^5*c^3*d^3 + 90*(4*A*B + B^2)*a^2*b^4*c^2
*d^4)*i^3*x^2 + 6*(4*(90*A*B + 13*B^2)*b^6*c^5*d - 15*(60*A*B + 11*B^2)*a*b^5*c^4*d^2 + 150*(4*A*B + B^2)*a^2*
b^4*c^3*d^3)*i^3*x + (100*(6*A*B + B^2)*b^6*c^6 - 288*(5*A*B + B^2)*a*b^5*c^5*d + 225*(4*A*B + B^2)*a^2*b^4*c^
4*d^2)*i^3)*log((b*e*x + a*e)/(d*x + c)))/((b^13*c^3 - 3*a*b^12*c^2*d + 3*a^2*b^11*c*d^2 - a^3*b^10*d^3)*g^7*x
^6 + 6*(a*b^12*c^3 - 3*a^2*b^11*c^2*d + 3*a^3*b^10*c*d^2 - a^4*b^9*d^3)*g^7*x^5 + 15*(a^2*b^11*c^3 - 3*a^3*b^1
0*c^2*d + 3*a^4*b^9*c*d^2 - a^5*b^8*d^3)*g^7*x^4 + 20*(a^3*b^10*c^3 - 3*a^4*b^9*c^2*d + 3*a^5*b^8*c*d^2 - a^6*
b^7*d^3)*g^7*x^3 + 15*(a^4*b^9*c^3 - 3*a^5*b^8*c^2*d + 3*a^6*b^7*c*d^2 - a^7*b^6*d^3)*g^7*x^2 + 6*(a^5*b^8*c^3
- 3*a^6*b^7*c^2*d + 3*a^7*b^6*c*d^2 - a^8*b^5*d^3)*g^7*x + (a^6*b^7*c^3 - 3*a^7*b^6*c^2*d + 3*a^8*b^5*c*d^2 -
a^9*b^4*d^3)*g^7)

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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)**7,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 )}^{7}}\,{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)^7,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)^7, x)