3.2.95 \(\int \frac {(a+b x+c x^2) \log (1-d x) \text {PolyLog}(2,d x)}{x^2} \, dx\) [195]

Optimal. Leaf size=218 \[ 3 c x+\frac {3 c (1-d x) \log (1-d x)}{d}-\frac {c (1-d x) \log ^2(1-d x)}{d}+\frac {a (1-d x) \log ^2(1-d x)}{x}+\left (a-\frac {c}{d^2}\right ) d \log (d x) \log ^2(1-d x)-2 a d \text {PolyLog}(2,d x)-c x \text {PolyLog}(2,d x)+\left (a-\frac {c}{d^2}\right ) d \log (1-d x) \text {PolyLog}(2,d x)-\left (\frac {a}{x}-c x\right ) \log (1-d x) \text {PolyLog}(2,d x)-\frac {1}{2} b \text {PolyLog}(2,d x)^2+2 \left (a-\frac {c}{d^2}\right ) d \log (1-d x) \text {PolyLog}(2,1-d x)-a d \text {PolyLog}(3,d x)-2 \left (a-\frac {c}{d^2}\right ) d \text {PolyLog}(3,1-d x) \]

[Out]

3*c*x+3*c*(-d*x+1)*ln(-d*x+1)/d-c*(-d*x+1)*ln(-d*x+1)^2/d+a*(-d*x+1)*ln(-d*x+1)^2/x+(a-c/d^2)*d*ln(d*x)*ln(-d*
x+1)^2-2*a*d*polylog(2,d*x)-c*x*polylog(2,d*x)+(a-c/d^2)*d*ln(-d*x+1)*polylog(2,d*x)-(a/x-c*x)*ln(-d*x+1)*poly
log(2,d*x)-1/2*b*polylog(2,d*x)^2+2*(a-c/d^2)*d*ln(-d*x+1)*polylog(2,-d*x+1)-a*d*polylog(3,d*x)-2*(a-c/d^2)*d*
polylog(3,-d*x+1)

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Rubi [A]
time = 0.33, antiderivative size = 218, normalized size of antiderivative = 1.00, number of steps used = 19, number of rules used = 21, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.808, Rules used = {6874, 6721, 2436, 2332, 6726, 2442, 36, 29, 31, 6724, 6740, 6736, 14, 6741, 2333, 2444, 2438, 6731, 2443, 2481, 2421} \begin {gather*} -2 d \left (a-\frac {c}{d^2}\right ) \text {Li}_3(1-d x)+d \left (a-\frac {c}{d^2}\right ) \text {Li}_2(d x) \log (1-d x)+2 d \left (a-\frac {c}{d^2}\right ) \text {Li}_2(1-d x) \log (1-d x)+d \left (a-\frac {c}{d^2}\right ) \log (d x) \log ^2(1-d x)-\left (\frac {a}{x}-c x\right ) \text {Li}_2(d x) \log (1-d x)-2 a d \text {Li}_2(d x)-a d \text {Li}_3(d x)+\frac {a (1-d x) \log ^2(1-d x)}{x}-\frac {1}{2} b \text {Li}_2(d x){}^2-c x \text {Li}_2(d x)-\frac {c (1-d x) \log ^2(1-d x)}{d}+\frac {3 c (1-d x) \log (1-d x)}{d}+3 c x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x])/x^2,x]

[Out]

3*c*x + (3*c*(1 - d*x)*Log[1 - d*x])/d - (c*(1 - d*x)*Log[1 - d*x]^2)/d + (a*(1 - d*x)*Log[1 - d*x]^2)/x + (a
- c/d^2)*d*Log[d*x]*Log[1 - d*x]^2 - 2*a*d*PolyLog[2, d*x] - c*x*PolyLog[2, d*x] + (a - c/d^2)*d*Log[1 - d*x]*
PolyLog[2, d*x] - (a/x - c*x)*Log[1 - d*x]*PolyLog[2, d*x] - (b*PolyLog[2, d*x]^2)/2 + 2*(a - c/d^2)*d*Log[1 -
d*x]*PolyLog[2, 1 - d*x] - a*d*PolyLog[3, d*x] - 2*(a - c/d^2)*d*PolyLog[3, 1 - d*x]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rule 31

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

Rule 36

Int[1/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :> Dist[b/(b*c - a*d), Int[1/(a + b*x), x], x] -
Dist[d/(b*c - a*d), Int[1/(c + d*x), x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0]

Rule 2332

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2333

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

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 2436

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

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 2442

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

Rule 2443

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

Rule 2444

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

Rule 2481

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_.) + Log[(h_.)*((i_.) + (j_.)*(x_))^(m_.)]*
(g_.))*((k_.) + (l_.)*(x_))^(r_.), x_Symbol] :> Dist[1/e, Subst[Int[(k*(x/d))^r*(a + b*Log[c*x^n])^p*(f + g*Lo
g[h*((e*i - d*j)/e + j*(x/e))^m]), x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, h, i, j, k, l, n, p, r},
x] && EqQ[e*k - d*l, 0]

Rule 6721

Int[PolyLog[n_, (a_.)*((b_.)*(x_)^(p_.))^(q_.)], x_Symbol] :> Simp[x*PolyLog[n, a*(b*x^p)^q], x] - Dist[p*q, I
nt[PolyLog[n - 1, a*(b*x^p)^q], x], x] /; FreeQ[{a, b, p, q}, x] && GtQ[n, 0]

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]

Rule 6726

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

Rule 6731

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

Rule 6736

Int[(Log[1 + (e_.)*(x_)]*PolyLog[2, (c_.)*(x_)])/(x_), x_Symbol] :> Simp[-PolyLog[2, c*x]^2/2, x] /; FreeQ[{c,
e}, x] && EqQ[c + e, 0]

Rule 6740

Int[((g_.) + Log[1 + (e_.)*(x_)]*(h_.))*(Px_)*(x_)^(m_)*PolyLog[2, (c_.)*(x_)], x_Symbol] :> Dist[Coeff[Px, x,
-m - 1], Int[(g + h*Log[1 + e*x])*(PolyLog[2, c*x]/x), x], x] + Int[x^m*(Px - Coeff[Px, x, -m - 1]*x^(-m - 1)
)*(g + h*Log[1 + e*x])*PolyLog[2, c*x], x] /; FreeQ[{c, e, g, h}, x] && PolyQ[Px, x] && ILtQ[m, 0] && EqQ[c +
e, 0] && NeQ[Coeff[Px, x, -m - 1], 0]

Rule 6741

Int[((g_.) + Log[(f_.)*((d_.) + (e_.)*(x_))^(n_.)]*(h_.))*(Px_)*(x_)^(m_.)*PolyLog[2, (c_.)*((a_.) + (b_.)*(x_
))], x_Symbol] :> With[{u = IntHide[x^m*Px, x]}, Simp[u*(g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)], x]
+ (Dist[b, Int[ExpandIntegrand[(g + h*Log[f*(d + e*x)^n])*Log[1 - a*c - b*c*x], u/(a + b*x), x], x], x] - Dis
t[e*h*n, Int[ExpandIntegrand[PolyLog[2, c*(a + b*x)], u/(d + e*x), x], x], x])] /; FreeQ[{a, b, c, d, e, f, g,
h, n}, x] && PolyQ[Px, x] && IntegerQ[m]

Rule 6874

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {align*} \int \frac {\left (a+b x+c x^2\right ) \log (1-d x) \text {Li}_2(d x)}{x^2} \, dx &=b \int \frac {\log (1-d x) \text {Li}_2(d x)}{x} \, dx+\int \frac {\left (a+c x^2\right ) \log (1-d x) \text {Li}_2(d x)}{x^2} \, dx\\ &=-\left (\frac {a}{x}-c x\right ) \log (1-d x) \text {Li}_2(d x)-\frac {1}{2} b \text {Li}_2(d x){}^2+d \int \left (-\frac {c \text {Li}_2(d x)}{d}-\frac {a \text {Li}_2(d x)}{x}+\frac {\left (-c+a d^2\right ) \text {Li}_2(d x)}{d (-1+d x)}\right ) \, dx+\int \left (c \log ^2(1-d x)-\frac {a \log ^2(1-d x)}{x^2}\right ) \, dx\\ &=-\left (\frac {a}{x}-c x\right ) \log (1-d x) \text {Li}_2(d x)-\frac {1}{2} b \text {Li}_2(d x){}^2-a \int \frac {\log ^2(1-d x)}{x^2} \, dx+c \int \log ^2(1-d x) \, dx-c \int \text {Li}_2(d x) \, dx-(a d) \int \frac {\text {Li}_2(d x)}{x} \, dx+\left (-c+a d^2\right ) \int \frac {\text {Li}_2(d x)}{-1+d x} \, dx\\ &=\frac {a (1-d x) \log ^2(1-d x)}{x}-c x \text {Li}_2(d x)-\frac {\left (c-a d^2\right ) \log (1-d x) \text {Li}_2(d x)}{d}-\left (\frac {a}{x}-c x\right ) \log (1-d x) \text {Li}_2(d x)-\frac {1}{2} b \text {Li}_2(d x){}^2-a d \text {Li}_3(d x)-c \int \log (1-d x) \, dx-\frac {c \text {Subst}\left (\int \log ^2(x) \, dx,x,1-d x\right )}{d}+(2 a d) \int \frac {\log (1-d x)}{x} \, dx+\frac {\left (-c+a d^2\right ) \int \frac {\log ^2(1-d x)}{x} \, dx}{d}\\ &=-\frac {c (1-d x) \log ^2(1-d x)}{d}+\frac {a (1-d x) \log ^2(1-d x)}{x}-\frac {\left (c-a d^2\right ) \log (d x) \log ^2(1-d x)}{d}-2 a d \text {Li}_2(d x)-c x \text {Li}_2(d x)-\frac {\left (c-a d^2\right ) \log (1-d x) \text {Li}_2(d x)}{d}-\left (\frac {a}{x}-c x\right ) \log (1-d x) \text {Li}_2(d x)-\frac {1}{2} b \text {Li}_2(d x){}^2-a d \text {Li}_3(d x)+\frac {c \text {Subst}(\int \log (x) \, dx,x,1-d x)}{d}+\frac {(2 c) \text {Subst}(\int \log (x) \, dx,x,1-d x)}{d}-\left (2 \left (c-a d^2\right )\right ) \int \frac {\log (d x) \log (1-d x)}{1-d x} \, dx\\ &=3 c x+\frac {3 c (1-d x) \log (1-d x)}{d}-\frac {c (1-d x) \log ^2(1-d x)}{d}+\frac {a (1-d x) \log ^2(1-d x)}{x}-\frac {\left (c-a d^2\right ) \log (d x) \log ^2(1-d x)}{d}-2 a d \text {Li}_2(d x)-c x \text {Li}_2(d x)-\frac {\left (c-a d^2\right ) \log (1-d x) \text {Li}_2(d x)}{d}-\left (\frac {a}{x}-c x\right ) \log (1-d x) \text {Li}_2(d x)-\frac {1}{2} b \text {Li}_2(d x){}^2-a d \text {Li}_3(d x)+\frac {\left (2 \left (c-a d^2\right )\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (d \left (\frac {1}{d}-\frac {x}{d}\right )\right )}{x} \, dx,x,1-d x\right )}{d}\\ &=3 c x+\frac {3 c (1-d x) \log (1-d x)}{d}-\frac {c (1-d x) \log ^2(1-d x)}{d}+\frac {a (1-d x) \log ^2(1-d x)}{x}-\frac {\left (c-a d^2\right ) \log (d x) \log ^2(1-d x)}{d}-2 a d \text {Li}_2(d x)-c x \text {Li}_2(d x)-\frac {\left (c-a d^2\right ) \log (1-d x) \text {Li}_2(d x)}{d}-\left (\frac {a}{x}-c x\right ) \log (1-d x) \text {Li}_2(d x)-\frac {1}{2} b \text {Li}_2(d x){}^2-\frac {2 \left (c-a d^2\right ) \log (1-d x) \text {Li}_2(1-d x)}{d}-a d \text {Li}_3(d x)+\frac {\left (2 \left (c-a d^2\right )\right ) \text {Subst}\left (\int \frac {\text {Li}_2(x)}{x} \, dx,x,1-d x\right )}{d}\\ &=3 c x+\frac {3 c (1-d x) \log (1-d x)}{d}-\frac {c (1-d x) \log ^2(1-d x)}{d}+\frac {a (1-d x) \log ^2(1-d x)}{x}-\frac {\left (c-a d^2\right ) \log (d x) \log ^2(1-d x)}{d}-2 a d \text {Li}_2(d x)-c x \text {Li}_2(d x)-\frac {\left (c-a d^2\right ) \log (1-d x) \text {Li}_2(d x)}{d}-\left (\frac {a}{x}-c x\right ) \log (1-d x) \text {Li}_2(d x)-\frac {1}{2} b \text {Li}_2(d x){}^2-\frac {2 \left (c-a d^2\right ) \log (1-d x) \text {Li}_2(1-d x)}{d}-a d \text {Li}_3(d x)+\frac {2 \left (c-a d^2\right ) \text {Li}_3(1-d x)}{d}\\ \end {align*}

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Mathematica [A]
time = 0.56, size = 280, normalized size = 1.28 \begin {gather*} \frac {2 \left (-c d x^2+(a d+c x) (-1+d x) \log (1-d x)\right ) \text {PolyLog}(2,d x)-b d x \text {PolyLog}(2,d x)^2+2 \left (-2 c x+3 c d x^2+3 c x \log (1-d x)-3 c d x^2 \log (1-d x)+2 a d^2 x \log (d x) \log (1-d x)+a d \log ^2(1-d x)-c x \log ^2(1-d x)-a d^2 x \log ^2(1-d x)+c d x^2 \log ^2(1-d x)-c x \log (d x) \log ^2(1-d x)+a d^2 x \log (d x) \log ^2(1-d x)+2 x \left (a d^2+\left (-c+a d^2\right ) \log (1-d x)\right ) \text {PolyLog}(2,1-d x)-a d^2 x \text {PolyLog}(3,d x)+2 c x \text {PolyLog}(3,1-d x)-2 a d^2 x \text {PolyLog}(3,1-d x)\right )}{2 d x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x])/x^2,x]

[Out]

(2*(-(c*d*x^2) + (a*d + c*x)*(-1 + d*x)*Log[1 - d*x])*PolyLog[2, d*x] - b*d*x*PolyLog[2, d*x]^2 + 2*(-2*c*x +
3*c*d*x^2 + 3*c*x*Log[1 - d*x] - 3*c*d*x^2*Log[1 - d*x] + 2*a*d^2*x*Log[d*x]*Log[1 - d*x] + a*d*Log[1 - d*x]^2
- c*x*Log[1 - d*x]^2 - a*d^2*x*Log[1 - d*x]^2 + c*d*x^2*Log[1 - d*x]^2 - c*x*Log[d*x]*Log[1 - d*x]^2 + a*d^2*
x*Log[d*x]*Log[1 - d*x]^2 + 2*x*(a*d^2 + (-c + a*d^2)*Log[1 - d*x])*PolyLog[2, 1 - d*x] - a*d^2*x*PolyLog[3, d
*x] + 2*c*x*PolyLog[3, 1 - d*x] - 2*a*d^2*x*PolyLog[3, 1 - d*x]))/(2*d*x)

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Maple [F]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\left (c \,x^{2}+b x +a \right ) \ln \left (-d x +1\right ) \polylog \left (2, d x \right )}{x^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c*x^2+b*x+a)*ln(-d*x+1)*polylog(2,d*x)/x^2,x)

[Out]

int((c*x^2+b*x+a)*ln(-d*x+1)*polylog(2,d*x)/x^2,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((c*x^2+b*x+a)*log(-d*x+1)*polylog(2,d*x)/x^2,x, algorithm="maxima")

[Out]

integrate((c*x^2 + b*x + a)*dilog(d*x)*log(-d*x + 1)/x^2, 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((c*x^2+b*x+a)*log(-d*x+1)*polylog(2,d*x)/x^2,x, algorithm="fricas")

[Out]

integral((c*x^2 + b*x + a)*dilog(d*x)*log(-d*x + 1)/x^2, x)

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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a + b x + c x^{2}\right ) \log {\left (- d x + 1 \right )} \operatorname {Li}_{2}\left (d x\right )}{x^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((c*x**2+b*x+a)*ln(-d*x+1)*polylog(2,d*x)/x**2,x)

[Out]

Integral((a + b*x + c*x**2)*log(-d*x + 1)*polylog(2, d*x)/x**2, x)

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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((c*x^2+b*x+a)*log(-d*x+1)*polylog(2,d*x)/x^2,x, algorithm="giac")

[Out]

integrate((c*x^2 + b*x + a)*dilog(d*x)*log(-d*x + 1)/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(1 - d*x)*polylog(2, d*x)*(a + b*x + c*x^2))/x^2,x)

[Out]

int((log(1 - d*x)*polylog(2, d*x)*(a + b*x + c*x^2))/x^2, x)

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