3.1.68 \(\int \frac {(c i+d i x)^2 (A+B \log (\frac {e (a+b x)}{c+d x}))^2}{a g+b g x} \, dx\) [68]

Optimal. Leaf size=535 \[ -\frac {B d (b c-a d) i^2 (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {2 B (b c-a d)^2 i^2 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {d (b c-a d) i^2 (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3 g}+\frac {i^2 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b g}+\frac {B^2 (b c-a d)^2 i^2 \log (c+d x)}{b^3 g}+\frac {B (b c-a d)^2 i^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g}-\frac {(b c-a d)^2 i^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g}+\frac {2 B^2 (b c-a d)^2 i^2 \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right )}{b^3 g}-\frac {B^2 (b c-a d)^2 i^2 \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g}+\frac {2 B (b c-a d)^2 i^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g}+\frac {2 B^2 (b c-a d)^2 i^2 \text {Li}_3\left (\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g} \]

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.49, antiderivative size = 535, normalized size of antiderivative = 1.00, number of steps used = 15, number of rules used = 11, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.262, Rules used = {2562, 2389, 2379, 2421, 6724, 2355, 2354, 2438, 2356, 2351, 31} \begin {gather*} \frac {2 B i^2 (b c-a d)^2 \text {PolyLog}\left (2,\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{b^3 g}+\frac {2 B^2 i^2 (b c-a d)^2 \text {PolyLog}\left (2,\frac {d (a+b x)}{b (c+d x)}\right )}{b^3 g}-\frac {B^2 i^2 (b c-a d)^2 \text {PolyLog}\left (2,\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g}+\frac {2 B^2 i^2 (b c-a d)^2 \text {PolyLog}\left (3,\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g}+\frac {d i^2 (a+b x) (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{b^3 g}-\frac {B d i^2 (a+b x) (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{b^3 g}+\frac {2 B i^2 (b c-a d)^2 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{b^3 g}-\frac {i^2 (b c-a d)^2 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{b^3 g}+\frac {B i^2 (b c-a d)^2 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{b^3 g}+\frac {i^2 (c+d x)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{2 b g}+\frac {B^2 i^2 (b c-a d)^2 \log (c+d x)}{b^3 g} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-((B*d*(b*c - a*d)*i^2*(a + b*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b^3*g)) + (2*B*(b*c - a*d)^2*i^2*Log[(
b*c - a*d)/(b*(c + d*x))]*(A + B*Log[(e*(a + b*x))/(c + d*x)]))/(b^3*g) + (d*(b*c - a*d)*i^2*(a + b*x)*(A + B*
Log[(e*(a + b*x))/(c + d*x)])^2)/(b^3*g) + (i^2*(c + d*x)^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2)/(2*b*g) +
(B^2*(b*c - a*d)^2*i^2*Log[c + d*x])/(b^3*g) + (B*(b*c - a*d)^2*i^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])*Log[1
- (b*(c + d*x))/(d*(a + b*x))])/(b^3*g) - ((b*c - a*d)^2*i^2*(A + B*Log[(e*(a + b*x))/(c + d*x)])^2*Log[1 - (
b*(c + d*x))/(d*(a + b*x))])/(b^3*g) + (2*B^2*(b*c - a*d)^2*i^2*PolyLog[2, (d*(a + b*x))/(b*(c + d*x))])/(b^3*
g) - (B^2*(b*c - a*d)^2*i^2*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))])/(b^3*g) + (2*B*(b*c - a*d)^2*i^2*(A + B*L
og[(e*(a + b*x))/(c + d*x)])*PolyLog[2, (b*(c + d*x))/(d*(a + b*x))])/(b^3*g) + (2*B^2*(b*c - a*d)^2*i^2*PolyL
og[3, (b*(c + d*x))/(d*(a + b*x))])/(b^3*g)

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 2351

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

Rule 2354

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

Rule 2355

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((d_) + (e_.)*(x_))^2, x_Symbol] :> Simp[x*((a + b*Log[c*x^n])
^p/(d*(d + e*x))), x] - Dist[b*n*(p/d), Int[(a + b*Log[c*x^n])^(p - 1)/(d + e*x), x], x] /; FreeQ[{a, b, c, d,
e, n, p}, x] && GtQ[p, 0]

Rule 2356

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_))^(q_.), x_Symbol] :> Simp[(d + e*x)^(q + 1)
*((a + b*Log[c*x^n])^p/(e*(q + 1))), x] - Dist[b*n*(p/(e*(q + 1))), Int[((d + e*x)^(q + 1)*(a + b*Log[c*x^n])^
(p - 1))/x, x], x] /; FreeQ[{a, b, c, d, e, n, p, q}, x] && GtQ[p, 0] && NeQ[q, -1] && (EqQ[p, 1] || (Integers
Q[2*p, 2*q] &&  !IGtQ[q, 0]) || (EqQ[p, 2] && NeQ[q, 1]))

Rule 2379

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

Rule 2389

Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_))^(q_))/(x_), x_Symbol] :> Dist[1/d, Int[(d
+ e*x)^(q + 1)*((a + b*Log[c*x^n])^p/x), x], x] - Dist[e/d, Int[(d + e*x)^q*(a + b*Log[c*x^n])^p, x], x] /; F
reeQ[{a, b, c, d, e, n}, x] && IGtQ[p, 0] && LtQ[q, -1] && IntegerQ[2*q]

Rule 2421

Int[(Log[(d_.)*((e_) + (f_.)*(x_)^(m_.))]*((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.))/(x_), x_Symbol] :> Simp
[(-PolyLog[2, (-d)*f*x^m])*((a + b*Log[c*x^n])^p/m), x] + Dist[b*n*(p/m), Int[PolyLog[2, (-d)*f*x^m]*((a + b*L
og[c*x^n])^(p - 1)/x), x], x] /; FreeQ[{a, b, c, d, e, f, m, n}, x] && IGtQ[p, 0] && EqQ[d*e, 1]

Rule 2438

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]

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]

Rule 6724

Int[PolyLog[n_, (c_.)*((a_.) + (b_.)*(x_))^(p_.)]/((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[PolyLog[n + 1, c*(a
+ b*x)^p]/(e*p), x] /; FreeQ[{a, b, c, d, e, n, p}, x] && EqQ[b*d, a*e]

Rubi steps

\begin {align*} \int \frac {(68 c+68 d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{a g+b g x} \, dx &=\int \left (\frac {4624 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {68 d (68 c+68 d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 (a g+b g x)}\right ) \, dx\\ &=\frac {\left (4624 (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 g+b g x} \, dx}{b^2}+\frac {(68 d) \int (68 c+68 d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{b g}+\frac {(4624 d (b c-a d)) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{b^2 g}\\ &=\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {B \int \frac {4624 (b c-a d) (c+d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{a+b x} \, dx}{b g}-\frac {(9248 B d (b c-a d)) \int \frac {(b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)} \, dx}{b^2 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{e (a+b x)} \, dx}{b^3 g}\\ &=\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {(4624 B (b c-a d)) \int \frac {(c+d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{a+b x} \, dx}{b g}-\frac {\left (9248 B d (b c-a d)^2\right ) \int \frac {x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)} \, dx}{b^2 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{a+b x} \, dx}{b^3 e g}\\ &=\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {(4624 B (b c-a d)) \int \left (\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b}+\frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b (a+b x)}\right ) \, dx}{b g}-\frac {\left (9248 B d (b c-a d)^2\right ) \int \left (-\frac {a \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)}+\frac {c \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (c+d x)}\right ) \, dx}{b^2 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \frac {(b c-a d) e \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{(a+b x) (c+d x)} \, dx}{b^3 e g}\\ &=\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {(4624 B d (b c-a d)) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{b^2 g}+\frac {(9248 a B d (b c-a d)) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^2 g}-\frac {(9248 B c d (b c-a d)) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^2 g}-\frac {\left (4624 B (b c-a d)^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B (b c-a d)^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{(a+b x) (c+d x)} \, dx}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {\left (9248 B^2 c (b c-a d)\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (c+d x)}{e (a+b x)} \, dx}{b^2 g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{b^3 g}-\frac {\left (4624 B^2 d (b c-a d)\right ) \int \log \left (\frac {e (a+b x)}{c+d x}\right ) \, dx}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{b^3 g}-\frac {\left (9248 B (b c-a d)^3\right ) \int \left (\frac {d \left (-A-B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{(b c-a d) (c+d x)}+\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{(b c-a d) (a+b x)}\right ) \, dx}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B d (b c-a d)^2\right ) \int \frac {\left (-A-B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{c+d x} \, dx}{b^3 g}+\frac {\left (4624 B^2 d (b c-a d)^2\right ) \int \frac {1}{c+d x} \, dx}{b^3 g}+\frac {\left (9248 B^2 c (b c-a d)\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{b^2 e g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^3 e g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^3 e g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \left (\frac {A \log (a g+b g x)}{a+b x}+\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right ) \log (a g+b g x)}{a+b x}\right ) \, dx}{b^2 g}-\frac {\left (9248 B d (b c-a d)^2\right ) \int \left (\frac {A \log (a g+b g x)}{-c-d x}+\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right ) \log (a g+b g x)}{-c-d x}\right ) \, dx}{b^3 g}+\frac {\left (9248 B^2 c (b c-a d)\right ) \int \left (\frac {b e \log (c+d x)}{a+b x}-\frac {d e \log (c+d x)}{c+d x}\right ) \, dx}{b^2 e g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \left (\frac {b e \log (a+b x)}{a+b x}-\frac {d e \log (a+b x)}{c+d x}\right ) \, dx}{b^3 e g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \left (\frac {b e \log (a+b x)}{a+b x}-\frac {d e \log (a+b x)}{c+d x}\right ) \, dx}{b^3 e g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {\left (9248 B^2 c (b c-a d)\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B^2 c d (b c-a d)\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^2 g}+\frac {\left (9248 a B^2 d^2 (b c-a d)\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^3 g}-\frac {\left (9248 A B (b c-a d)^2\right ) \int \frac {\log (a g+b g x)}{a+b x} \, dx}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (a g+b g x)}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 A B d (b c-a d)^2\right ) \int \frac {\log (a g+b g x)}{-c-d x} \, dx}{b^3 g}-\frac {\left (4624 B^2 d (b c-a d)^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^3 g}-\frac {\left (9248 B^2 d (b c-a d)^2\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (a g+b g x)}{-c-d x} \, dx}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {\left (9248 A B (b c-a d)^2\right ) \int \frac {\log \left (\frac {b g (-c-d x)}{-b c g+a d g}\right )}{a g+b g x} \, dx}{b^2}-\frac {\left (9248 A B (b c-a d)^2\right ) \text {Subst}\left (\int \frac {g \log (x)}{x} \, dx,x,a g+b g x\right )}{b^3 g^2}-\frac {\left (9248 B^2 c (b c-a d)\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^2 g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B^2 c d (b c-a d)\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^3 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {\log ^2(a g+b g x)}{a+b x} \, dx}{b^2 g}-\frac {\left (4624 B^2 d (b c-a d)^2\right ) \int \frac {\log ^2(a g+b g x)}{c+d x} \, dx}{b^3 g}-\frac {\left (9248 B^2 d (b c-a d)^2\right ) \int \frac {\log (a+b x) \log (a g+b g x)}{-c-d x} \, dx}{b^3 g}-\frac {\left (9248 B^2 d (b c-a d)^2\right ) \int \frac {\log \left (\frac {1}{c+d x}\right ) \log (a g+b g x)}{-c-d x} \, dx}{b^3 g}-\frac {\left (9248 B^2 d (b c-a d)^2 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \int \frac {\log (a g+b g x)}{-c-d x} \, dx}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \int \frac {\log \left (\frac {b g (c+d x)}{b c g-a d g}\right ) \log (a g+b g x)}{a g+b g x} \, dx}{b^2}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {g \log ^2(x)}{x} \, dx,x,a g+b g x\right )}{b^3 g^2}-\frac {\left (9248 B^2 c (b c-a d)\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^2 g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 A B (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a g+b g x\right )}{b^3 g}-\frac {\left (9248 A B (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log \left (1-\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^3 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log \left (\frac {-b c+a d}{d}-\frac {b x}{d}\right ) \log \left (\frac {-b c g+a d g}{d}-\frac {b g x}{d}\right )}{x} \, dx,x,-c-d x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log \left (\frac {1}{x}\right ) \log \left (\frac {-b c g+a d g}{d}+\frac {b g x}{d}\right )}{x} \, dx,x,c+d x\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \int \frac {\log \left (\frac {b g (-c-d x)}{-b c g+a d g}\right )}{a g+b g x} \, dx}{b^2}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log ^2\left (\frac {1}{x}\right )}{\frac {-b c g+a d g}{d}+\frac {b g x}{d}} \, dx,x,c+d x\right )}{b^2 d}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c g+a d g}{d}-\frac {b g x}{d}\right )}{\frac {-b c g+a d g}{d}-\frac {b g x}{d}} \, dx,x,-c-d x\right )}{b^2 d}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log ^2(x)}{x} \, dx,x,a g+b g x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {b g \left (\frac {b c g-a d g}{b g}+\frac {d x}{b g}\right )}{b c g-a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c+a d}{d}-\frac {b x}{d}\right )}{\frac {-b c+a d}{d}-\frac {b x}{d}} \, dx,x,-c-d x\right )}{b^2 d g}-\frac {\left (9248 B^2 (b c-a d)^2 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \text {Subst}\left (\int \frac {\log \left (1-\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int x^2 \, dx,x,\log (g (a+b x))\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c+a d}{b}-\frac {d x}{b}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c g+a d g}{b g}-\frac {d x}{b g}\right )}{x} \, dx,x,a g+b g x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log \left (\frac {1}{x}\right ) \log \left (1+\frac {b g x}{-b c g+a d g}\right )}{x} \, dx,x,c+d x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {d x}{b c g-a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^3(g (a+b x))}{3 b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log (-c-d x)}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}-\frac {9248 B^2 (b c-a d)^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {\left (4624 B^2 d (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log ^2(x)}{\frac {-b c g+a d g}{b g}-\frac {d x}{b g}} \, dx,x,a g+b g x\right )}{b^4 g^2}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b g x}{-b c g+a d g}\right )}{x} \, dx,x,c+d x\right )}{b^3 g}-\frac {\left (4624 B^2 d (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log ^2(x)}{\frac {-b c+a d}{b}-\frac {d x}{b}} \, dx,x,a+b x\right )}{b^4 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^3(g (a+b x))}{3 b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log (-c-d x)}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}-\frac {9248 B^2 (b c-a d)^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (1-\frac {d x}{-b c+a d}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (1-\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^3(g (a+b x))}{3 b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log (-c-d x)}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}-\frac {9248 B^2 (b c-a d)^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (\frac {d x}{-b c+a d}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^3(g (a+b x))}{3 b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log (-c-d x)}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}-\frac {9248 B^2 (b c-a d)^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}\\ \end {align*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1987\) vs. \(2(535)=1070\).
time = 2.18, size = 1987, normalized size = 3.71 \begin {gather*} \text {Too large to display} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(i^2*(12*A^2*b*d*(2*b*c - a*d)*x + 6*A^2*b^2*d^2*x^2 + 12*A^2*(b*c - a*d)^2*Log[a + b*x] - 24*A*b*B*c*(a*d*Log
[a/b + x]^2 - 2*a*d*Log[a/b + x]*(1 + Log[a + b*x]) + 2*(-(b*c) + a*d + Log[c/d + x]*(b*c + a*d*Log[a + b*x] -
a*d*Log[(d*(a + b*x))/(-(b*c) + a*d)]) + (-(b*d*x) + a*d*Log[a + b*x])*Log[(e*(a + b*x))/(c + d*x)]) - 2*a*d*
PolyLog[2, (b*(c + d*x))/(b*c - a*d)]) + 12*A*b^2*B*c^2*(Log[a/b + x]^2 - 2*Log[a + b*x]*(Log[a/b + x] - Log[c
/d + x] - Log[(e*(a + b*x))/(c + d*x)]) - 2*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c
+ d*x))/(b*c - a*d)])) + 6*A*B*(-4*a*d^2*(a + b*x)*(-1 + Log[a/b + x]) + 2*a^2*d^2*Log[a/b + x]^2 + 4*a*b*d*(
c + d*x)*(-1 + Log[c/d + x]) + d^2*(b*x*(2*a - b*x) + 2*b^2*x^2*Log[a/b + x] - 2*a^2*Log[a + b*x]) - 2*d^2*(b*
x*(-2*a + b*x) + 2*a^2*Log[a + b*x])*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)]) + b^2*(d*x*(
-2*c + d*x) - 2*d^2*x^2*Log[c/d + x] + 2*c^2*Log[c + d*x]) - 4*a^2*d^2*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c)
+ a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) + 8*b*B^2*c*(Log[(e*(a + b*x))/(c + d*x)]*(-(a*d*Log[(e*(a
+ b*x))/(c + d*x)]^2) + 6*(b*c - a*d)*Log[(b*c - a*d)/(b*c + b*d*x)] + 3*d*Log[(e*(a + b*x))/(c + d*x)]*(a + b
*x + a*Log[(b*c - a*d)/(b*c + b*d*x)])) + 6*(b*c - a*d + a*d*Log[(e*(a + b*x))/(c + d*x)])*PolyLog[2, (d*(a +
b*x))/(b*(c + d*x))] - 6*a*d*PolyLog[3, (d*(a + b*x))/(b*(c + d*x))]) + B^2*(4*a^2*d^2*Log[a/b + x]^3 - 12*a*d
^2*(2*b*x - 2*(a + b*x)*Log[a/b + x] + (a + b*x)*Log[a/b + x]^2) - 3*d^2*(b*x*(6*a - b*x) + (-6*a^2 - 4*a*b*x
+ 2*b^2*x^2)*Log[a/b + x] + 2*(a^2 - b^2*x^2)*Log[a/b + x]^2) - 12*a*b*d*(2*d*x - 2*(c + d*x)*Log[c/d + x] + (
c + d*x)*Log[c/d + x]^2) - 3*b^2*(d*x*(6*c - d*x) + (-6*c^2 - 4*c*d*x + 2*d^2*x^2)*Log[c/d + x] + 2*(c^2 - d^2
*x^2)*Log[c/d + x]^2) + 6*d^2*(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x])*(-Log[a/b + x] + Log[c/d + x] + Log[(e*(
a + b*x))/(c + d*x)])^2 - 6*(Log[a/b + x] - Log[c/d + x] - Log[(e*(a + b*x))/(c + d*x)])*(-4*a*d^2*(a + b*x)*(
-1 + Log[a/b + x]) + 2*a^2*d^2*Log[a/b + x]^2 + 4*a*b*d*(c + d*x)*(-1 + Log[c/d + x]) + d^2*(b*x*(2*a - b*x) +
2*b^2*x^2*Log[a/b + x] - 2*a^2*Log[a + b*x]) + b^2*(d*x*(-2*c + d*x) - 2*d^2*x^2*Log[c/d + x] + 2*c^2*Log[c +
d*x]) - 4*a^2*d^2*(Log[c/d + x]*Log[(d*(a + b*x))/(-(b*c) + a*d)] + PolyLog[2, (b*(c + d*x))/(b*c - a*d)])) +
6*(2*a*b*c*d + 3*b^2*c*d*x + 3*a*b*d^2*x - b^2*d^2*x^2 - 2*a*b*d^2*x*Log[c/d + x] + b^2*d^2*x^2*Log[c/d + x]
- a^2*d^2*Log[a + b*x] - b^2*c^2*Log[c + d*x] - 2*a*b*c*d*Log[c + d*x] - Log[a/b + x]*(b*d*(2*a*c + b*x*(2*c -
d*x)) - 2*d^2*(a^2 - b^2*x^2)*Log[c/d + x] + (-2*b^2*c^2 + 2*a^2*d^2)*Log[(b*(c + d*x))/(b*c - a*d)]) + 2*(b^
2*c^2 - a^2*d^2)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 4*a*d*(a*d + 2*b*d*x - b*d*x*Log[c/d + x] - b*c*Lo
g[c + d*x] + Log[a/b + x]*(-(d*(a + b*x)) + d*(a + b*x)*Log[c/d + x] + (b*c - a*d)*Log[(b*(c + d*x))/(b*c - a*
d)]) + (b*c - a*d)*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*a^2*d^2*(Log[a/b + x]^2*(Log[c/d + x] - Log[(
b*(c + d*x))/(b*c - a*d)]) - 2*Log[a/b + x]*PolyLog[2, (d*(a + b*x))/(-(b*c) + a*d)] + 2*PolyLog[3, (d*(a + b*
x))/(-(b*c) + a*d)])) + 12*a^2*d^2*(Log[c/d + x]^2*Log[(d*(a + b*x))/(-(b*c) + a*d)] + 2*Log[c/d + x]*PolyLog[
2, (b*(c + d*x))/(b*c - a*d)] - 2*PolyLog[3, (b*(c + d*x))/(b*c - a*d)])) - 12*b^2*B^2*c^2*(Log[(-(b*c) + a*d)
/(d*(a + b*x))]*Log[(e*(a + b*x))/(c + d*x)]^2 - 2*Log[(e*(a + b*x))/(c + d*x)]*PolyLog[2, (b*(c + d*x))/(d*(a
+ b*x))] - 2*PolyLog[3, (b*(c + d*x))/(d*(a + b*x))])))/(12*b^3*g)

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Maple [F]
time = 0.27, size = 0, normalized size = 0.00 \[\int \frac {\left (d i x +c i \right )^{2} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )^{2}}{b g x +a g}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2*A^2*c*d*(x/(b*g) - a*log(b*x + a)/(b^2*g)) - 1/2*A^2*d^2*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2
*g)) - A^2*c^2*log(b*g*x + a*g)/(b*g) - 1/2*(B^2*b^2*d^2*x^2 + 2*(2*b^2*c*d - a*b*d^2)*B^2*x + 2*(b^2*c^2 - 2*
a*b*c*d + a^2*d^2)*B^2*log(b*x + a))*log(d*x + c)^2/(b^3*g) + integrate(-(2*A*B*b^3*c^3 + B^2*b^3*c^3 + (2*A*B
*b^3*d^3 + B^2*b^3*d^3)*x^3 + 3*(2*A*B*b^3*c*d^2 + B^2*b^3*c*d^2)*x^2 + (B^2*b^3*d^3*x^3 + 3*B^2*b^3*c*d^2*x^2
+ 3*B^2*b^3*c^2*d*x + B^2*b^3*c^3)*log(b*x + a)^2 + 3*(2*A*B*b^3*c^2*d + B^2*b^3*c^2*d)*x + 2*(A*B*b^3*c^3 +
B^2*b^3*c^3 + (A*B*b^3*d^3 + B^2*b^3*d^3)*x^3 + 3*(A*B*b^3*c*d^2 + B^2*b^3*c*d^2)*x^2 + 3*(A*B*b^3*c^2*d + B^2
*b^3*c^2*d)*x)*log(b*x + a) - (2*A*B*b^3*c^3 + 2*B^2*b^3*c^3 + (2*A*B*b^3*d^3 + 3*B^2*b^3*d^3)*x^3 + (6*A*B*b^
3*c*d^2 + (10*b^3*c*d^2 - a*b^2*d^3)*B^2)*x^2 + 2*(3*A*B*b^3*c^2*d + (3*b^3*c^2*d + 2*a*b^2*c*d^2 - a^2*b*d^3)
*B^2)*x + 2*(B^2*b^3*d^3*x^3 + 3*B^2*b^3*c*d^2*x^2 + (4*b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*B^2*x + (b^3*c^
3 + a*b^2*c^2*d - 2*a^2*b*c*d^2 + a^3*d^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d*g*x^2 + a*b^3*c*g + (b^4*c*
g + a*b^3*d*g)*x), x)

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Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(-(A^2*d^2*x^2 + 2*A^2*c*d*x + A^2*c^2 + (B^2*d^2*x^2 + 2*B^2*c*d*x + B^2*c^2)*log((b*x + a)*e/(d*x +
c))^2 + 2*(A*B*d^2*x^2 + 2*A*B*c*d*x + A*B*c^2)*log((b*x + a)*e/(d*x + c)))/(b*g*x + a*g), x)

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

[Out]

Timed out

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {{\left (c\,i+d\,i\,x\right )}^2\,{\left (A+B\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )\right )}^2}{a\,g+b\,g\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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