3.24.65 \(\int \frac {(-4+26 x-30 x^2) \log (2 x^2-2 x^3)+(-1+11 x-10 x^2) \log ^2(2 x^2-2 x^3)}{-1+x} \, dx\)

Optimal. Leaf size=24 \[ \left (x-5 x^2\right ) \log ^2\left (\log \left (e^{2 (1-x) x^2}\right )\right ) \]

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Rubi [B]  time = 0.66, antiderivative size = 224, normalized size of antiderivative = 9.33, number of steps used = 47, number of rules used = 18, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.327, Rules used = {6742, 2513, 2418, 2389, 2295, 2390, 2301, 2395, 43, 2357, 2315, 2304, 77, 2498, 2411, 2334, 2416, 2394} \begin {gather*} \frac {5 x^2}{2}-\frac {1}{20} (1-10 x)^2 \log ^2\left (2 (1-x) x^2\right )-5 x^2 \log (x-1)-20 x^2 \log (x)-\frac {2}{5} \left (-50 x^2+20 x-\log (x)\right ) \log (x)-\frac {1}{10} \log (1-x) \left (-\log \left (2 (1-x) x^2\right )+\log (x-1)+2 \log (x)\right )-\frac {1}{5} \log (x) \left (-\log \left (2 (1-x) x^2\right )+\log (x-1)+2 \log (x)\right )-\frac {5}{2} (1-x)^2-5 x-\frac {161}{20} \log ^2(x-1)-\frac {\log ^2(x)}{5}+8 (1-x) \log (x-1)+5 \log (1-x)-\frac {1}{10} \left (-50 (1-x)^2+180 (1-x)-81 \log (x-1)\right ) \log (x-1)+8 x \log (x)+\frac {1}{5} \log (x-1) \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((-4 + 26*x - 30*x^2)*Log[2*x^2 - 2*x^3] + (-1 + 11*x - 10*x^2)*Log[2*x^2 - 2*x^3]^2)/(-1 + x),x]

[Out]

(-5*(1 - x)^2)/2 - 5*x + (5*x^2)/2 + 5*Log[1 - x] + 8*(1 - x)*Log[-1 + x] - 5*x^2*Log[-1 + x] - ((180*(1 - x)
- 50*(1 - x)^2 - 81*Log[-1 + x])*Log[-1 + x])/10 - (161*Log[-1 + x]^2)/20 + 8*x*Log[x] - 20*x^2*Log[x] + (Log[
-1 + x]*Log[x])/5 - (2*(20*x - 50*x^2 - Log[x])*Log[x])/5 - Log[x]^2/5 - (Log[1 - x]*(Log[-1 + x] + 2*Log[x] -
Log[2*(1 - x)*x^2]))/10 - (Log[x]*(Log[-1 + x] + 2*Log[x] - Log[2*(1 - x)*x^2]))/5 - ((1 - 10*x)^2*Log[2*(1 -
x)*x^2]^2)/20

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rule 2295

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

Rule 2301

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

Rule 2304

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 2315

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

Rule 2334

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

Rule 2357

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

Rule 2389

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 2390

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

Rule 2394

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

Rule 2395

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 2411

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_.) + (g_.)*(x_))^(q_.)*((h_.) + (i_.)*(x_))
^(r_.), x_Symbol] :> Dist[1/e, Subst[Int[((g*x)/e)^q*((e*h - d*i)/e + (i*x)/e)^r*(a + b*Log[c*x^n])^p, x], x,
d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, h, i, n, p, q, r}, x] && EqQ[e*f - d*g, 0] && (IGtQ[p, 0] || IGtQ[
r, 0]) && IntegerQ[2*r]

Rule 2416

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((h_.)*(x_))^(m_.)*((f_) + (g_.)*(x_)^(r_.))^(q
_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*Log[c*(d + e*x)^n])^p, (h*x)^m*(f + g*x^r)^q, x], x] /; FreeQ[{a,
b, c, d, e, f, g, h, m, n, p, q, r}, x] && IntegerQ[m] && IntegerQ[q]

Rule 2418

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

Rule 2498

Int[Log[(e_.)*((f_.)*((a_.) + (b_.)*(x_))^(p_.)*((c_.) + (d_.)*(x_))^(q_.))^(r_.)]^(s_)*((g_.) + (h_.)*(x_))^(
m_.), x_Symbol] :> Simp[((g + h*x)^(m + 1)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^s)/(h*(m + 1)), x] + (-Dist[(b
*p*r*s)/(h*(m + 1)), Int[((g + h*x)^(m + 1)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^(s - 1))/(a + b*x), x], x] -
Dist[(d*q*r*s)/(h*(m + 1)), Int[((g + h*x)^(m + 1)*Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r]^(s - 1))/(c + d*x), x]
, x]) /; FreeQ[{a, b, c, d, e, f, g, h, m, p, q, r, s}, x] && NeQ[b*c - a*d, 0] && IGtQ[s, 0] && NeQ[m, -1]

Rule 2513

Int[Log[(e_.)*((f_.)*((a_.) + (b_.)*(x_))^(p_.)*((c_.) + (d_.)*(x_))^(q_.))^(r_.)]*(RFx_.), x_Symbol] :> Dist[
p*r, Int[RFx*Log[a + b*x], x], x] + (Dist[q*r, Int[RFx*Log[c + d*x], x], x] - Dist[p*r*Log[a + b*x] + q*r*Log[
c + d*x] - Log[e*(f*(a + b*x)^p*(c + d*x)^q)^r], Int[RFx, x], x]) /; FreeQ[{a, b, c, d, e, f, p, q, r}, x] &&
RationalFunctionQ[RFx, x] && NeQ[b*c - a*d, 0] &&  !MatchQ[RFx, (u_.)*(a + b*x)^(m_.)*(c + d*x)^(n_.) /; Integ
ersQ[m, n]]

Rule 6742

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 (-2+3 x) (-1+5 x) \log \left (-2 (-1+x) x^2\right )}{-1+x}-(-1+10 x) \log ^2\left (-2 (-1+x) x^2\right )\right ) \, dx\\ &=-\left (2 \int \frac {(-2+3 x) (-1+5 x) \log \left (-2 (-1+x) x^2\right )}{-1+x} \, dx\right )-\int (-1+10 x) \log ^2\left (-2 (-1+x) x^2\right ) \, dx\\ &=-\frac {1}{20} (1-10 x)^2 \log ^2\left (2 (1-x) x^2\right )+\frac {1}{10} \int \frac {(-1+10 x)^2 \log \left (-2 (-1+x) x^2\right )}{-1+x} \, dx+\frac {1}{5} \int \frac {(-1+10 x)^2 \log \left (-2 (-1+x) x^2\right )}{x} \, dx-2 \int \frac {(-2+3 x) (-1+5 x) \log (-1+x)}{-1+x} \, dx-4 \int \frac {(-2+3 x) (-1+5 x) \log (x)}{-1+x} \, dx+\left (2 \left (\log (-1+x)+2 \log (x)-\log \left (-2 (-1+x) x^2\right )\right )\right ) \int \frac {(-2+3 x) (-1+5 x)}{-1+x} \, dx\\ &=-\frac {1}{20} (1-10 x)^2 \log ^2\left (2 (1-x) x^2\right )+\frac {1}{10} \int \frac {(-1+10 x)^2 \log (-1+x)}{-1+x} \, dx+\frac {1}{5} \int \frac {(-1+10 x)^2 \log (-1+x)}{x} \, dx+\frac {1}{5} \int \frac {(-1+10 x)^2 \log (x)}{-1+x} \, dx+\frac {2}{5} \int \frac {(-1+10 x)^2 \log (x)}{x} \, dx-2 \int \left (2 \log (-1+x)+\frac {4 \log (-1+x)}{-1+x}+15 x \log (-1+x)\right ) \, dx-4 \int \left (2 \log (x)+\frac {4 \log (x)}{-1+x}+15 x \log (x)\right ) \, dx+\left (2 \left (\log (-1+x)+2 \log (x)-\log \left (-2 (-1+x) x^2\right )\right )\right ) \int \left (2+\frac {4}{-1+x}+15 x\right ) \, dx+\frac {1}{10} \left (-\log (-1+x)-2 \log (x)+\log \left (-2 (-1+x) x^2\right )\right ) \int \frac {(-1+10 x)^2}{-1+x} \, dx+\frac {1}{5} \left (-\log (-1+x)-2 \log (x)+\log \left (-2 (-1+x) x^2\right )\right ) \int \frac {(-1+10 x)^2}{x} \, dx\\ &=-\frac {2}{5} \left (20 x-50 x^2-\log (x)\right ) \log (x)+4 x \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )+15 x^2 \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )+8 \log (1-x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{20} (1-10 x)^2 \log ^2\left (2 (1-x) x^2\right )+\frac {1}{10} \operatorname {Subst}\left (\int \frac {(9+10 x)^2 \log (x)}{x} \, dx,x,-1+x\right )+\frac {1}{5} \int \left (-20 \log (-1+x)+\frac {\log (-1+x)}{x}+100 x \log (-1+x)\right ) \, dx+\frac {1}{5} \int \left (80 \log (x)+\frac {81 \log (x)}{-1+x}+100 x \log (x)\right ) \, dx-\frac {2}{5} \int \left (-20+50 x+\frac {\log (x)}{x}\right ) \, dx-4 \int \log (-1+x) \, dx-8 \int \frac {\log (-1+x)}{-1+x} \, dx-8 \int \log (x) \, dx-16 \int \frac {\log (x)}{-1+x} \, dx-30 \int x \log (-1+x) \, dx-60 \int x \log (x) \, dx+\frac {1}{10} \left (-\log (-1+x)-2 \log (x)+\log \left (-2 (-1+x) x^2\right )\right ) \int \left (80+\frac {81}{-1+x}+100 x\right ) \, dx+\frac {1}{5} \left (-\log (-1+x)-2 \log (x)+\log \left (-2 (-1+x) x^2\right )\right ) \int \left (-20+\frac {1}{x}+100 x\right ) \, dx\\ &=16 x+5 x^2-15 x^2 \log (-1+x)-\frac {1}{10} \left (180 (1-x)-50 (1-x)^2-81 \log (-1+x)\right ) \log (-1+x)-8 x \log (x)-30 x^2 \log (x)-\frac {2}{5} \left (20 x-50 x^2-\log (x)\right ) \log (x)-\frac {1}{10} \log (1-x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{5} \log (x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{20} (1-10 x)^2 \log ^2\left (2 (1-x) x^2\right )+16 \text {Li}_2(1-x)-\frac {1}{10} \operatorname {Subst}\left (\int \left (180+50 x+\frac {81 \log (x)}{x}\right ) \, dx,x,-1+x\right )+\frac {1}{5} \int \frac {\log (-1+x)}{x} \, dx-\frac {2}{5} \int \frac {\log (x)}{x} \, dx-4 \int \log (-1+x) \, dx-4 \operatorname {Subst}(\int \log (x) \, dx,x,-1+x)-8 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-1+x\right )+15 \int \frac {x^2}{-1+x} \, dx+16 \int \log (x) \, dx+\frac {81}{5} \int \frac {\log (x)}{-1+x} \, dx+20 \int x \log (-1+x) \, dx+20 \int x \log (x) \, dx\\ &=-\frac {5}{2} (1-x)^2-14 x+4 (1-x) \log (-1+x)-5 x^2 \log (-1+x)-\frac {1}{10} \left (180 (1-x)-50 (1-x)^2-81 \log (-1+x)\right ) \log (-1+x)-4 \log ^2(-1+x)+8 x \log (x)-20 x^2 \log (x)+\frac {1}{5} \log (-1+x) \log (x)-\frac {2}{5} \left (20 x-50 x^2-\log (x)\right ) \log (x)-\frac {\log ^2(x)}{5}-\frac {1}{10} \log (1-x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{5} \log (x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{20} (1-10 x)^2 \log ^2\left (2 (1-x) x^2\right )-\frac {\text {Li}_2(1-x)}{5}-\frac {1}{5} \int \frac {\log (x)}{-1+x} \, dx-4 \operatorname {Subst}(\int \log (x) \, dx,x,-1+x)-\frac {81}{10} \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-1+x\right )-10 \int \frac {x^2}{-1+x} \, dx+15 \int \left (1+\frac {1}{-1+x}+x\right ) \, dx\\ &=-\frac {5}{2} (1-x)^2+5 x+\frac {15 x^2}{2}+15 \log (1-x)+8 (1-x) \log (-1+x)-5 x^2 \log (-1+x)-\frac {1}{10} \left (180 (1-x)-50 (1-x)^2-81 \log (-1+x)\right ) \log (-1+x)-\frac {161}{20} \log ^2(-1+x)+8 x \log (x)-20 x^2 \log (x)+\frac {1}{5} \log (-1+x) \log (x)-\frac {2}{5} \left (20 x-50 x^2-\log (x)\right ) \log (x)-\frac {\log ^2(x)}{5}-\frac {1}{10} \log (1-x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{5} \log (x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{20} (1-10 x)^2 \log ^2\left (2 (1-x) x^2\right )-10 \int \left (1+\frac {1}{-1+x}+x\right ) \, dx\\ &=-\frac {5}{2} (1-x)^2-5 x+\frac {5 x^2}{2}+5 \log (1-x)+8 (1-x) \log (-1+x)-5 x^2 \log (-1+x)-\frac {1}{10} \left (180 (1-x)-50 (1-x)^2-81 \log (-1+x)\right ) \log (-1+x)-\frac {161}{20} \log ^2(-1+x)+8 x \log (x)-20 x^2 \log (x)+\frac {1}{5} \log (-1+x) \log (x)-\frac {2}{5} \left (20 x-50 x^2-\log (x)\right ) \log (x)-\frac {\log ^2(x)}{5}-\frac {1}{10} \log (1-x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{5} \log (x) \left (\log (-1+x)+2 \log (x)-\log \left (2 (1-x) x^2\right )\right )-\frac {1}{20} (1-10 x)^2 \log ^2\left (2 (1-x) x^2\right )\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.12, size = 64, normalized size = 2.67 \begin {gather*} 2 \log (-1+x) \log \left (2 (1-x) x^2\right )-5 x^2 \log ^2\left (2 (1-x) x^2\right )-2 \log (-1+x) \log \left (-2 (-1+x) x^2\right )+x \log ^2\left (-2 (-1+x) x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-4 + 26*x - 30*x^2)*Log[2*x^2 - 2*x^3] + (-1 + 11*x - 10*x^2)*Log[2*x^2 - 2*x^3]^2)/(-1 + x),x]

[Out]

2*Log[-1 + x]*Log[2*(1 - x)*x^2] - 5*x^2*Log[2*(1 - x)*x^2]^2 - 2*Log[-1 + x]*Log[-2*(-1 + x)*x^2] + x*Log[-2*
(-1 + x)*x^2]^2

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fricas [A]  time = 0.47, size = 25, normalized size = 1.04 \begin {gather*} -{\left (5 \, x^{2} - x\right )} \log \left (-2 \, x^{3} + 2 \, x^{2}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x^2+11*x-1)*log(-2*x^3+2*x^2)^2+(-30*x^2+26*x-4)*log(-2*x^3+2*x^2))/(x-1),x, algorithm="fricas
")

[Out]

-(5*x^2 - x)*log(-2*x^3 + 2*x^2)^2

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giac [A]  time = 0.33, size = 25, normalized size = 1.04 \begin {gather*} -{\left (5 \, x^{2} - x\right )} \log \left (-2 \, x^{3} + 2 \, x^{2}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x^2+11*x-1)*log(-2*x^3+2*x^2)^2+(-30*x^2+26*x-4)*log(-2*x^3+2*x^2))/(x-1),x, algorithm="giac")

[Out]

-(5*x^2 - x)*log(-2*x^3 + 2*x^2)^2

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maple [A]  time = 0.46, size = 23, normalized size = 0.96

method	result	size
risch	\(\left (-5 x^{2}+x \right ) \ln \left (-2 x^{3}+2 x^{2}\right )^{2}\)	\(23\)
norman	\(\ln \left (-2 x^{3}+2 x^{2}\right )^{2} x -5 \ln \left (-2 x^{3}+2 x^{2}\right )^{2} x^{2}\)	\(37\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-10*x^2+11*x-1)*ln(-2*x^3+2*x^2)^2+(-30*x^2+26*x-4)*ln(-2*x^3+2*x^2))/(x-1),x,method=_RETURNVERBOSE)

[Out]

(-5*x^2+x)*ln(-2*x^3+2*x^2)^2

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maxima [C]  time = 0.65, size = 138, normalized size = 5.75 \begin {gather*} 5 \, {\left (\pi ^{2} - 2 i \, \pi \log \relax (2) - \log \relax (2)^{2}\right )} x^{2} - {\left (5 \, x^{2} - x\right )} \log \left (x - 1\right )^{2} - 4 \, {\left (5 \, x^{2} - x\right )} \log \relax (x)^{2} - {\left (\pi ^{2} - 2 i \, \pi \log \relax (2) - \log \relax (2)^{2}\right )} x + 2 \, {\left (5 \, {\left (-i \, \pi - \log \relax (2)\right )} x^{2} + {\left (i \, \pi + \log \relax (2)\right )} x - 2 \, {\left (5 \, x^{2} - x\right )} \log \relax (x)\right )} \log \left (x - 1\right ) + 4 \, {\left (5 \, {\left (-i \, \pi - \log \relax (2)\right )} x^{2} + {\left (i \, \pi + \log \relax (2)\right )} x\right )} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x^2+11*x-1)*log(-2*x^3+2*x^2)^2+(-30*x^2+26*x-4)*log(-2*x^3+2*x^2))/(x-1),x, algorithm="maxima
")

[Out]

5*(pi^2 - 2*I*pi*log(2) - log(2)^2)*x^2 - (5*x^2 - x)*log(x - 1)^2 - 4*(5*x^2 - x)*log(x)^2 - (pi^2 - 2*I*pi*l
og(2) - log(2)^2)*x + 2*(5*(-I*pi - log(2))*x^2 + (I*pi + log(2))*x - 2*(5*x^2 - x)*log(x))*log(x - 1) + 4*(5*
(-I*pi - log(2))*x^2 + (I*pi + log(2))*x)*log(x)

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mupad [B]  time = 1.46, size = 22, normalized size = 0.92 \begin {gather*} -x\,{\ln \left (2\,x^2-2\,x^3\right )}^2\,\left (5\,x-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(2*x^2 - 2*x^3)*(30*x^2 - 26*x + 4) + log(2*x^2 - 2*x^3)^2*(10*x^2 - 11*x + 1))/(x - 1),x)

[Out]

-x*log(2*x^2 - 2*x^3)^2*(5*x - 1)

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sympy [A]  time = 0.17, size = 19, normalized size = 0.79 \begin {gather*} \left (- 5 x^{2} + x\right ) \log {\left (- 2 x^{3} + 2 x^{2} \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x**2+11*x-1)*ln(-2*x**3+2*x**2)**2+(-30*x**2+26*x-4)*ln(-2*x**3+2*x**2))/(x-1),x)

[Out]

(-5*x**2 + x)*log(-2*x**3 + 2*x**2)**2

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