3.71.45 \(\int \frac {4+52 x+52 x^2-36 x^3-40 x^4+(20+60 x+60 x^2+20 x^3) \log (3)+(-4+24 x-12 x^2+120 x^3+(-20-80 x-60 x^2) \log (3)) \log (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3))+(8 x-80 x^2+40 x \log (3)) \log ^2(1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3))}{1-10 x+5 \log (3)} \, dx\)

Optimal. Leaf size=28 \[ \left (-(1+x)^2+2 x \log \left ((-1+5 (2 x-\log (3)))^2\right )\right )^2 \]

________________________________________________________________________________________

Rubi [B]  time = 0.91, antiderivative size = 418, normalized size of antiderivative = 14.93, number of steps used = 31, number of rules used = 14, integrand size = 146, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.096, Rules used = {6688, 12, 6742, 43, 2418, 2395, 2389, 2295, 2390, 2301, 2401, 2296, 2305, 2304} \begin {gather*} x^4+\frac {58 x^3}{15}-4 x^3 \log \left ((-10 x+1+\log (243))^2\right )+\frac {2}{15} x^3 (1+\log (243))-\frac {13 x^2}{5}+\frac {1}{50} x^2 (1+\log (243))^2+\frac {29}{50} x^2 (1+\log (243))-\frac {26 x}{5}+\frac {1}{25} (-10 x+1+\log (243))^2 \log ^2\left ((-10 x+1+\log (243))^2\right )-\frac {2}{25} (1+\log (243)) (-10 x+1+\log (243)) \log ^2\left ((-10 x+1+\log (243))^2\right )+\frac {1}{25} (1+\log (243))^2 \log ^2\left ((-10 x+1+\log (243))^2\right )-\frac {1}{50} x \log (3) (11+\log (243))^2+\frac {1}{250} x (1+\log (243))^3+\frac {29}{250} x (1+\log (243))^2+\frac {147}{25} x (1+\log (243))+\frac {8}{5} x (3-5 \log (9))+\frac {2}{25} (-10 x+1+\log (243))^2-\frac {1}{500} \log (3) (11+\log (243))^3 \log (-10 x+1+\log (243))+\frac {(1+\log (243))^4 \log (-10 x+1+\log (243))}{2500}+\frac {29 (1+\log (243))^3 \log (-10 x+1+\log (243))}{2500}-\frac {13}{250} (1+\log (243))^2 \log (-10 x+1+\log (243))-\frac {13}{25} (1+\log (243)) \log (-10 x+1+\log (243))-\frac {2}{5} \log (-10 x+1+\log (243))-\frac {2}{25} (-10 x+1+\log (243))^2 \log \left ((-10 x+1+\log (243))^2\right )+\frac {8}{25} (1+\log (243)) (-10 x+1+\log (243)) \log \left ((-10 x+1+\log (243))^2\right )+\frac {2}{25} (3-5 \log (9)) (-10 x+1+\log (243)) \log \left ((-10 x+1+\log (243))^2\right )-\frac {1}{10} (x+1)^2 \log (3) (11+\log (243))-\frac {2}{3} (x+1)^3 \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4 + 52*x + 52*x^2 - 36*x^3 - 40*x^4 + (20 + 60*x + 60*x^2 + 20*x^3)*Log[3] + (-4 + 24*x - 12*x^2 + 120*x^
3 + (-20 - 80*x - 60*x^2)*Log[3])*Log[1 - 20*x + 100*x^2 + (10 - 100*x)*Log[3] + 25*Log[3]^2] + (8*x - 80*x^2
+ 40*x*Log[3])*Log[1 - 20*x + 100*x^2 + (10 - 100*x)*Log[3] + 25*Log[3]^2]^2)/(1 - 10*x + 5*Log[3]),x]

[Out]

(-26*x)/5 - (13*x^2)/5 + (58*x^3)/15 + x^4 - (2*(1 + x)^3*Log[3])/3 + (8*x*(3 - 5*Log[9]))/5 + (147*x*(1 + Log
[243]))/25 + (29*x^2*(1 + Log[243]))/50 + (2*x^3*(1 + Log[243]))/15 + (29*x*(1 + Log[243])^2)/250 + (x^2*(1 +
Log[243])^2)/50 + (x*(1 + Log[243])^3)/250 - ((1 + x)^2*Log[3]*(11 + Log[243]))/10 - (x*Log[3]*(11 + Log[243])
^2)/50 + (2*(1 - 10*x + Log[243])^2)/25 - (2*Log[1 - 10*x + Log[243]])/5 - (13*(1 + Log[243])*Log[1 - 10*x + L
og[243]])/25 - (13*(1 + Log[243])^2*Log[1 - 10*x + Log[243]])/250 + (29*(1 + Log[243])^3*Log[1 - 10*x + Log[24
3]])/2500 + ((1 + Log[243])^4*Log[1 - 10*x + Log[243]])/2500 - (Log[3]*(11 + Log[243])^3*Log[1 - 10*x + Log[24
3]])/500 - 4*x^3*Log[(1 - 10*x + Log[243])^2] + (2*(3 - 5*Log[9])*(1 - 10*x + Log[243])*Log[(1 - 10*x + Log[24
3])^2])/25 + (8*(1 + Log[243])*(1 - 10*x + Log[243])*Log[(1 - 10*x + Log[243])^2])/25 - (2*(1 - 10*x + Log[243
])^2*Log[(1 - 10*x + Log[243])^2])/25 + ((1 + Log[243])^2*Log[(1 - 10*x + Log[243])^2]^2)/25 - (2*(1 + Log[243
])*(1 - 10*x + Log[243])*Log[(1 - 10*x + Log[243])^2]^2)/25 + ((1 - 10*x + Log[243])^2*Log[(1 - 10*x + Log[243
])^2]^2)/25

Rule 12

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

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 2295

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

Rule 2296

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 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 2305

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

Rule 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 2401

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

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 6688

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

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 \frac {4 \left (1+13 x+13 x^2-9 x^3-10 x^4+5 (1+x)^3 \log (3)+\left (-1+30 x^3+x (6-20 \log (3))-5 \log (3)-3 x^2 (1+\log (243))\right ) \log \left ((1-10 x+\log (243))^2\right )+2 x (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )\right )}{1-10 x+\log (243)} \, dx\\ &=4 \int \frac {1+13 x+13 x^2-9 x^3-10 x^4+5 (1+x)^3 \log (3)+\left (-1+30 x^3+x (6-20 \log (3))-5 \log (3)-3 x^2 (1+\log (243))\right ) \log \left ((1-10 x+\log (243))^2\right )+2 x (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )}{1-10 x+\log (243)} \, dx\\ &=4 \int \left (-\frac {13 x}{-1+10 x-\log (243)}-\frac {13 x^2}{-1+10 x-\log (243)}+\frac {9 x^3}{-1+10 x-\log (243)}+\frac {10 x^4}{-1+10 x-\log (243)}-\frac {5 (1+x)^3 \log (3)}{-1+10 x-\log (243)}+\frac {1}{1-10 x+\log (243)}+\frac {\left (-1+30 x^3+2 x (3-10 \log (3))-\log (243)-3 x^2 (1+\log (243))\right ) \log \left ((1-10 x+\log (243))^2\right )}{1-10 x+\log (243)}+2 x \log ^2\left ((1-10 x+\log (243))^2\right )\right ) \, dx\\ &=-\frac {2}{5} \log (1-10 x+\log (243))+4 \int \frac {\left (-1+30 x^3+2 x (3-10 \log (3))-\log (243)-3 x^2 (1+\log (243))\right ) \log \left ((1-10 x+\log (243))^2\right )}{1-10 x+\log (243)} \, dx+8 \int x \log ^2\left ((1-10 x+\log (243))^2\right ) \, dx+36 \int \frac {x^3}{-1+10 x-\log (243)} \, dx+40 \int \frac {x^4}{-1+10 x-\log (243)} \, dx-52 \int \frac {x}{-1+10 x-\log (243)} \, dx-52 \int \frac {x^2}{-1+10 x-\log (243)} \, dx-(20 \log (3)) \int \frac {(1+x)^3}{-1+10 x-\log (243)} \, dx\\ &=-\frac {2}{5} \log (1-10 x+\log (243))+4 \int \left (-3 x^2 \log \left ((1-10 x+\log (243))^2\right )+\frac {1}{5} (-3+5 \log (9)) \log \left ((1-10 x+\log (243))^2\right )-\frac {2 (1+\log (243))^2 \log \left ((1-10 x+\log (243))^2\right )}{5 (1-10 x+\log (243))}\right ) \, dx+8 \int \left (\frac {1}{10} (1+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )-\frac {1}{10} (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )\right ) \, dx+36 \int \left (\frac {x^2}{10}+\frac {1}{100} x (1+\log (243))+\frac {(1+\log (243))^2}{1000}+\frac {(1+\log (243))^3}{1000 (-1+10 x-\log (243))}\right ) \, dx+40 \int \left (\frac {x^3}{10}+\frac {1}{100} x^2 (1+\log (243))+\frac {x (1+\log (243))^2}{1000}+\frac {(1+\log (243))^3}{10000}+\frac {(1+\log (243))^4}{10000 (-1+10 x-\log (243))}\right ) \, dx-52 \int \left (\frac {1}{10}+\frac {1+\log (243)}{10 (-1+10 x-\log (243))}\right ) \, dx-52 \int \left (\frac {x}{10}+\frac {1}{100} (1+\log (243))+\frac {(1+\log (243))^2}{100 (-1+10 x-\log (243))}\right ) \, dx-(20 \log (3)) \int \left (\frac {1}{10} (1+x)^2+\frac {1}{100} (1+x) (11+\log (243))+\frac {(11+\log (243))^2}{1000}+\frac {(11+\log (243))^3}{1000 (-1+10 x-\log (243))}\right ) \, dx\\ &=-\frac {26 x}{5}-\frac {13 x^2}{5}+\frac {6 x^3}{5}+x^4-\frac {2}{3} (1+x)^3 \log (3)-\frac {13}{25} x (1+\log (243))+\frac {9}{50} x^2 (1+\log (243))+\frac {2}{15} x^3 (1+\log (243))+\frac {9}{250} x (1+\log (243))^2+\frac {1}{50} x^2 (1+\log (243))^2+\frac {1}{250} x (1+\log (243))^3-\frac {1}{10} (1+x)^2 \log (3) (11+\log (243))-\frac {1}{50} x \log (3) (11+\log (243))^2-\frac {2}{5} \log (1-10 x+\log (243))-\frac {13}{25} (1+\log (243)) \log (1-10 x+\log (243))-\frac {13}{250} (1+\log (243))^2 \log (1-10 x+\log (243))+\frac {9 (1+\log (243))^3 \log (1-10 x+\log (243))}{2500}+\frac {(1+\log (243))^4 \log (1-10 x+\log (243))}{2500}-\frac {1}{500} \log (3) (11+\log (243))^3 \log (1-10 x+\log (243))-\frac {4}{5} \int (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right ) \, dx-12 \int x^2 \log \left ((1-10 x+\log (243))^2\right ) \, dx-\frac {1}{5} (4 (3-5 \log (9))) \int \log \left ((1-10 x+\log (243))^2\right ) \, dx+\frac {1}{5} (4 (1+\log (243))) \int \log ^2\left ((1-10 x+\log (243))^2\right ) \, dx-\frac {1}{5} \left (8 (1+\log (243))^2\right ) \int \frac {\log \left ((1-10 x+\log (243))^2\right )}{1-10 x+\log (243)} \, dx\\ &=-\frac {26 x}{5}-\frac {13 x^2}{5}+\frac {6 x^3}{5}+x^4-\frac {2}{3} (1+x)^3 \log (3)-\frac {13}{25} x (1+\log (243))+\frac {9}{50} x^2 (1+\log (243))+\frac {2}{15} x^3 (1+\log (243))+\frac {9}{250} x (1+\log (243))^2+\frac {1}{50} x^2 (1+\log (243))^2+\frac {1}{250} x (1+\log (243))^3-\frac {1}{10} (1+x)^2 \log (3) (11+\log (243))-\frac {1}{50} x \log (3) (11+\log (243))^2-\frac {2}{5} \log (1-10 x+\log (243))-\frac {13}{25} (1+\log (243)) \log (1-10 x+\log (243))-\frac {13}{250} (1+\log (243))^2 \log (1-10 x+\log (243))+\frac {9 (1+\log (243))^3 \log (1-10 x+\log (243))}{2500}+\frac {(1+\log (243))^4 \log (1-10 x+\log (243))}{2500}-\frac {1}{500} \log (3) (11+\log (243))^3 \log (1-10 x+\log (243))-4 x^3 \log \left ((1-10 x+\log (243))^2\right )+\frac {2}{25} \operatorname {Subst}\left (\int x \log ^2\left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )-80 \int \frac {x^3}{1-10 x+\log (243)} \, dx+\frac {1}{25} (2 (3-5 \log (9))) \operatorname {Subst}\left (\int \log \left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )-\frac {1}{25} (2 (1+\log (243))) \operatorname {Subst}\left (\int \log ^2\left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )+\frac {1}{25} \left (4 (1+\log (243))^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (x^2\right )}{x} \, dx,x,1-10 x+\log (243)\right )\\ &=-\frac {26 x}{5}-\frac {13 x^2}{5}+\frac {6 x^3}{5}+x^4-\frac {2}{3} (1+x)^3 \log (3)+\frac {8}{5} x (3-5 \log (9))-\frac {13}{25} x (1+\log (243))+\frac {9}{50} x^2 (1+\log (243))+\frac {2}{15} x^3 (1+\log (243))+\frac {9}{250} x (1+\log (243))^2+\frac {1}{50} x^2 (1+\log (243))^2+\frac {1}{250} x (1+\log (243))^3-\frac {1}{10} (1+x)^2 \log (3) (11+\log (243))-\frac {1}{50} x \log (3) (11+\log (243))^2-\frac {2}{5} \log (1-10 x+\log (243))-\frac {13}{25} (1+\log (243)) \log (1-10 x+\log (243))-\frac {13}{250} (1+\log (243))^2 \log (1-10 x+\log (243))+\frac {9 (1+\log (243))^3 \log (1-10 x+\log (243))}{2500}+\frac {(1+\log (243))^4 \log (1-10 x+\log (243))}{2500}-\frac {1}{500} \log (3) (11+\log (243))^3 \log (1-10 x+\log (243))-4 x^3 \log \left ((1-10 x+\log (243))^2\right )+\frac {2}{25} (3-5 \log (9)) (1-10 x+\log (243)) \log \left ((1-10 x+\log (243))^2\right )+\frac {1}{25} (1+\log (243))^2 \log ^2\left ((1-10 x+\log (243))^2\right )-\frac {2}{25} (1+\log (243)) (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )+\frac {1}{25} (1-10 x+\log (243))^2 \log ^2\left ((1-10 x+\log (243))^2\right )-\frac {4}{25} \operatorname {Subst}\left (\int x \log \left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )-80 \int \left (-\frac {x^2}{10}-\frac {1}{100} x (1+\log (243))-\frac {(1+\log (243))^2}{1000}-\frac {(1+\log (243))^3}{1000 (-1+10 x-\log (243))}\right ) \, dx+\frac {1}{25} (8 (1+\log (243))) \operatorname {Subst}\left (\int \log \left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )\\ &=-\frac {26 x}{5}-\frac {13 x^2}{5}+\frac {58 x^3}{15}+x^4-\frac {2}{3} (1+x)^3 \log (3)+\frac {8}{5} x (3-5 \log (9))+\frac {147}{25} x (1+\log (243))+\frac {29}{50} x^2 (1+\log (243))+\frac {2}{15} x^3 (1+\log (243))+\frac {29}{250} x (1+\log (243))^2+\frac {1}{50} x^2 (1+\log (243))^2+\frac {1}{250} x (1+\log (243))^3-\frac {1}{10} (1+x)^2 \log (3) (11+\log (243))-\frac {1}{50} x \log (3) (11+\log (243))^2+\frac {2}{25} (1-10 x+\log (243))^2-\frac {2}{5} \log (1-10 x+\log (243))-\frac {13}{25} (1+\log (243)) \log (1-10 x+\log (243))-\frac {13}{250} (1+\log (243))^2 \log (1-10 x+\log (243))+\frac {29 (1+\log (243))^3 \log (1-10 x+\log (243))}{2500}+\frac {(1+\log (243))^4 \log (1-10 x+\log (243))}{2500}-\frac {1}{500} \log (3) (11+\log (243))^3 \log (1-10 x+\log (243))-4 x^3 \log \left ((1-10 x+\log (243))^2\right )+\frac {2}{25} (3-5 \log (9)) (1-10 x+\log (243)) \log \left ((1-10 x+\log (243))^2\right )+\frac {8}{25} (1+\log (243)) (1-10 x+\log (243)) \log \left ((1-10 x+\log (243))^2\right )-\frac {2}{25} (1-10 x+\log (243))^2 \log \left ((1-10 x+\log (243))^2\right )+\frac {1}{25} (1+\log (243))^2 \log ^2\left ((1-10 x+\log (243))^2\right )-\frac {2}{25} (1+\log (243)) (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )+\frac {1}{25} (1-10 x+\log (243))^2 \log ^2\left ((1-10 x+\log (243))^2\right )\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.09, size = 72, normalized size = 2.57 \begin {gather*} \frac {1}{250} x \left (1000+1500 x+1000 x^2+250 x^3-5655 \log (3)+1131 \log (243)-160 \log (3) \log (243)+32 \log ^2(243)-1000 (1+x)^2 \log \left ((1-10 x+\log (243))^2\right )+1000 x \log ^2\left ((1-10 x+\log (243))^2\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4 + 52*x + 52*x^2 - 36*x^3 - 40*x^4 + (20 + 60*x + 60*x^2 + 20*x^3)*Log[3] + (-4 + 24*x - 12*x^2 +
120*x^3 + (-20 - 80*x - 60*x^2)*Log[3])*Log[1 - 20*x + 100*x^2 + (10 - 100*x)*Log[3] + 25*Log[3]^2] + (8*x - 8
0*x^2 + 40*x*Log[3])*Log[1 - 20*x + 100*x^2 + (10 - 100*x)*Log[3] + 25*Log[3]^2]^2)/(1 - 10*x + 5*Log[3]),x]

[Out]

(x*(1000 + 1500*x + 1000*x^2 + 250*x^3 - 5655*Log[3] + 1131*Log[243] - 160*Log[3]*Log[243] + 32*Log[243]^2 - 1
000*(1 + x)^2*Log[(1 - 10*x + Log[243])^2] + 1000*x*Log[(1 - 10*x + Log[243])^2]^2))/250

________________________________________________________________________________________

fricas [B]  time = 0.76, size = 88, normalized size = 3.14 \begin {gather*} x^{4} + 4 \, x^{2} \log \left (100 \, x^{2} - 10 \, {\left (10 \, x - 1\right )} \log \relax (3) + 25 \, \log \relax (3)^{2} - 20 \, x + 1\right )^{2} + 4 \, x^{3} + 6 \, x^{2} - 4 \, {\left (x^{3} + 2 \, x^{2} + x\right )} \log \left (100 \, x^{2} - 10 \, {\left (10 \, x - 1\right )} \log \relax (3) + 25 \, \log \relax (3)^{2} - 20 \, x + 1\right ) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((40*x*log(3)-80*x^2+8*x)*log(25*log(3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)^2+((-60*x^2-80*x-20)*lo
g(3)+120*x^3-12*x^2+24*x-4)*log(25*log(3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)+(20*x^3+60*x^2+60*x+20)*log(3)-
40*x^4-36*x^3+52*x^2+52*x+4)/(5*log(3)-10*x+1),x, algorithm="fricas")

[Out]

x^4 + 4*x^2*log(100*x^2 - 10*(10*x - 1)*log(3) + 25*log(3)^2 - 20*x + 1)^2 + 4*x^3 + 6*x^2 - 4*(x^3 + 2*x^2 +
x)*log(100*x^2 - 10*(10*x - 1)*log(3) + 25*log(3)^2 - 20*x + 1) + 4*x

________________________________________________________________________________________

giac [B]  time = 0.44, size = 88, normalized size = 3.14 \begin {gather*} x^{4} + 4 \, x^{2} \log \left (100 \, x^{2} - 100 \, x \log \relax (3) + 25 \, \log \relax (3)^{2} - 20 \, x + 10 \, \log \relax (3) + 1\right )^{2} + 4 \, x^{3} + 6 \, x^{2} - 4 \, {\left (x^{3} + 2 \, x^{2} + x\right )} \log \left (100 \, x^{2} - 100 \, x \log \relax (3) + 25 \, \log \relax (3)^{2} - 20 \, x + 10 \, \log \relax (3) + 1\right ) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((40*x*log(3)-80*x^2+8*x)*log(25*log(3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)^2+((-60*x^2-80*x-20)*lo
g(3)+120*x^3-12*x^2+24*x-4)*log(25*log(3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)+(20*x^3+60*x^2+60*x+20)*log(3)-
40*x^4-36*x^3+52*x^2+52*x+4)/(5*log(3)-10*x+1),x, algorithm="giac")

[Out]

x^4 + 4*x^2*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1)^2 + 4*x^3 + 6*x^2 - 4*(x^3 + 2*x^
2 + x)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) + 4*x

________________________________________________________________________________________

maple [B]  time = 0.17, size = 90, normalized size = 3.21

method	result	size
risch	\(4 x^{2} \ln \left (25 \ln \relax (3)^{2}+\left (-100 x +10\right ) \ln \relax (3)+100 x^{2}-20 x +1\right )^{2}+\left (-4 x^{3}-8 x^{2}-4 x \right ) \ln \left (25 \ln \relax (3)^{2}+\left (-100 x +10\right ) \ln \relax (3)+100 x^{2}-20 x +1\right )+x^{4}+4 x^{3}+6 x^{2}+4 x\)	\(90\)
norman	\(x^{4}+4 x +6 x^{2}+4 x^{3}-4 x \ln \left (25 \ln \relax (3)^{2}+\left (-100 x +10\right ) \ln \relax (3)+100 x^{2}-20 x +1\right )-8 x^{2} \ln \left (25 \ln \relax (3)^{2}+\left (-100 x +10\right ) \ln \relax (3)+100 x^{2}-20 x +1\right )+4 x^{2} \ln \left (25 \ln \relax (3)^{2}+\left (-100 x +10\right ) \ln \relax (3)+100 x^{2}-20 x +1\right )^{2}-4 x^{3} \ln \left (25 \ln \relax (3)^{2}+\left (-100 x +10\right ) \ln \relax (3)+100 x^{2}-20 x +1\right )\)	\(138\)
default	\(4 x +x^{4}+4 x^{3}+6 x^{2}+4 \ln \relax (3)^{2} \ln \left (10 x -5 \ln \relax (3)-1\right ) \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )+\frac {8 \ln \relax (3) \ln \left (10 x -5 \ln \relax (3)-1\right ) \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )}{5}-\ln \relax (3)^{2} \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )^{2}+4 \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )^{2} x^{2}-4 \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right ) x^{3}+6 \ln \relax (3)^{2} \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )-\frac {2 \ln \relax (3) \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )^{2}}{5}-8 \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right ) x^{2}+\frac {12 \ln \relax (3) \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )}{5}-\frac {12 x \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )}{5}-\frac {4 \ln \left (10 x -5 \ln \relax (3)-1\right )^{2}}{25}+8 \ln \relax (3) \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right ) x -12 \ln \left (10 x -5 \ln \relax (3)-1\right ) \ln \relax (3)^{2}-\frac {24 \ln \left (10 x -5 \ln \relax (3)-1\right ) \ln \relax (3)}{5}+\left (-8 \ln \relax (3)-\frac {8}{5}\right ) x \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )-\frac {12 \ln \left (10 x -5 \ln \relax (3)-1\right )}{25}-\frac {\ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )^{2}}{25}+\frac {6 \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )}{25}-4 \ln \relax (3)^{2} \ln \left (10 x -5 \ln \relax (3)-1\right )^{2}-\frac {8 \ln \relax (3) \ln \left (10 x -5 \ln \relax (3)-1\right )^{2}}{5}+\frac {4 \ln \left (10 x -5 \ln \relax (3)-1\right ) \ln \left (25 \ln \relax (3)^{2}-100 x \ln \relax (3)+100 x^{2}+10 \ln \relax (3)-20 x +1\right )}{25}\)	\(603\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((40*x*ln(3)-80*x^2+8*x)*ln(25*ln(3)^2+(-100*x+10)*ln(3)+100*x^2-20*x+1)^2+((-60*x^2-80*x-20)*ln(3)+120*x^
3-12*x^2+24*x-4)*ln(25*ln(3)^2+(-100*x+10)*ln(3)+100*x^2-20*x+1)+(20*x^3+60*x^2+60*x+20)*ln(3)-40*x^4-36*x^3+5
2*x^2+52*x+4)/(5*ln(3)-10*x+1),x,method=_RETURNVERBOSE)

[Out]

4*x^2*ln(25*ln(3)^2+(-100*x+10)*ln(3)+100*x^2-20*x+1)^2+(-4*x^3-8*x^2-4*x)*ln(25*ln(3)^2+(-100*x+10)*ln(3)+100
*x^2-20*x+1)+x^4+4*x^3+6*x^2+4*x

________________________________________________________________________________________

maxima [B]  time = 0.53, size = 1507, normalized size = 53.82 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((40*x*log(3)-80*x^2+8*x)*log(25*log(3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)^2+((-60*x^2-80*x-20)*lo
g(3)+120*x^3-12*x^2+24*x-4)*log(25*log(3)^2+(-100*x+10)*log(3)+100*x^2-20*x+1)+(20*x^3+60*x^2+60*x+20)*log(3)-
40*x^4-36*x^3+52*x^2+52*x+4)/(5*log(3)-10*x+1),x, algorithm="maxima")

[Out]

x^4 + 2/15*x^3*(5*log(3) + 1) - 2/5*((5*log(3) + 1)*log(10*x - 5*log(3) - 1) + 10*x)*log(3)*log(100*x^2 - 100*
x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1)^2 + 8/75*(25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3) - 1)
^3 - 8/75*(5*log(3) + 1)*log(10*x - 5*log(3) - 1)^3 + 1/50*(25*log(3)^2 + 10*log(3) + 1)*x^2 + 58/15*x^3 + 59/
50*x^2*(5*log(3) + 1) + 3/50*(50*x^2 + 10*x*(5*log(3) + 1) + (25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3)
- 1))*log(3)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) + 4/5*((5*log(3) + 1)*log(10*x
- 5*log(3) - 1) + 10*x)*log(3)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) + 2/25*(50*x^2
+ 10*x*(5*log(3) + 1) + (25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3) - 1))*log(100*x^2 - 100*x*log(3) +
25*log(3)^2 - 20*x + 10*log(3) + 1)^2 - 2/25*((5*log(3) + 1)*log(10*x - 5*log(3) - 1) + 10*x)*log(100*x^2 - 10
0*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1)^2 + 2*log(3)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x
+ 10*log(3) + 1)*log(10*x - 5*log(3) - 1) + 3/250*(125*log(3)^3 + 75*log(3)^2 + 15*log(3) + 1)*log(10*x - 5*lo
g(3) - 1)^2 + 117/250*(25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 - 2/25*(5*log(3) + 1)*log(10*x
- 5*log(3) - 1)^2 + 1/250*(125*log(3)^3 + 75*log(3)^2 + 15*log(3) + 1)*x + 119/250*(25*log(3)^2 + 10*log(3) +
1)*x + 24/5*x^2 + 258/25*x*(5*log(3) + 1) - 4/15*(2*(5*log(3) + 1)*log(10*x - 5*log(3) - 1)^3 + 6*(5*log(3) +
1)*log(10*x - 5*log(3) - 1)^2 - 3*((5*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 + 2*(5*log(3) + 1)*log(10*x - 5*l
og(3) - 1) + 20*x)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) + 12*(5*log(3) + 1)*log(10
*x - 5*log(3) - 1) + 120*x)*log(3) - 1/1500*(1000*x^3 + 150*x^2*(5*log(3) + 1) + 30*(25*log(3)^2 + 10*log(3) +
1)*x + 3*(125*log(3)^3 + 75*log(3)^2 + 15*log(3) + 1)*log(10*x - 5*log(3) - 1))*log(3) - 3/50*((25*log(3)^2 +
10*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 + 50*x^2 + 30*x*(5*log(3) + 1) + 3*(25*log(3)^2 + 10*log(3) + 1)*lo
g(10*x - 5*log(3) - 1))*log(3) - 4/5*((5*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 + 2*(5*log(3) + 1)*log(10*x -
5*log(3) - 1) + 20*x)*log(3) - 3/50*(50*x^2 + 10*x*(5*log(3) + 1) + (25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5
*log(3) - 1))*log(3) - 3/5*((5*log(3) + 1)*log(10*x - 5*log(3) - 1) + 10*x)*log(3) - 2*(log(100*x^2 - 100*x*lo
g(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1)*log(10*x - 5*log(3) - 1) - log(10*x - 5*log(3) - 1)^2)*log(3) - 1/2
50*(1000*x^3 + 150*x^2*(5*log(3) + 1) + 30*(25*log(3)^2 + 10*log(3) + 1)*x + 3*(125*log(3)^3 + 75*log(3)^2 + 1
5*log(3) + 1)*log(10*x - 5*log(3) - 1))*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) - 4/2
5*((25*log(3)^2 + 10*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 + 50*x^2 + 30*x*(5*log(3) + 1) + 3*(25*log(3)^2 +
10*log(3) + 1)*log(10*x - 5*log(3) - 1))*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) + 4/
25*((5*log(3) + 1)*log(10*x - 5*log(3) - 1)^2 + 2*(5*log(3) + 1)*log(10*x - 5*log(3) - 1) + 20*x)*log(100*x^2
- 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) + 3/250*(50*x^2 + 10*x*(5*log(3) + 1) + (25*log(3)^2 + 10
*log(3) + 1)*log(10*x - 5*log(3) - 1))*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3) + 1) - 6/25
*((5*log(3) + 1)*log(10*x - 5*log(3) - 1) + 10*x)*log(100*x^2 - 100*x*log(3) + 25*log(3)^2 - 20*x + 10*log(3)
+ 1) + 1/2500*(625*log(3)^4 + 500*log(3)^3 + 150*log(3)^2 + 20*log(3) + 1)*log(10*x - 5*log(3) - 1) + 119/2500
*(125*log(3)^3 + 75*log(3)^2 + 15*log(3) + 1)*log(10*x - 5*log(3) - 1) + 129/125*(25*log(3)^2 + 10*log(3) + 1)
*log(10*x - 5*log(3) - 1) - 17/25*(5*log(3) + 1)*log(10*x - 5*log(3) - 1) - 2*log(3)*log(10*x - 5*log(3) - 1)
+ 2/5*log(10*x - 5*log(3) - 1)^2 - 34/5*x - 2/5*log(10*x - 5*log(3) - 1)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {52\,x-\ln \left (25\,{\ln \relax (3)}^2-\ln \relax (3)\,\left (100\,x-10\right )-20\,x+100\,x^2+1\right )\,\left (\ln \relax (3)\,\left (60\,x^2+80\,x+20\right )-24\,x+12\,x^2-120\,x^3+4\right )+\ln \relax (3)\,\left (20\,x^3+60\,x^2+60\,x+20\right )+{\ln \left (25\,{\ln \relax (3)}^2-\ln \relax (3)\,\left (100\,x-10\right )-20\,x+100\,x^2+1\right )}^2\,\left (8\,x+40\,x\,\ln \relax (3)-80\,x^2\right )+52\,x^2-36\,x^3-40\,x^4+4}{5\,\ln \relax (3)-10\,x+1} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((52*x - log(25*log(3)^2 - log(3)*(100*x - 10) - 20*x + 100*x^2 + 1)*(log(3)*(80*x + 60*x^2 + 20) - 24*x +
12*x^2 - 120*x^3 + 4) + log(3)*(60*x + 60*x^2 + 20*x^3 + 20) + log(25*log(3)^2 - log(3)*(100*x - 10) - 20*x +
100*x^2 + 1)^2*(8*x + 40*x*log(3) - 80*x^2) + 52*x^2 - 36*x^3 - 40*x^4 + 4)/(5*log(3) - 10*x + 1),x)

[Out]

int((52*x - log(25*log(3)^2 - log(3)*(100*x - 10) - 20*x + 100*x^2 + 1)*(log(3)*(80*x + 60*x^2 + 20) - 24*x +
12*x^2 - 120*x^3 + 4) + log(3)*(60*x + 60*x^2 + 20*x^3 + 20) + log(25*log(3)^2 - log(3)*(100*x - 10) - 20*x +
100*x^2 + 1)^2*(8*x + 40*x*log(3) - 80*x^2) + 52*x^2 - 36*x^3 - 40*x^4 + 4)/(5*log(3) - 10*x + 1), x)

________________________________________________________________________________________

sympy [B]  time = 0.27, size = 92, normalized size = 3.29 \begin {gather*} x^{4} + 4 x^{3} + 4 x^{2} \log {\left (100 x^{2} - 20 x + \left (10 - 100 x\right ) \log {\relax (3 )} + 1 + 25 \log {\relax (3 )}^{2} \right )}^{2} + 6 x^{2} + 4 x + \left (- 4 x^{3} - 8 x^{2} - 4 x\right ) \log {\left (100 x^{2} - 20 x + \left (10 - 100 x\right ) \log {\relax (3 )} + 1 + 25 \log {\relax (3 )}^{2} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((40*x*ln(3)-80*x**2+8*x)*ln(25*ln(3)**2+(-100*x+10)*ln(3)+100*x**2-20*x+1)**2+((-60*x**2-80*x-20)*l
n(3)+120*x**3-12*x**2+24*x-4)*ln(25*ln(3)**2+(-100*x+10)*ln(3)+100*x**2-20*x+1)+(20*x**3+60*x**2+60*x+20)*ln(3
)-40*x**4-36*x**3+52*x**2+52*x+4)/(5*ln(3)-10*x+1),x)

[Out]

x**4 + 4*x**3 + 4*x**2*log(100*x**2 - 20*x + (10 - 100*x)*log(3) + 1 + 25*log(3)**2)**2 + 6*x**2 + 4*x + (-4*x
**3 - 8*x**2 - 4*x)*log(100*x**2 - 20*x + (10 - 100*x)*log(3) + 1 + 25*log(3)**2)

________________________________________________________________________________________