3.26.89 \(\int \frac {-675 x^2+990 x^3-450 x^4+828 x^5-63 x^6+126 x^7+(270 x^2-468 x^3+90 x^4-180 x^5) \log (1-4 x+4 x^2)+(-27 x^2+54 x^3) \log ^2(1-4 x+4 x^2)}{-1+2 x} \, dx\)

Optimal. Leaf size=22 \[ 9 x^3 \left (5+x^2-\log \left ((1-2 x)^2\right )\right )^2 \]

________________________________________________________________________________________

Rubi [B]  time = 0.60, antiderivative size = 197, normalized size of antiderivative = 8.95, number of steps used = 26, number of rules used = 14, integrand size = 97, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.144, Rules used = {6742, 1620, 2418, 2389, 2295, 2395, 43, 2390, 2301, 2398, 2411, 2334, 12, 14} \begin {gather*} 9 x^7+90 x^5-18 x^5 \log \left ((1-2 x)^2\right )+217 x^3+9 x^3 \log ^2\left ((1-2 x)^2\right )-78 x^3 \log \left ((1-2 x)^2\right )-15 x^2+9 x^2 \log \left ((1-2 x)^2\right )+21 x-(1-2 x)^3+\frac {27}{4} (1-2 x)^2+\frac {9}{2} \log ^2(1-2 x)+\frac {9}{8} \log ^2\left ((1-2 x)^2\right )-\frac {15}{2} \log (1-2 x)-\frac {9}{2} (1-2 x) \log \left ((1-2 x)^2\right )+\frac {3}{4} \left (2 (1-2 x)^3-9 (1-2 x)^2+18 (1-2 x)-6 \log (1-2 x)\right ) \log \left ((1-2 x)^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-675*x^2 + 990*x^3 - 450*x^4 + 828*x^5 - 63*x^6 + 126*x^7 + (270*x^2 - 468*x^3 + 90*x^4 - 180*x^5)*Log[1
- 4*x + 4*x^2] + (-27*x^2 + 54*x^3)*Log[1 - 4*x + 4*x^2]^2)/(-1 + 2*x),x]

[Out]

(27*(1 - 2*x)^2)/4 - (1 - 2*x)^3 + 21*x - 15*x^2 + 217*x^3 + 90*x^5 + 9*x^7 - (15*Log[1 - 2*x])/2 + (9*Log[1 -
2*x]^2)/2 - (9*(1 - 2*x)*Log[(1 - 2*x)^2])/2 + 9*x^2*Log[(1 - 2*x)^2] - 78*x^3*Log[(1 - 2*x)^2] - 18*x^5*Log[
(1 - 2*x)^2] + (3*(18*(1 - 2*x) - 9*(1 - 2*x)^2 + 2*(1 - 2*x)^3 - 6*Log[1 - 2*x])*Log[(1 - 2*x)^2])/4 + (9*Log
[(1 - 2*x)^2]^2)/8 + 9*x^3*Log[(1 - 2*x)^2]^2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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 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 1620

Int[(Px_)*((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[Px*(a + b*x)
^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && PolyQ[Px, x] && (IntegersQ[m, n] || IGtQ[m, -2]) &&
GtQ[Expon[Px, x], 2]

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 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 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 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 2398

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_)*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Simp[((
f + g*x)^(q + 1)*(a + b*Log[c*(d + e*x)^n])^p)/(g*(q + 1)), x] - Dist[(b*e*n*p)/(g*(q + 1)), Int[((f + g*x)^(q
+ 1)*(a + b*Log[c*(d + e*x)^n])^(p - 1))/(d + e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n, q}, x] && NeQ[e*
f - d*g, 0] && GtQ[p, 0] && NeQ[q, -1] && IntegersQ[2*p, 2*q] && ( !IGtQ[q, 0] || (EqQ[p, 2] && 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 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 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 {9 x^2 \left (-75+110 x-50 x^2+92 x^3-7 x^4+14 x^5\right )}{-1+2 x}-\frac {18 x^2 \left (-15+26 x-5 x^2+10 x^3\right ) \log \left ((1-2 x)^2\right )}{-1+2 x}+27 x^2 \log ^2\left ((1-2 x)^2\right )\right ) \, dx\\ &=9 \int \frac {x^2 \left (-75+110 x-50 x^2+92 x^3-7 x^4+14 x^5\right )}{-1+2 x} \, dx-18 \int \frac {x^2 \left (-15+26 x-5 x^2+10 x^3\right ) \log \left ((1-2 x)^2\right )}{-1+2 x} \, dx+27 \int x^2 \log ^2\left ((1-2 x)^2\right ) \, dx\\ &=9 x^3 \log ^2\left ((1-2 x)^2\right )+9 \int \left (-\frac {21}{4}-\frac {21 x}{2}+54 x^2-2 x^3+46 x^4+7 x^6-\frac {21}{4 (-1+2 x)}\right ) \, dx-18 \int \left (-\frac {1}{2} \log \left ((1-2 x)^2\right )-x \log \left ((1-2 x)^2\right )+13 x^2 \log \left ((1-2 x)^2\right )+5 x^4 \log \left ((1-2 x)^2\right )-\frac {\log \left ((1-2 x)^2\right )}{2 (-1+2 x)}\right ) \, dx+72 \int \frac {x^3 \log \left ((1-2 x)^2\right )}{1-2 x} \, dx\\ &=-\frac {189 x}{4}-\frac {189 x^2}{4}+162 x^3-\frac {9 x^4}{2}+\frac {414 x^5}{5}+9 x^7-\frac {189}{8} \log (1-2 x)+9 x^3 \log ^2\left ((1-2 x)^2\right )+9 \int \log \left ((1-2 x)^2\right ) \, dx+9 \int \frac {\log \left ((1-2 x)^2\right )}{-1+2 x} \, dx+18 \int x \log \left ((1-2 x)^2\right ) \, dx-36 \operatorname {Subst}\left (\int \frac {\left (\frac {1}{2}-\frac {x}{2}\right )^3 \log \left (x^2\right )}{x} \, dx,x,1-2 x\right )-90 \int x^4 \log \left ((1-2 x)^2\right ) \, dx-234 \int x^2 \log \left ((1-2 x)^2\right ) \, dx\\ &=-\frac {189 x}{4}-\frac {189 x^2}{4}+162 x^3-\frac {9 x^4}{2}+\frac {414 x^5}{5}+9 x^7-\frac {189}{8} \log (1-2 x)+9 x^2 \log \left ((1-2 x)^2\right )-78 x^3 \log \left ((1-2 x)^2\right )-18 x^5 \log \left ((1-2 x)^2\right )+\frac {3}{4} \left (18 (1-2 x)-9 (1-2 x)^2+2 (1-2 x)^3-6 \log (1-2 x)\right ) \log \left ((1-2 x)^2\right )+9 x^3 \log ^2\left ((1-2 x)^2\right )-\frac {9}{2} \operatorname {Subst}\left (\int \log \left (x^2\right ) \, dx,x,1-2 x\right )+\frac {9}{2} \operatorname {Subst}\left (\int \frac {\log \left (x^2\right )}{x} \, dx,x,1-2 x\right )+36 \int \frac {x^2}{1-2 x} \, dx-72 \int \frac {x^5}{1-2 x} \, dx+72 \operatorname {Subst}\left (\int \frac {x \left (-18+9 x-2 x^2\right )+6 \log (x)}{48 x} \, dx,x,1-2 x\right )-312 \int \frac {x^3}{1-2 x} \, dx\\ &=-\frac {261 x}{4}-\frac {189 x^2}{4}+162 x^3-\frac {9 x^4}{2}+\frac {414 x^5}{5}+9 x^7-\frac {189}{8} \log (1-2 x)-\frac {9}{2} (1-2 x) \log \left ((1-2 x)^2\right )+9 x^2 \log \left ((1-2 x)^2\right )-78 x^3 \log \left ((1-2 x)^2\right )-18 x^5 \log \left ((1-2 x)^2\right )+\frac {3}{4} \left (18 (1-2 x)-9 (1-2 x)^2+2 (1-2 x)^3-6 \log (1-2 x)\right ) \log \left ((1-2 x)^2\right )+\frac {9}{8} \log ^2\left ((1-2 x)^2\right )+9 x^3 \log ^2\left ((1-2 x)^2\right )+\frac {3}{2} \operatorname {Subst}\left (\int \frac {x \left (-18+9 x-2 x^2\right )+6 \log (x)}{x} \, dx,x,1-2 x\right )+36 \int \left (-\frac {1}{4}-\frac {x}{2}-\frac {1}{4 (-1+2 x)}\right ) \, dx-72 \int \left (-\frac {1}{32}-\frac {x}{16}-\frac {x^2}{8}-\frac {x^3}{4}-\frac {x^4}{2}-\frac {1}{32 (-1+2 x)}\right ) \, dx-312 \int \left (-\frac {1}{8}-\frac {x}{4}-\frac {x^2}{2}-\frac {1}{8 (-1+2 x)}\right ) \, dx\\ &=-33 x-15 x^2+217 x^3+90 x^5+9 x^7-\frac {15}{2} \log (1-2 x)-\frac {9}{2} (1-2 x) \log \left ((1-2 x)^2\right )+9 x^2 \log \left ((1-2 x)^2\right )-78 x^3 \log \left ((1-2 x)^2\right )-18 x^5 \log \left ((1-2 x)^2\right )+\frac {3}{4} \left (18 (1-2 x)-9 (1-2 x)^2+2 (1-2 x)^3-6 \log (1-2 x)\right ) \log \left ((1-2 x)^2\right )+\frac {9}{8} \log ^2\left ((1-2 x)^2\right )+9 x^3 \log ^2\left ((1-2 x)^2\right )+\frac {3}{2} \operatorname {Subst}\left (\int \left (-18+9 x-2 x^2+\frac {6 \log (x)}{x}\right ) \, dx,x,1-2 x\right )\\ &=\frac {27}{4} (1-2 x)^2-(1-2 x)^3+21 x-15 x^2+217 x^3+90 x^5+9 x^7-\frac {15}{2} \log (1-2 x)-\frac {9}{2} (1-2 x) \log \left ((1-2 x)^2\right )+9 x^2 \log \left ((1-2 x)^2\right )-78 x^3 \log \left ((1-2 x)^2\right )-18 x^5 \log \left ((1-2 x)^2\right )+\frac {3}{4} \left (18 (1-2 x)-9 (1-2 x)^2+2 (1-2 x)^3-6 \log (1-2 x)\right ) \log \left ((1-2 x)^2\right )+\frac {9}{8} \log ^2\left ((1-2 x)^2\right )+9 x^3 \log ^2\left ((1-2 x)^2\right )+9 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,1-2 x\right )\\ &=\frac {27}{4} (1-2 x)^2-(1-2 x)^3+21 x-15 x^2+217 x^3+90 x^5+9 x^7-\frac {15}{2} \log (1-2 x)+\frac {9}{2} \log ^2(1-2 x)-\frac {9}{2} (1-2 x) \log \left ((1-2 x)^2\right )+9 x^2 \log \left ((1-2 x)^2\right )-78 x^3 \log \left ((1-2 x)^2\right )-18 x^5 \log \left ((1-2 x)^2\right )+\frac {3}{4} \left (18 (1-2 x)-9 (1-2 x)^2+2 (1-2 x)^3-6 \log (1-2 x)\right ) \log \left ((1-2 x)^2\right )+\frac {9}{8} \log ^2\left ((1-2 x)^2\right )+9 x^3 \log ^2\left ((1-2 x)^2\right )\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.18, size = 78, normalized size = 3.55 \begin {gather*} 9 \left (25 x^3+10 x^5+x^7+\frac {43}{24} \log (1-2 x)-\frac {43}{48} \log \left ((1-2 x)^2\right )-10 x^3 \log \left ((1-2 x)^2\right )-2 x^5 \log \left ((1-2 x)^2\right )+x^3 \log ^2\left ((1-2 x)^2\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-675*x^2 + 990*x^3 - 450*x^4 + 828*x^5 - 63*x^6 + 126*x^7 + (270*x^2 - 468*x^3 + 90*x^4 - 180*x^5)*
Log[1 - 4*x + 4*x^2] + (-27*x^2 + 54*x^3)*Log[1 - 4*x + 4*x^2]^2)/(-1 + 2*x),x]

[Out]

9*(25*x^3 + 10*x^5 + x^7 + (43*Log[1 - 2*x])/24 - (43*Log[(1 - 2*x)^2])/48 - 10*x^3*Log[(1 - 2*x)^2] - 2*x^5*L
og[(1 - 2*x)^2] + x^3*Log[(1 - 2*x)^2]^2)

________________________________________________________________________________________

fricas [B]  time = 0.59, size = 56, normalized size = 2.55 \begin {gather*} 9 \, x^{7} + 90 \, x^{5} + 9 \, x^{3} \log \left (4 \, x^{2} - 4 \, x + 1\right )^{2} + 225 \, x^{3} - 18 \, {\left (x^{5} + 5 \, x^{3}\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((54*x^3-27*x^2)*log(4*x^2-4*x+1)^2+(-180*x^5+90*x^4-468*x^3+270*x^2)*log(4*x^2-4*x+1)+126*x^7-63*x^
6+828*x^5-450*x^4+990*x^3-675*x^2)/(2*x-1),x, algorithm="fricas")

[Out]

9*x^7 + 90*x^5 + 9*x^3*log(4*x^2 - 4*x + 1)^2 + 225*x^3 - 18*(x^5 + 5*x^3)*log(4*x^2 - 4*x + 1)

________________________________________________________________________________________

giac [B]  time = 0.37, size = 56, normalized size = 2.55 \begin {gather*} 9 \, x^{7} + 90 \, x^{5} + 9 \, x^{3} \log \left (4 \, x^{2} - 4 \, x + 1\right )^{2} + 225 \, x^{3} - 18 \, {\left (x^{5} + 5 \, x^{3}\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((54*x^3-27*x^2)*log(4*x^2-4*x+1)^2+(-180*x^5+90*x^4-468*x^3+270*x^2)*log(4*x^2-4*x+1)+126*x^7-63*x^
6+828*x^5-450*x^4+990*x^3-675*x^2)/(2*x-1),x, algorithm="giac")

[Out]

9*x^7 + 90*x^5 + 9*x^3*log(4*x^2 - 4*x + 1)^2 + 225*x^3 - 18*(x^5 + 5*x^3)*log(4*x^2 - 4*x + 1)

________________________________________________________________________________________

maple [B]  time = 0.42, size = 58, normalized size = 2.64

method	result	size
risch	\(9 x^{3} \ln \left (4 x^{2}-4 x +1\right )^{2}+\left (-18 x^{5}-90 x^{3}\right ) \ln \left (4 x^{2}-4 x +1\right )+9 x^{7}+90 x^{5}+225 x^{3}\)	\(58\)
norman	\(225 x^{3}+90 x^{5}+9 x^{7}+9 x^{3} \ln \left (4 x^{2}-4 x +1\right )^{2}-18 x^{5} \ln \left (4 x^{2}-4 x +1\right )-90 \ln \left (4 x^{2}-4 x +1\right ) x^{3}\)	\(67\)
default	\(9 x^{7}+90 x^{5}+225 x^{3}-\frac {9 \ln \left (4 x^{2}-4 x +1\right )^{2}}{8}-\frac {33 \ln \left (2 x -1\right )}{2}-18 x^{5} \ln \left (4 x^{2}-4 x +1\right )+\frac {9 \ln \left (2 x -1\right ) \ln \left (4 x^{2}-4 x +1\right )}{2}+9 x^{3} \ln \left (4 x^{2}-4 x +1\right )^{2}-90 \ln \left (4 x^{2}-4 x +1\right ) x^{3}+\frac {33 \ln \left (4 x^{2}-4 x +1\right )}{4}-\frac {9 \ln \left (2 x -1\right )^{2}}{2}\)	\(132\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((54*x^3-27*x^2)*ln(4*x^2-4*x+1)^2+(-180*x^5+90*x^4-468*x^3+270*x^2)*ln(4*x^2-4*x+1)+126*x^7-63*x^6+828*x^
5-450*x^4+990*x^3-675*x^2)/(2*x-1),x,method=_RETURNVERBOSE)

[Out]

9*x^3*ln(4*x^2-4*x+1)^2+(-18*x^5-90*x^3)*ln(4*x^2-4*x+1)+9*x^7+90*x^5+225*x^3

________________________________________________________________________________________

maxima [B]  time = 0.48, size = 314, normalized size = 14.27 \begin {gather*} 9 \, x^{7} + 90 \, x^{5} + 225 \, x^{3} + \frac {9}{8} \, {\left (8 \, x^{3} + 6 \, x^{2} + 6 \, x + 3 \, \log \left (2 \, x - 1\right )\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right )^{2} - \frac {27}{8} \, {\left (2 \, x^{2} + 2 \, x + \log \left (2 \, x - 1\right )\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right )^{2} - \frac {3}{16} \, {\left (96 \, x^{5} + 60 \, x^{4} + 40 \, x^{3} + 30 \, x^{2} + 30 \, x + 15 \, \log \left (2 \, x - 1\right )\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right ) + \frac {15}{16} \, {\left (12 \, x^{4} + 8 \, x^{3} + 6 \, x^{2} + 6 \, x + 3 \, \log \left (2 \, x - 1\right )\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right ) - \frac {3}{4} \, {\left (16 \, x^{3} + 30 \, x^{2} + 9 \, \log \left (2 \, x - 1\right )^{2} + 66 \, x + 33 \, \log \left (2 \, x - 1\right )\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right ) - \frac {39}{4} \, {\left (8 \, x^{3} + 6 \, x^{2} + 6 \, x + 3 \, \log \left (2 \, x - 1\right )\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right ) + \frac {27}{4} \, {\left (2 \, x^{2} + \log \left (2 \, x - 1\right )^{2} + 6 \, x + 3 \, \log \left (2 \, x - 1\right )\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right ) + \frac {135}{4} \, {\left (2 \, x^{2} + 2 \, x + \log \left (2 \, x - 1\right )\right )} \log \left (4 \, x^{2} - 4 \, x + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((54*x^3-27*x^2)*log(4*x^2-4*x+1)^2+(-180*x^5+90*x^4-468*x^3+270*x^2)*log(4*x^2-4*x+1)+126*x^7-63*x^
6+828*x^5-450*x^4+990*x^3-675*x^2)/(2*x-1),x, algorithm="maxima")

[Out]

9*x^7 + 90*x^5 + 225*x^3 + 9/8*(8*x^3 + 6*x^2 + 6*x + 3*log(2*x - 1))*log(4*x^2 - 4*x + 1)^2 - 27/8*(2*x^2 + 2
*x + log(2*x - 1))*log(4*x^2 - 4*x + 1)^2 - 3/16*(96*x^5 + 60*x^4 + 40*x^3 + 30*x^2 + 30*x + 15*log(2*x - 1))*
log(4*x^2 - 4*x + 1) + 15/16*(12*x^4 + 8*x^3 + 6*x^2 + 6*x + 3*log(2*x - 1))*log(4*x^2 - 4*x + 1) - 3/4*(16*x^
3 + 30*x^2 + 9*log(2*x - 1)^2 + 66*x + 33*log(2*x - 1))*log(4*x^2 - 4*x + 1) - 39/4*(8*x^3 + 6*x^2 + 6*x + 3*l
og(2*x - 1))*log(4*x^2 - 4*x + 1) + 27/4*(2*x^2 + log(2*x - 1)^2 + 6*x + 3*log(2*x - 1))*log(4*x^2 - 4*x + 1)
+ 135/4*(2*x^2 + 2*x + log(2*x - 1))*log(4*x^2 - 4*x + 1)

________________________________________________________________________________________

mupad [B]  time = 0.27, size = 25, normalized size = 1.14 \begin {gather*} 9\,x^3\,{\left (x^2-\ln \left (4\,x^2-4\,x+1\right )+5\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(4*x^2 - 4*x + 1)^2*(27*x^2 - 54*x^3) - log(4*x^2 - 4*x + 1)*(270*x^2 - 468*x^3 + 90*x^4 - 180*x^5) +
675*x^2 - 990*x^3 + 450*x^4 - 828*x^5 + 63*x^6 - 126*x^7)/(2*x - 1),x)

[Out]

9*x^3*(x^2 - log(4*x^2 - 4*x + 1) + 5)^2

________________________________________________________________________________________

sympy [B]  time = 0.18, size = 56, normalized size = 2.55 \begin {gather*} 9 x^{7} + 90 x^{5} + 9 x^{3} \log {\left (4 x^{2} - 4 x + 1 \right )}^{2} + 225 x^{3} + \left (- 18 x^{5} - 90 x^{3}\right ) \log {\left (4 x^{2} - 4 x + 1 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((54*x**3-27*x**2)*ln(4*x**2-4*x+1)**2+(-180*x**5+90*x**4-468*x**3+270*x**2)*ln(4*x**2-4*x+1)+126*x*
*7-63*x**6+828*x**5-450*x**4+990*x**3-675*x**2)/(2*x-1),x)

[Out]

9*x**7 + 90*x**5 + 9*x**3*log(4*x**2 - 4*x + 1)**2 + 225*x**3 + (-18*x**5 - 90*x**3)*log(4*x**2 - 4*x + 1)

________________________________________________________________________________________