3.1.83 \(\int \frac {(c i+d i x)^3 (A+B \log (\frac {e (a+b x)}{c+d x}))^2}{(a g+b g x)^7} \, dx\) [83]

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

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.27, antiderivative size = 463, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 4, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2562, 2395, 2342, 2341} \begin {gather*} -\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} \end {gather*}

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]

-1/32*(B^2*d^2*i^3*(c + d*x)^4)/((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)

Rule 2341

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Log[c*x^
n])/(d*(m + 1))), x] - Simp[b*n*((d*x)^(m + 1)/(d*(m + 1)^2)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2342

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Lo
g[c*x^n])^p/(d*(m + 1))), x] - Dist[b*n*(p/(m + 1)), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]

Rule 2395

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol]
:> With[{u = ExpandIntegrand[(a + b*Log[c*x^n])^p, (f*x)^m*(d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[
{a, b, c, d, e, f, m, n, p, q, r}, x] && IntegerQ[q] && (GtQ[q, 0] || (IGtQ[p, 0] && IntegerQ[m] && IntegerQ[r
]))

Rule 2562

Int[((A_.) + Log[(e_.)*((a_.) + (b_.)*(x_))^(n_.)*((c_.) + (d_.)*(x_))^(mn_)]*(B_.))^(p_.)*((f_.) + (g_.)*(x_)
)^(m_.)*((h_.) + (i_.)*(x_))^(q_.), x_Symbol] :> Dist[(b*c - a*d)^(m + q + 1)*(g/b)^m*(i/d)^q, Subst[Int[x^m*(
(A + B*Log[e*x^n])^p/(b - d*x)^(m + q + 2)), x], x, (a + b*x)/(c + d*x)], x] /; FreeQ[{a, b, c, d, e, f, g, h,
i, A, B, n, p}, x] && EqQ[n + mn, 0] && IGtQ[n, 0] && NeQ[b*c - a*d, 0] && EqQ[b*f - a*g, 0] && EqQ[d*h - c*i
, 0] && IntegersQ[m, q]

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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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*}

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Mathematica [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
time = 4.47, size = 2583, normalized size = 5.58 \begin {gather*} \text {Result too large to show} \end {gather*}

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] Leaf count of result is larger than twice the leaf count of optimal. \(1081\) vs. \(2(445)=890\).
time = 1.04, size = 1082, normalized size = 2.34 Too large to display

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,method=_RETURNVERBOSE)

[Out]

-1/d^2*e*(a*d-b*c)*(-1/6*i^3*d^2*e^5/(a*d-b*c)^4/g^7*A^2*b^2/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^6+2/5*i^3*d^3*e^4/(
a*d-b*c)^4/g^7*A^2*b/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^5-1/4*i^3*d^4*e^3/(a*d-b*c)^4/g^7*A^2/(b*e/d+(a*d-b*c)*e/d/
(d*x+c))^4+2*i^3*d^2*e^5/(a*d-b*c)^4/g^7*A*B*b^2*(-1/6/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^6*ln(b*e/d+(a*d-b*c)*e/d/
(d*x+c))-1/36/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^6)-4*i^3*d^3*e^4/(a*d-b*c)^4/g^7*A*B*b*(-1/5/(b*e/d+(a*d-b*c)*e/d/
(d*x+c))^5*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))-1/25/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^5)+2*i^3*d^4*e^3/(a*d-b*c)^4/g^7
*A*B*(-1/4/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))-1/16/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^
4)+i^3*d^2*e^5/(a*d-b*c)^4/g^7*B^2*b^2*(-1/6/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^6*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2
-1/18/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^6*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))-1/108/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^6)-2
*i^3*d^3*e^4/(a*d-b*c)^4/g^7*B^2*b*(-1/5/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^5*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2-2/2
5/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^5*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))-2/125/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^5)+i^3*d
^4*e^3/(a*d-b*c)^4/g^7*B^2*(-1/4/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))^2-1/8/(b*e/d+
(a*d-b*c)*e/d/(d*x+c))^4*ln(b*e/d+(a*d-b*c)*e/d/(d*x+c))-1/32/(b*e/d+(a*d-b*c)*e/d/(d*x+c))^4))

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Maxima [B] Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 20306 vs. \(2 (424) = 848\).
time = 3.05, size = 20306, normalized size = 43.86 \begin {gather*} \text {Too large to display} \end {gather*}

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]

1/10*I*(6*b*x + a)*B^2*c^2*d*log(b*x*e/(d*x + c) + a*e/(d*x + c))^2/(b^8*g^7*x^6 + 6*a*b^7*g^7*x^5 + 15*a^2*b^
6*g^7*x^4 + 20*a^3*b^5*g^7*x^3 + 15*a^4*b^4*g^7*x^2 + 6*a^5*b^3*g^7*x + a^6*b^2*g^7) + 1/20*I*(15*b^2*x^2 + 6*
a*b*x + a^2)*B^2*c*d^2*log(b*x*e/(d*x + c) + a*e/(d*x + c))^2/(b^9*g^7*x^6 + 6*a*b^8*g^7*x^5 + 15*a^2*b^7*g^7*
x^4 + 20*a^3*b^6*g^7*x^3 + 15*a^4*b^5*g^7*x^2 + 6*a^5*b^4*g^7*x + a^6*b^3*g^7) + 1/60*I*(20*b^3*x^3 + 15*a*b^2
*x^2 + 6*a^2*b*x + a^3)*B^2*d^3*log(b*x*e/(d*x + c) + a*e/(d*x + c))^2/(b^10*g^7*x^6 + 6*a*b^9*g^7*x^5 + 15*a^
2*b^8*g^7*x^4 + 20*a^3*b^7*g^7*x^3 + 15*a^4*b^6*g^7*x^2 + 6*a^5*b^5*g^7*x + a^6*b^4*g^7) - 1/10800*I*(60*((60*
b^5*d^5*x^5 - 10*b^5*c^5 + 62*a*b^4*c^4*d - 163*a^2*b^3*c^3*d^2 + 237*a^3*b^2*c^2*d^3 - 213*a^4*b*c*d^4 + 147*
a^5*d^5 - 30*(b^5*c*d^4 - 11*a*b^4*d^5)*x^4 + 20*(b^5*c^2*d^3 - 8*a*b^4*c*d^4 + 37*a^2*b^3*d^5)*x^3 - 15*(b^5*
c^3*d^2 - 7*a*b^4*c^2*d^3 + 23*a^2*b^3*c*d^4 - 57*a^3*b^2*d^5)*x^2 + 6*(2*b^5*c^4*d - 13*a*b^4*c^3*d^2 + 37*a^
2*b^3*c^2*d^3 - 63*a^3*b^2*c*d^4 + 87*a^4*b*d^5)*x)/((b^12*c^5 - 5*a*b^11*c^4*d + 10*a^2*b^10*c^3*d^2 - 10*a^3
*b^9*c^2*d^3 + 5*a^4*b^8*c*d^4 - a^5*b^7*d^5)*g^7*x^6 + 6*(a*b^11*c^5 - 5*a^2*b^10*c^4*d + 10*a^3*b^9*c^3*d^2
- 10*a^4*b^8*c^2*d^3 + 5*a^5*b^7*c*d^4 - a^6*b^6*d^5)*g^7*x^5 + 15*(a^2*b^10*c^5 - 5*a^3*b^9*c^4*d + 10*a^4*b^
8*c^3*d^2 - 10*a^5*b^7*c^2*d^3 + 5*a^6*b^6*c*d^4 - a^7*b^5*d^5)*g^7*x^4 + 20*(a^3*b^9*c^5 - 5*a^4*b^8*c^4*d +
10*a^5*b^7*c^3*d^2 - 10*a^6*b^6*c^2*d^3 + 5*a^7*b^5*c*d^4 - a^8*b^4*d^5)*g^7*x^3 + 15*(a^4*b^8*c^5 - 5*a^5*b^7
*c^4*d + 10*a^6*b^6*c^3*d^2 - 10*a^7*b^5*c^2*d^3 + 5*a^8*b^4*c*d^4 - a^9*b^3*d^5)*g^7*x^2 + 6*(a^5*b^7*c^5 - 5
*a^6*b^6*c^4*d + 10*a^7*b^5*c^3*d^2 - 10*a^8*b^4*c^2*d^3 + 5*a^9*b^3*c*d^4 - a^10*b^2*d^5)*g^7*x + (a^6*b^6*c^
5 - 5*a^7*b^5*c^4*d + 10*a^8*b^4*c^3*d^2 - 10*a^9*b^3*c^2*d^3 + 5*a^10*b^2*c*d^4 - a^11*b*d^5)*g^7) + 60*d^6*l
og(b*x + a)/((b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b
^2*c*d^5 + a^6*b*d^6)*g^7) - 60*d^6*log(d*x + c)/((b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c
^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b^2*c*d^5 + a^6*b*d^6)*g^7))*log(b*x*e/(d*x + c) + a*e/(d*x + c)) - (100*b
^6*c^6 - 864*a*b^5*c^5*d + 3375*a^2*b^4*c^4*d^2 - 8000*a^3*b^3*c^3*d^3 + 13500*a^4*b^2*c^2*d^4 - 21600*a^5*b*c
*d^5 + 13489*a^6*d^6 - 8820*(b^6*c*d^5 - a*b^5*d^6)*x^5 + 90*(29*b^6*c^2*d^4 - 548*a*b^5*c*d^5 + 519*a^2*b^4*d
^6)*x^4 - 60*(19*b^6*c^3*d^3 - 231*a*b^5*c^2*d^4 + 1875*a^2*b^4*c*d^5 - 1663*a^3*b^3*d^6)*x^3 + 15*(37*b^6*c^4
*d^2 - 376*a*b^5*c^3*d^3 + 1950*a^2*b^4*c^2*d^4 - 8800*a^3*b^3*c*d^5 + 7189*a^4*b^2*d^6)*x^2 + 1800*(b^6*d^6*x
^6 + 6*a*b^5*d^6*x^5 + 15*a^2*b^4*d^6*x^4 + 20*a^3*b^3*d^6*x^3 + 15*a^4*b^2*d^6*x^2 + 6*a^5*b*d^6*x + a^6*d^6)
*log(b*x + a)^2 + 1800*(b^6*d^6*x^6 + 6*a*b^5*d^6*x^5 + 15*a^2*b^4*d^6*x^4 + 20*a^3*b^3*d^6*x^3 + 15*a^4*b^2*d
^6*x^2 + 6*a^5*b*d^6*x + a^6*d^6)*log(d*x + c)^2 - 6*(44*b^6*c^5*d - 405*a*b^5*c^4*d^2 + 1750*a^2*b^4*c^3*d^3
- 5000*a^3*b^3*c^2*d^4 + 13500*a^4*b^2*c*d^5 - 9889*a^5*b*d^6)*x - 8820*(b^6*d^6*x^6 + 6*a*b^5*d^6*x^5 + 15*a^
2*b^4*d^6*x^4 + 20*a^3*b^3*d^6*x^3 + 15*a^4*b^2*d^6*x^2 + 6*a^5*b*d^6*x + a^6*d^6)*log(b*x + a) + 180*(49*b^6*
d^6*x^6 + 294*a*b^5*d^6*x^5 + 735*a^2*b^4*d^6*x^4 + 980*a^3*b^3*d^6*x^3 + 735*a^4*b^2*d^6*x^2 + 294*a^5*b*d^6*
x + 49*a^6*d^6 - 20*(b^6*d^6*x^6 + 6*a*b^5*d^6*x^5 + 15*a^2*b^4*d^6*x^4 + 20*a^3*b^3*d^6*x^3 + 15*a^4*b^2*d^6*
x^2 + 6*a^5*b*d^6*x + a^6*d^6)*log(b*x + a))*log(d*x + c))/(a^6*b^7*c^6*g^7 - 6*a^7*b^6*c^5*d*g^7 + 15*a^8*b^5
*c^4*d^2*g^7 - 20*a^9*b^4*c^3*d^3*g^7 + 15*a^10*b^3*c^2*d^4*g^7 - 6*a^11*b^2*c*d^5*g^7 + a^12*b*d^6*g^7 + (b^1
3*c^6*g^7 - 6*a*b^12*c^5*d*g^7 + 15*a^2*b^11*c^4*d^2*g^7 - 20*a^3*b^10*c^3*d^3*g^7 + 15*a^4*b^9*c^2*d^4*g^7 -
6*a^5*b^8*c*d^5*g^7 + a^6*b^7*d^6*g^7)*x^6 + 6*(a*b^12*c^6*g^7 - 6*a^2*b^11*c^5*d*g^7 + 15*a^3*b^10*c^4*d^2*g^
7 - 20*a^4*b^9*c^3*d^3*g^7 + 15*a^5*b^8*c^2*d^4*g^7 - 6*a^6*b^7*c*d^5*g^7 + a^7*b^6*d^6*g^7)*x^5 + 15*(a^2*b^1
1*c^6*g^7 - 6*a^3*b^10*c^5*d*g^7 + 15*a^4*b^9*c^4*d^2*g^7 - 20*a^5*b^8*c^3*d^3*g^7 + 15*a^6*b^7*c^2*d^4*g^7 -
6*a^7*b^6*c*d^5*g^7 + a^8*b^5*d^6*g^7)*x^4 + 20*(a^3*b^10*c^6*g^7 - 6*a^4*b^9*c^5*d*g^7 + 15*a^5*b^8*c^4*d^2*g
^7 - 20*a^6*b^7*c^3*d^3*g^7 + 15*a^7*b^6*c^2*d^4*g^7 - 6*a^8*b^5*c*d^5*g^7 + a^9*b^4*d^6*g^7)*x^3 + 15*(a^4*b^
9*c^6*g^7 - 6*a^5*b^8*c^5*d*g^7 + 15*a^6*b^7*c^4*d^2*g^7 - 20*a^7*b^6*c^3*d^3*g^7 + 15*a^8*b^5*c^2*d^4*g^7 - 6
*a^9*b^4*c*d^5*g^7 + a^10*b^3*d^6*g^7)*x^2 + 6*(a^5*b^8*c^6*g^7 - 6*a^6*b^7*c^5*d*g^7 + 15*a^7*b^6*c^4*d^2*g^7
- 20*a^8*b^5*c^3*d^3*g^7 + 15*a^9*b^4*c^2*d^4*g^7 - 6*a^10*b^3*c*d^5*g^7 + a^11*b^2*d^6*g^7)*x))*B^2*c^3 + 1/
18000*I*(60*((22*a*b^5*c^5 - 140*a^2*b^4*c^4*d + 385*a^3*b^3*c^3*d^2 - 615*a^4*b^2*c^2*d^3 + 735*a^5*b*c*d^4 -
87*a^6*d^5 + 60*(6*b^6*c*d^4 - a*b^5*d^5)*x^5 - 30*(6*b^6*c^2*d^3 - 67*a*b^5*c*d^4 + 11*a^2*b^4*d^5)*x^4 + 20
*(6*b^6*c^3*d^2 - 49*a*b^5*c^2*d^3 + 230*a^2*b^4*c*d^4 - 37*a^3*b^3*d^5)*x^3 - 15*(6*b^6*c^4*d - 43*a*b^5*c^3*
d^2 + 145*a^2*b^4*c^2*d^3 - 365*a^3*b^3*c*d^4 +...

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Fricas [B] Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 1568 vs. \(2 (424) = 848\).
time = 0.44, size = 1568, normalized size = 3.39 \begin {gather*} \frac {1000 \, {\left (18 i \, A^{2} + 6 i \, A B + i \, B^{2}\right )} b^{6} c^{6} + 1728 \, {\left (-25 i \, A^{2} - 10 i \, A B - 2 i \, B^{2}\right )} a b^{5} c^{5} d + 3375 \, {\left (8 i \, A^{2} + 4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} c^{4} d^{2} - {\left (1800 i \, A^{2} + 2220 i \, A B + 919 i \, B^{2}\right )} a^{6} d^{6} + 60 \, {\left ({\left (60 i \, A B + 37 i \, B^{2}\right )} b^{6} c d^{5} + {\left (-60 i \, A B - 37 i \, B^{2}\right )} a b^{5} d^{6}\right )} x^{5} + 30 \, {\left ({\left (-60 i \, A B + 23 i \, B^{2}\right )} b^{6} c^{2} d^{4} + 36 \, {\left (20 i \, A B + 9 i \, B^{2}\right )} a b^{5} c d^{5} + {\left (-660 i \, A B - 347 i \, B^{2}\right )} a^{2} b^{4} d^{6}\right )} x^{4} + 20 \, {\left ({\left (1800 i \, A^{2} + 60 i \, A B - 53 i \, B^{2}\right )} b^{6} c^{3} d^{3} + 27 \, {\left (-200 i \, A^{2} - 20 i \, A B + 11 i \, B^{2}\right )} a b^{5} c^{2} d^{4} + 675 \, {\left (8 i \, A^{2} + 4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} c d^{5} + {\left (-1800 i \, A^{2} - 2220 i \, A B - 919 i \, B^{2}\right )} a^{3} b^{3} d^{6}\right )} x^{3} + 15 \, {\left ({\left (5400 i \, A^{2} + 1140 i \, A B + 73 i \, B^{2}\right )} b^{6} c^{4} d^{2} + 72 \, {\left (-200 i \, A^{2} - 60 i \, A B - 7 i \, B^{2}\right )} a b^{5} c^{3} d^{3} + 1350 \, {\left (8 i \, A^{2} + 4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} c^{2} d^{4} + {\left (-1800 i \, A^{2} - 2220 i \, A B - 919 i \, B^{2}\right )} a^{4} b^{2} d^{6}\right )} x^{2} + 1800 \, {\left (i \, B^{2} b^{6} d^{6} x^{6} + 6 i \, B^{2} a b^{5} d^{6} x^{5} + 15 i \, B^{2} a^{2} b^{4} d^{6} x^{4} + 10 i \, B^{2} b^{6} c^{6} - 24 i \, B^{2} a b^{5} c^{5} d + 15 i \, B^{2} a^{2} b^{4} c^{4} d^{2} + 20 \, {\left (i \, B^{2} b^{6} c^{3} d^{3} - 3 i \, B^{2} a b^{5} c^{2} d^{4} + 3 i \, B^{2} a^{2} b^{4} c d^{5}\right )} x^{3} + 15 \, {\left (3 i \, B^{2} b^{6} c^{4} d^{2} - 8 i \, B^{2} a b^{5} c^{3} d^{3} + 6 i \, B^{2} a^{2} b^{4} c^{2} d^{4}\right )} x^{2} + 6 \, {\left (6 i \, B^{2} b^{6} c^{5} d - 15 i \, B^{2} a b^{5} c^{4} d^{2} + 10 i \, B^{2} a^{2} b^{4} c^{3} d^{3}\right )} x\right )} \log \left (\frac {{\left (b x + a\right )} e}{d x + c}\right )^{2} + 6 \, {\left (8 \, {\left (1350 i \, A^{2} + 390 i \, A B + 53 i \, B^{2}\right )} b^{6} c^{5} d + 45 \, {\left (-600 i \, A^{2} - 220 i \, A B - 39 i \, B^{2}\right )} a b^{5} c^{4} d^{2} + 2250 \, {\left (8 i \, A^{2} + 4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} c^{3} d^{3} + {\left (-1800 i \, A^{2} - 2220 i \, A B - 919 i \, B^{2}\right )} a^{5} b d^{6}\right )} x + 60 \, {\left ({\left (60 i \, A B + 37 i \, B^{2}\right )} b^{6} d^{6} x^{6} + 100 \, {\left (6 i \, A B + i \, B^{2}\right )} b^{6} c^{6} + 288 \, {\left (-5 i \, A B - i \, B^{2}\right )} a b^{5} c^{5} d + 225 \, {\left (4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} c^{4} d^{2} + 6 \, {\left (10 i \, B^{2} b^{6} c d^{5} + 3 \, {\left (20 i \, A B + 9 i \, B^{2}\right )} a b^{5} d^{6}\right )} x^{5} + 15 \, {\left (-2 i \, B^{2} b^{6} c^{2} d^{4} + 24 i \, B^{2} a b^{5} c d^{5} + 15 \, {\left (4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} d^{6}\right )} x^{4} + 20 \, {\left ({\left (60 i \, A B + i \, B^{2}\right )} b^{6} c^{3} d^{3} + 9 \, {\left (-20 i \, A B - i \, B^{2}\right )} a b^{5} c^{2} d^{4} + 45 \, {\left (4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} c d^{5}\right )} x^{3} + 15 \, {\left ({\left (180 i \, A B + 19 i \, B^{2}\right )} b^{6} c^{4} d^{2} + 24 \, {\left (-20 i \, A B - 3 i \, B^{2}\right )} a b^{5} c^{3} d^{3} + 90 \, {\left (4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} c^{2} d^{4}\right )} x^{2} + 6 \, {\left (4 \, {\left (90 i \, A B + 13 i \, B^{2}\right )} b^{6} c^{5} d + 15 \, {\left (-60 i \, A B - 11 i \, B^{2}\right )} a b^{5} c^{4} d^{2} + 150 \, {\left (4 i \, A B + i \, B^{2}\right )} a^{2} b^{4} c^{3} d^{3}\right )} x\right )} \log \left (\frac {{\left (b x + a\right )} e}{d x + c}\right )}{108000 \, {\left ({\left (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}\right )} g^{7} x^{6} + 6 \, {\left (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}\right )} g^{7} x^{5} + 15 \, {\left (a^{2} b^{11} c^{3} - 3 \, a^{3} b^{10} c^{2} d + 3 \, a^{4} b^{9} c d^{2} - a^{5} b^{8} d^{3}\right )} g^{7} x^{4} + 20 \, {\left (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}\right )} g^{7} x^{3} + 15 \, {\left (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}\right )} g^{7} x^{2} + 6 \, {\left (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}\right )} g^{7} x + {\left (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}\right )} g^{7}\right )}} \end {gather*}

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*(1000*(18*I*A^2 + 6*I*A*B + I*B^2)*b^6*c^6 + 1728*(-25*I*A^2 - 10*I*A*B - 2*I*B^2)*a*b^5*c^5*d + 3375
*(8*I*A^2 + 4*I*A*B + I*B^2)*a^2*b^4*c^4*d^2 - (1800*I*A^2 + 2220*I*A*B + 919*I*B^2)*a^6*d^6 + 60*((60*I*A*B +
37*I*B^2)*b^6*c*d^5 + (-60*I*A*B - 37*I*B^2)*a*b^5*d^6)*x^5 + 30*((-60*I*A*B + 23*I*B^2)*b^6*c^2*d^4 + 36*(20
*I*A*B + 9*I*B^2)*a*b^5*c*d^5 + (-660*I*A*B - 347*I*B^2)*a^2*b^4*d^6)*x^4 + 20*((1800*I*A^2 + 60*I*A*B - 53*I*
B^2)*b^6*c^3*d^3 + 27*(-200*I*A^2 - 20*I*A*B + 11*I*B^2)*a*b^5*c^2*d^4 + 675*(8*I*A^2 + 4*I*A*B + I*B^2)*a^2*b
^4*c*d^5 + (-1800*I*A^2 - 2220*I*A*B - 919*I*B^2)*a^3*b^3*d^6)*x^3 + 15*((5400*I*A^2 + 1140*I*A*B + 73*I*B^2)*
b^6*c^4*d^2 + 72*(-200*I*A^2 - 60*I*A*B - 7*I*B^2)*a*b^5*c^3*d^3 + 1350*(8*I*A^2 + 4*I*A*B + I*B^2)*a^2*b^4*c^
2*d^4 + (-1800*I*A^2 - 2220*I*A*B - 919*I*B^2)*a^4*b^2*d^6)*x^2 + 1800*(I*B^2*b^6*d^6*x^6 + 6*I*B^2*a*b^5*d^6*
x^5 + 15*I*B^2*a^2*b^4*d^6*x^4 + 10*I*B^2*b^6*c^6 - 24*I*B^2*a*b^5*c^5*d + 15*I*B^2*a^2*b^4*c^4*d^2 + 20*(I*B^
2*b^6*c^3*d^3 - 3*I*B^2*a*b^5*c^2*d^4 + 3*I*B^2*a^2*b^4*c*d^5)*x^3 + 15*(3*I*B^2*b^6*c^4*d^2 - 8*I*B^2*a*b^5*c
^3*d^3 + 6*I*B^2*a^2*b^4*c^2*d^4)*x^2 + 6*(6*I*B^2*b^6*c^5*d - 15*I*B^2*a*b^5*c^4*d^2 + 10*I*B^2*a^2*b^4*c^3*d
^3)*x)*log((b*x + a)*e/(d*x + c))^2 + 6*(8*(1350*I*A^2 + 390*I*A*B + 53*I*B^2)*b^6*c^5*d + 45*(-600*I*A^2 - 22
0*I*A*B - 39*I*B^2)*a*b^5*c^4*d^2 + 2250*(8*I*A^2 + 4*I*A*B + I*B^2)*a^2*b^4*c^3*d^3 + (-1800*I*A^2 - 2220*I*A
*B - 919*I*B^2)*a^5*b*d^6)*x + 60*((60*I*A*B + 37*I*B^2)*b^6*d^6*x^6 + 100*(6*I*A*B + I*B^2)*b^6*c^6 + 288*(-5
*I*A*B - I*B^2)*a*b^5*c^5*d + 225*(4*I*A*B + I*B^2)*a^2*b^4*c^4*d^2 + 6*(10*I*B^2*b^6*c*d^5 + 3*(20*I*A*B + 9*
I*B^2)*a*b^5*d^6)*x^5 + 15*(-2*I*B^2*b^6*c^2*d^4 + 24*I*B^2*a*b^5*c*d^5 + 15*(4*I*A*B + I*B^2)*a^2*b^4*d^6)*x^
4 + 20*((60*I*A*B + I*B^2)*b^6*c^3*d^3 + 9*(-20*I*A*B - I*B^2)*a*b^5*c^2*d^4 + 45*(4*I*A*B + I*B^2)*a^2*b^4*c*
d^5)*x^3 + 15*((180*I*A*B + 19*I*B^2)*b^6*c^4*d^2 + 24*(-20*I*A*B - 3*I*B^2)*a*b^5*c^3*d^3 + 90*(4*I*A*B + I*B
^2)*a^2*b^4*c^2*d^4)*x^2 + 6*(4*(90*I*A*B + 13*I*B^2)*b^6*c^5*d + 15*(-60*I*A*B - 11*I*B^2)*a*b^5*c^4*d^2 + 15
0*(4*I*A*B + I*B^2)*a^2*b^4*c^3*d^3)*x)*log((b*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^10*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)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((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 [A]
time = 4.16, size = 709, normalized size = 1.53 \begin {gather*} \frac {{\left (18000 i \, B^{2} b^{2} e^{7} \log \left (\frac {b x e + a e}{d x + c}\right )^{2} - \frac {43200 i \, {\left (b x e + a e\right )} B^{2} b d e^{6} \log \left (\frac {b x e + a e}{d x + c}\right )^{2}}{d x + c} + \frac {27000 i \, {\left (b x e + a e\right )}^{2} B^{2} d^{2} e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )^{2}}{{\left (d x + c\right )}^{2}} + 36000 i \, A B b^{2} e^{7} \log \left (\frac {b x e + a e}{d x + c}\right ) + 6000 i \, B^{2} b^{2} e^{7} \log \left (\frac {b x e + a e}{d x + c}\right ) - \frac {86400 i \, {\left (b x e + a e\right )} A B b d e^{6} \log \left (\frac {b x e + a e}{d x + c}\right )}{d x + c} - \frac {17280 i \, {\left (b x e + a e\right )} B^{2} b d e^{6} \log \left (\frac {b x e + a e}{d x + c}\right )}{d x + c} + \frac {54000 i \, {\left (b x e + a e\right )}^{2} A B d^{2} e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )}{{\left (d x + c\right )}^{2}} + \frac {13500 i \, {\left (b x e + a e\right )}^{2} B^{2} d^{2} e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )}{{\left (d x + c\right )}^{2}} + 18000 i \, A^{2} b^{2} e^{7} + 6000 i \, A B b^{2} e^{7} + 1000 i \, B^{2} b^{2} e^{7} - \frac {43200 i \, {\left (b x e + a e\right )} A^{2} b d e^{6}}{d x + c} - \frac {17280 i \, {\left (b x e + a e\right )} A B b d e^{6}}{d x + c} - \frac {3456 i \, {\left (b x e + a e\right )} B^{2} b d e^{6}}{d x + c} + \frac {27000 i \, {\left (b x e + a e\right )}^{2} A^{2} d^{2} e^{5}}{{\left (d x + c\right )}^{2}} + \frac {13500 i \, {\left (b x e + a e\right )}^{2} A B d^{2} e^{5}}{{\left (d x + c\right )}^{2}} + \frac {3375 i \, {\left (b x e + a e\right )}^{2} B^{2} d^{2} e^{5}}{{\left (d x + c\right )}^{2}}\right )} {\left (\frac {b c}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}} - \frac {a d}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}}\right )}}{108000 \, {\left (\frac {{\left (b x e + a e\right )}^{6} b^{2} c^{2} g^{7}}{{\left (d x + c\right )}^{6}} - \frac {2 \, {\left (b x e + a e\right )}^{6} a b c d g^{7}}{{\left (d x + c\right )}^{6}} + \frac {{\left (b x e + a e\right )}^{6} a^{2} d^{2} g^{7}}{{\left (d x + c\right )}^{6}}\right )}} \end {gather*}

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]

1/108000*(18000*I*B^2*b^2*e^7*log((b*x*e + a*e)/(d*x + c))^2 - 43200*I*(b*x*e + a*e)*B^2*b*d*e^6*log((b*x*e +
a*e)/(d*x + c))^2/(d*x + c) + 27000*I*(b*x*e + a*e)^2*B^2*d^2*e^5*log((b*x*e + a*e)/(d*x + c))^2/(d*x + c)^2 +
36000*I*A*B*b^2*e^7*log((b*x*e + a*e)/(d*x + c)) + 6000*I*B^2*b^2*e^7*log((b*x*e + a*e)/(d*x + c)) - 86400*I*
(b*x*e + a*e)*A*B*b*d*e^6*log((b*x*e + a*e)/(d*x + c))/(d*x + c) - 17280*I*(b*x*e + a*e)*B^2*b*d*e^6*log((b*x*
e + a*e)/(d*x + c))/(d*x + c) + 54000*I*(b*x*e + a*e)^2*A*B*d^2*e^5*log((b*x*e + a*e)/(d*x + c))/(d*x + c)^2 +
13500*I*(b*x*e + a*e)^2*B^2*d^2*e^5*log((b*x*e + a*e)/(d*x + c))/(d*x + c)^2 + 18000*I*A^2*b^2*e^7 + 6000*I*A
*B*b^2*e^7 + 1000*I*B^2*b^2*e^7 - 43200*I*(b*x*e + a*e)*A^2*b*d*e^6/(d*x + c) - 17280*I*(b*x*e + a*e)*A*B*b*d*
e^6/(d*x + c) - 3456*I*(b*x*e + a*e)*B^2*b*d*e^6/(d*x + c) + 27000*I*(b*x*e + a*e)^2*A^2*d^2*e^5/(d*x + c)^2 +
13500*I*(b*x*e + a*e)^2*A*B*d^2*e^5/(d*x + c)^2 + 3375*I*(b*x*e + a*e)^2*B^2*d^2*e^5/(d*x + c)^2)*(b*c/((b*c*
e - a*d*e)*(b*c - a*d)) - a*d/((b*c*e - a*d*e)*(b*c - a*d)))/((b*x*e + a*e)^6*b^2*c^2*g^7/(d*x + c)^6 - 2*(b*x
*e + a*e)^6*a*b*c*d*g^7/(d*x + c)^6 + (b*x*e + a*e)^6*a^2*d^2*g^7/(d*x + c)^6)

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Mupad [B]
time = 14.17, size = 2500, normalized size = 5.40 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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]

((1800*A^2*a^5*d^5*i^3 + 18000*A^2*b^5*c^5*i^3 + 919*B^2*a^5*d^5*i^3 + 1000*B^2*b^5*c^5*i^3 + 2220*A*B*a^5*d^5
*i^3 + 6000*A*B*b^5*c^5*i^3 - 25200*A^2*a*b^4*c^4*d*i^3 + 1800*A^2*a^4*b*c*d^4*i^3 - 2456*B^2*a*b^4*c^4*d*i^3
+ 919*B^2*a^4*b*c*d^4*i^3 + 1800*A^2*a^2*b^3*c^3*d^2*i^3 + 1800*A^2*a^3*b^2*c^2*d^3*i^3 + 919*B^2*a^2*b^3*c^3*
d^2*i^3 + 919*B^2*a^3*b^2*c^2*d^3*i^3 + 2220*A*B*a^2*b^3*c^3*d^2*i^3 + 2220*A*B*a^3*b^2*c^2*d^3*i^3 - 11280*A*
B*a*b^4*c^4*d*i^3 + 2220*A*B*a^4*b*c*d^4*i^3)/(60*(a*d - b*c)) + (x^4*(347*B^2*a*b^4*d^5*i^3 + 23*B^2*b^5*c*d^
4*i^3 + 660*A*B*a*b^4*d^5*i^3 - 60*A*B*b^5*c*d^4*i^3))/(2*(a*d - b*c)) + (x^2*(1800*A^2*a^3*b^2*d^5*i^3 + 919*
B^2*a^3*b^2*d^5*i^3 + 5400*A^2*b^5*c^3*d^2*i^3 + 73*B^2*b^5*c^3*d^2*i^3 - 9000*A^2*a*b^4*c^2*d^3*i^3 + 1800*A^
2*a^2*b^3*c*d^4*i^3 - 431*B^2*a*b^4*c^2*d^3*i^3 + 919*B^2*a^2*b^3*c*d^4*i^3 + 2220*A*B*a^3*b^2*d^5*i^3 + 1140*
A*B*b^5*c^3*d^2*i^3 - 3180*A*B*a*b^4*c^2*d^3*i^3 + 2220*A*B*a^2*b^3*c*d^4*i^3))/(4*(a*d - b*c)) + (x^3*(1800*A
^2*a^2*b^3*d^5*i^3 + 919*B^2*a^2*b^3*d^5*i^3 + 1800*A^2*b^5*c^2*d^3*i^3 - 53*B^2*b^5*c^2*d^3*i^3 - 3600*A^2*a*
b^4*c*d^4*i^3 + 244*B^2*a*b^4*c*d^4*i^3 + 2220*A*B*a^2*b^3*d^5*i^3 + 60*A*B*b^5*c^2*d^3*i^3 - 480*A*B*a*b^4*c*
d^4*i^3))/(3*(a*d - b*c)) + (x*(1800*A^2*a^4*b*d^5*i^3 + 919*B^2*a^4*b*d^5*i^3 + 10800*A^2*b^5*c^4*d*i^3 + 424
*B^2*b^5*c^4*d*i^3 - 16200*A^2*a*b^4*c^3*d^2*i^3 + 1800*A^2*a^3*b^2*c*d^4*i^3 - 1331*B^2*a*b^4*c^3*d^2*i^3 + 9
19*B^2*a^3*b^2*c*d^4*i^3 + 2220*A*B*a^4*b*d^5*i^3 + 3120*A*B*b^5*c^4*d*i^3 + 1800*A^2*a^2*b^3*c^2*d^3*i^3 + 91
9*B^2*a^2*b^3*c^2*d^3*i^3 - 6780*A*B*a*b^4*c^3*d^2*i^3 + 2220*A*B*a^3*b^2*c*d^4*i^3 + 2220*A*B*a^2*b^3*c^2*d^3
*i^3))/(10*(a*d - b*c)) + (d*x^5*(37*B^2*b^5*d^4*i^3 + 60*A*B*b^5*d^4*i^3))/(a*d - b*c))/(x*(10800*a^5*b^6*c*g
^7 - 10800*a^6*b^5*d*g^7) - x^5*(10800*a^2*b^9*d*g^7 - 10800*a*b^10*c*g^7) + x^6*(1800*b^11*c*g^7 - 1800*a*b^1
0*d*g^7) + x^2*(27000*a^4*b^7*c*g^7 - 27000*a^5*b^6*d*g^7) + x^4*(27000*a^2*b^9*c*g^7 - 27000*a^3*b^8*d*g^7) +
x^3*(36000*a^3*b^8*c*g^7 - 36000*a^4*b^7*d*g^7) + 1800*a^6*b^5*c*g^7 - 1800*a^7*b^4*d*g^7) - log((e*(a + b*x)
)/(c + d*x))^2*((x*(a*(b*((B^2*a*d^3*i^3)/(60*b^5*g^7) + (B^2*c*d^2*i^3)/(20*b^4*g^7)) + (B^2*a*d^3*i^3)/(15*b
^4*g^7) + (B^2*c*d^2*i^3)/(5*b^3*g^7)) + b*(a*((B^2*a*d^3*i^3)/(60*b^5*g^7) + (B^2*c*d^2*i^3)/(20*b^4*g^7)) +
(B^2*c^2*d*i^3)/(10*b^3*g^7)) + (B^2*c^2*d*i^3)/(2*b^2*g^7)) + x^2*(b*(b*((B^2*a*d^3*i^3)/(60*b^5*g^7) + (B^2*
c*d^2*i^3)/(20*b^4*g^7)) + (B^2*a*d^3*i^3)/(15*b^4*g^7) + (B^2*c*d^2*i^3)/(5*b^3*g^7)) + (B^2*a*d^3*i^3)/(6*b^
3*g^7) + (B^2*c*d^2*i^3)/(2*b^2*g^7)) + a*(a*((B^2*a*d^3*i^3)/(60*b^5*g^7) + (B^2*c*d^2*i^3)/(20*b^4*g^7)) + (
B^2*c^2*d*i^3)/(10*b^3*g^7)) + (B^2*c^3*i^3)/(6*b^2*g^7) + (B^2*d^3*i^3*x^3)/(3*b^2*g^7))/(6*a^5*x + a^6/b + b
^5*x^6 + 15*a^4*b*x^2 + 6*a*b^4*x^5 + 20*a^3*b^2*x^3 + 15*a^2*b^3*x^4) - (B^2*d^6*i^3)/(60*b^4*g^7*(a^3*d^3 -
b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))) - (log((e*(a + b*x))/(c + d*x))*(a*(a*((B*d*i^3*(9*A*b*c - B*a*d +
B*b*c))/(90*b^5*g^7) + (A*B*a*d^2*i^3)/(30*b^5*g^7)) + (B*i^3*(36*A*b^2*c^2 - 3*B*a^2*d^2 + 5*B*b^2*c^2 - 2*B*
a*b*c*d))/(180*b^5*g^7)) + x^2*(b*(b*((B*d*i^3*(9*A*b*c - B*a*d + B*b*c))/(90*b^5*g^7) + (A*B*a*d^2*i^3)/(30*b
^5*g^7)) + (2*B*d*i^3*(9*A*b*c - B*a*d + B*b*c))/(45*b^4*g^7) + (2*A*B*a*d^2*i^3)/(15*b^4*g^7)) + (B*d*i^3*(9*
A*b*c - B*a*d + B*b*c))/(9*b^3*g^7) + (A*B*a*d^2*i^3)/(3*b^3*g^7) + (B^2*d^6*i^3*(b*((20*a^4*d^4 + b^4*c^4 + 2
1*a^2*b^2*c^2*d^2 - 7*a*b^3*c^3*d - 35*a^3*b*c*d^3)/(15*d^5) + b*(a*(a*((6*a^2*d^2 + b^2*c^2 - 7*a*b*c*d)/(30*
b*d^3) + (a*(a*d - b*c))/(6*b*d^2)) + (15*a^3*d^3 - b^3*c^3 + 7*a*b^2*c^2*d - 21*a^2*b*c*d^2)/(60*b*d^4)) + (2
0*a^4*d^4 + b^4*c^4 + 21*a^2*b^2*c^2*d^2 - 7*a*b^3*c^3*d - 35*a^3*b*c*d^3)/(60*b*d^5)) + a*(b*(a*((6*a^2*d^2 +
b^2*c^2 - 7*a*b*c*d)/(30*b*d^3) + (a*(a*d - b*c))/(6*b*d^2)) + (15*a^3*d^3 - b^3*c^3 + 7*a*b^2*c^2*d - 21*a^2
*b*c*d^2)/(60*b*d^4)) + a*(b*((6*a^2*d^2 + b^2*c^2 - 7*a*b*c*d)/(30*b*d^3) + (a*(a*d - b*c))/(6*b*d^2)) + (6*a
^2*d^2 + b^2*c^2 - 7*a*b*c*d)/(15*d^3) + (a*(a*d - b*c))/(3*d^2)) + (15*a^3*d^3 - b^3*c^3 + 7*a*b^2*c^2*d - 21
*a^2*b*c*d^2)/(20*d^4))) + a*(a*(b*(b*((6*a^2*d^2 + b^2*c^2 - 7*a*b*c*d)/(30*b*d^3) + (a*(a*d - b*c))/(6*b*d^2
)) + (6*a^2*d^2 + b^2*c^2 - 7*a*b*c*d)/(15*d^3) + (a*(a*d - b*c))/(3*d^2)) - a*((b^2*c - a*b*d)/(6*d^2) - (b*(
a*d - b*c))/(3*d^2)) + (b^3*c^2 + 6*a^2*b*d^2 - 7*a*b^2*c*d)/(10*d^3)) - (b^4*c^3 - 15*a^3*b*d^3 + 21*a^2*b^2*
c*d^2 - 7*a*b^3*c^2*d)/(10*d^4) + b*(b*(a*((6*a^2*d^2 + b^2*c^2 - 7*a*b*c*d)/(30*b*d^3) + (a*(a*d - b*c))/(6*b
*d^2)) + (15*a^3*d^3 - b^3*c^3 + 7*a*b^2*c^2*d - 21*a^2*b*c*d^2)/(60*b*d^4)) + a*(b*((6*a^2*d^2 + b^2*c^2 - 7*
a*b*c*d)/(30*b*d^3) + (a*(a*d - b*c))/(6*b*d^2)) + (6*a^2*d^2 + b^2*c^2 - 7*a*b*c*d)/(15*d^3) + (a*(a*d - b*c)
)/(3*d^2)) + (15*a^3*d^3 - b^3*c^3 + 7*a*b^2*c^2*d - 21*a^2*b*c*d^2)/(20*d^4))) + (b^5*c^4 + 20*a^4*b*d^4 - 35
*a^3*b^2*c*d^3 + 21*a^2*b^3*c^2*d^2 - 7*a*b^4*c^3*d)/(6*d^5)))/(30*b^4*g^7*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d
- 3*a^2*b*c*d^2))) + x*(b*(a*((B*d*i^3*(9*A*b*c...

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