3.21.43 \(\int \frac {-28512 x^2+4032 x^3-224 x^4+(-297432 x+77112 x^2-5256 x^3+104 x^4) \log (3-x)+(-708588+314928 x-29160 x^2+1008 x^3-12 x^4) \log ^2(3-x)}{59049 x^4-26244 x^5+2430 x^6-84 x^7+x^8} \, dx\)

Optimal. Leaf size=22 \[ \frac {4 \left (-\frac {4 x}{-27+x}+\log (3-x)\right )^2}{x^3} \]

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Rubi [B]  time = 1.35, antiderivative size = 114, normalized size of antiderivative = 5.18, number of steps used = 39, number of rules used = 22, integrand size = 98, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.224, Rules used = {6741, 6742, 44, 88, 72, 2418, 2395, 36, 31, 2390, 2301, 29, 2392, 2391, 2398, 2411, 2347, 2344, 2316, 2315, 2314, 2319} \begin {gather*} \frac {4 \log ^2(3-x)}{x^3}+\frac {32 \log (3-x)}{27 x^2}+\frac {64}{729 (27-x)}+\frac {64}{729 x}+\frac {64}{27 (27-x)^2}+\frac {32 \log (3-x)}{729 (27-x)}-\frac {8 (3-x) \log (3-x)}{27 x}+\frac {680 \log (3-x)}{729 x}-\frac {8}{27} \log (3-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-28512*x^2 + 4032*x^3 - 224*x^4 + (-297432*x + 77112*x^2 - 5256*x^3 + 104*x^4)*Log[3 - x] + (-708588 + 31
4928*x - 29160*x^2 + 1008*x^3 - 12*x^4)*Log[3 - x]^2)/(59049*x^4 - 26244*x^5 + 2430*x^6 - 84*x^7 + x^8),x]

[Out]

64/(27*(27 - x)^2) + 64/(729*(27 - x)) + 64/(729*x) - (8*Log[3 - x])/27 + (32*Log[3 - x])/(729*(27 - x)) + (32
*Log[3 - x])/(27*x^2) + (680*Log[3 - x])/(729*x) - (8*(3 - x)*Log[3 - x])/(27*x) + (4*Log[3 - x]^2)/x^3

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 44

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}, x] && NeQ[b*c - a*d, 0] && ILtQ[m, 0] && IntegerQ[n] &&  !(IGtQ[n, 0] && L
tQ[m + n + 2, 0])

Rule 72

Int[((e_.) + (f_.)*(x_))^(p_.)/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :> Int[ExpandIntegrand[(
e + f*x)^p/((a + b*x)*(c + d*x)), x], x] /; FreeQ[{a, b, c, d, e, f}, x] && IntegerQ[p]

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

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 2314

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 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 2316

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

Rule 2319

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 2344

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

Rule 2347

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 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 2391

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 2392

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*d])*Log[x], x] + Dist[
b, Int[Log[1 + (e*x)/d]/x, x], x] /; FreeQ[{a, b, c, d, e}, x] && GtQ[c*d, 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 6741

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

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 {-28512 x^2+4032 x^3-224 x^4+\left (-297432 x+77112 x^2-5256 x^3+104 x^4\right ) \log (3-x)+\left (-708588+314928 x-29160 x^2+1008 x^3-12 x^4\right ) \log ^2(3-x)}{(3-x) (27-x)^3 x^4} \, dx\\ &=\int \left (-\frac {224}{(-27+x)^3 (-3+x)}-\frac {28512}{(-27+x)^3 (-3+x) x^2}+\frac {4032}{(-27+x)^3 (-3+x) x}+\frac {8 \left (1377-306 x+13 x^2\right ) \log (3-x)}{(-27+x)^2 (-3+x) x^3}-\frac {12 \log ^2(3-x)}{x^4}\right ) \, dx\\ &=8 \int \frac {\left (1377-306 x+13 x^2\right ) \log (3-x)}{(-27+x)^2 (-3+x) x^3} \, dx-12 \int \frac {\log ^2(3-x)}{x^4} \, dx-224 \int \frac {1}{(-27+x)^3 (-3+x)} \, dx+4032 \int \frac {1}{(-27+x)^3 (-3+x) x} \, dx-28512 \int \frac {1}{(-27+x)^3 (-3+x) x^2} \, dx\\ &=\frac {4 \log ^2(3-x)}{x^3}+8 \int \frac {\log (3-x)}{(3-x) x^3} \, dx+8 \int \left (\frac {4 \log (3-x)}{729 (-27+x)^2}+\frac {\log (3-x)}{27 (-3+x)}-\frac {17 \log (3-x)}{27 x^3}-\frac {85 \log (3-x)}{729 x^2}-\frac {\log (3-x)}{27 x}\right ) \, dx-224 \int \left (\frac {1}{24 (-27+x)^3}-\frac {1}{576 (-27+x)^2}+\frac {1}{13824 (-27+x)}-\frac {1}{13824 (-3+x)}\right ) \, dx+4032 \int \left (\frac {1}{648 (-27+x)^3}-\frac {17}{139968 (-27+x)^2}+\frac {217}{30233088 (-27+x)}-\frac {1}{41472 (-3+x)}+\frac {1}{59049 x}\right ) \, dx-28512 \int \left (\frac {1}{17496 (-27+x)^3}-\frac {25}{3779136 (-27+x)^2}+\frac {139}{272097792 (-27+x)}-\frac {1}{124416 (-3+x)}+\frac {1}{59049 x^2}+\frac {4}{531441 x}\right ) \, dx\\ &=\frac {64}{27 (27-x)^2}+\frac {64}{729 (27-x)}+\frac {352}{729 x}+\frac {4}{27} \log (3-x)+\frac {4 \log ^2(3-x)}{x^3}-\frac {4 \log (27-x)}{2187}-\frac {320 \log (x)}{2187}+\frac {32}{729} \int \frac {\log (3-x)}{(-27+x)^2} \, dx+\frac {8}{27} \int \frac {\log (3-x)}{-3+x} \, dx-\frac {8}{27} \int \frac {\log (3-x)}{x} \, dx-\frac {680}{729} \int \frac {\log (3-x)}{x^2} \, dx-\frac {136}{27} \int \frac {\log (3-x)}{x^3} \, dx-8 \operatorname {Subst}\left (\int \frac {\log (x)}{(3-x)^3 x} \, dx,x,3-x\right )\\ &=\frac {64}{27 (27-x)^2}+\frac {64}{729 (27-x)}+\frac {352}{729 x}+\frac {4}{27} \log (3-x)+\frac {32 \log (3-x)}{729 (27-x)}+\frac {68 \log (3-x)}{27 x^2}+\frac {680 \log (3-x)}{729 x}+\frac {4 \log ^2(3-x)}{x^3}-\frac {4 \log (27-x)}{2187}-\frac {320 \log (x)}{2187}-\frac {8}{27} \log (3) \log (x)-\frac {32}{729} \int \frac {1}{(3-x) (-27+x)} \, dx-\frac {8}{27} \int \frac {\log \left (1-\frac {x}{3}\right )}{x} \, dx+\frac {8}{27} \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,3-x\right )+\frac {680}{729} \int \frac {1}{(3-x) x} \, dx+\frac {68}{27} \int \frac {1}{(3-x) x^2} \, dx-\frac {8}{3} \operatorname {Subst}\left (\int \frac {\log (x)}{(3-x)^3} \, dx,x,3-x\right )-\frac {8}{3} \operatorname {Subst}\left (\int \frac {\log (x)}{(3-x)^2 x} \, dx,x,3-x\right )\\ &=\frac {64}{27 (27-x)^2}+\frac {64}{729 (27-x)}+\frac {352}{729 x}+\frac {4}{27} \log (3-x)+\frac {32 \log (3-x)}{729 (27-x)}+\frac {32 \log (3-x)}{27 x^2}+\frac {680 \log (3-x)}{729 x}+\frac {4}{27} \log ^2(3-x)+\frac {4 \log ^2(3-x)}{x^3}-\frac {4 \log (27-x)}{2187}-\frac {320 \log (x)}{2187}-\frac {8}{27} \log (3) \log (x)+\frac {8 \text {Li}_2\left (\frac {x}{3}\right )}{27}+\frac {4 \int \frac {1}{3-x} \, dx}{2187}+\frac {4 \int \frac {1}{-27+x} \, dx}{2187}+\frac {680 \int \frac {1}{3-x} \, dx}{2187}+\frac {680 \int \frac {1}{x} \, dx}{2187}-\frac {8}{9} \operatorname {Subst}\left (\int \frac {\log (x)}{(3-x)^2} \, dx,x,3-x\right )-\frac {8}{9} \operatorname {Subst}\left (\int \frac {\log (x)}{(3-x) x} \, dx,x,3-x\right )+\frac {4}{3} \operatorname {Subst}\left (\int \frac {1}{(3-x)^2 x} \, dx,x,3-x\right )+\frac {68}{27} \int \left (-\frac {1}{9 (-3+x)}+\frac {1}{3 x^2}+\frac {1}{9 x}\right ) \, dx\\ &=\frac {64}{27 (27-x)^2}+\frac {64}{729 (27-x)}-\frac {260}{729 x}-\frac {4}{9} \log (3-x)+\frac {32 \log (3-x)}{729 (27-x)}+\frac {32 \log (3-x)}{27 x^2}+\frac {680 \log (3-x)}{729 x}-\frac {8 (3-x) \log (3-x)}{27 x}+\frac {4}{27} \log ^2(3-x)+\frac {4 \log ^2(3-x)}{x^3}+\frac {4 \log (x)}{9}-\frac {8}{27} \log (3) \log (x)+\frac {8 \text {Li}_2\left (\frac {x}{3}\right )}{27}+\frac {8}{27} \operatorname {Subst}\left (\int \frac {1}{3-x} \, dx,x,3-x\right )-\frac {8}{27} \operatorname {Subst}\left (\int \frac {\log (x)}{3-x} \, dx,x,3-x\right )-\frac {8}{27} \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,3-x\right )+\frac {4}{3} \operatorname {Subst}\left (\int \left (\frac {1}{3 (-3+x)^2}-\frac {1}{9 (-3+x)}+\frac {1}{9 x}\right ) \, dx,x,3-x\right )\\ &=\frac {64}{27 (27-x)^2}+\frac {64}{729 (27-x)}+\frac {64}{729 x}-\frac {8}{27} \log (3-x)+\frac {32 \log (3-x)}{729 (27-x)}+\frac {32 \log (3-x)}{27 x^2}+\frac {680 \log (3-x)}{729 x}-\frac {8 (3-x) \log (3-x)}{27 x}+\frac {4 \log ^2(3-x)}{x^3}+\frac {8 \text {Li}_2\left (\frac {x}{3}\right )}{27}-\frac {8}{27} \operatorname {Subst}\left (\int \frac {\log \left (\frac {x}{3}\right )}{3-x} \, dx,x,3-x\right )\\ &=\frac {64}{27 (27-x)^2}+\frac {64}{729 (27-x)}+\frac {64}{729 x}-\frac {8}{27} \log (3-x)+\frac {32 \log (3-x)}{729 (27-x)}+\frac {32 \log (3-x)}{27 x^2}+\frac {680 \log (3-x)}{729 x}-\frac {8 (3-x) \log (3-x)}{27 x}+\frac {4 \log ^2(3-x)}{x^3}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.18, size = 92, normalized size = 4.18 \begin {gather*} -\frac {4 \left (2 (-27+x)^2 x^3 \tanh ^{-1}\left (\frac {1}{12} (-15+x)\right )-x \left (472392-17496 x+729 x^2-54 x^3+x^4\right ) \log (3-x)-2187 (-27+x)^2 \log ^2(3-x)+x^2 \left (-34992+(-27+x)^2 x \log (27-x)\right )\right )}{2187 (-27+x)^2 x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-28512*x^2 + 4032*x^3 - 224*x^4 + (-297432*x + 77112*x^2 - 5256*x^3 + 104*x^4)*Log[3 - x] + (-70858
8 + 314928*x - 29160*x^2 + 1008*x^3 - 12*x^4)*Log[3 - x]^2)/(59049*x^4 - 26244*x^5 + 2430*x^6 - 84*x^7 + x^8),
x]

[Out]

(-4*(2*(-27 + x)^2*x^3*ArcTanh[(-15 + x)/12] - x*(472392 - 17496*x + 729*x^2 - 54*x^3 + x^4)*Log[3 - x] - 2187
*(-27 + x)^2*Log[3 - x]^2 + x^2*(-34992 + (-27 + x)^2*x*Log[27 - x])))/(2187*(-27 + x)^2*x^3)

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fricas [B]  time = 0.61, size = 56, normalized size = 2.55 \begin {gather*} \frac {4 \, {\left ({\left (x^{2} - 54 \, x + 729\right )} \log \left (-x + 3\right )^{2} + 16 \, x^{2} - 8 \, {\left (x^{2} - 27 \, x\right )} \log \left (-x + 3\right )\right )}}{x^{5} - 54 \, x^{4} + 729 \, x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x^4+1008*x^3-29160*x^2+314928*x-708588)*log(3-x)^2+(104*x^4-5256*x^3+77112*x^2-297432*x)*log(3
-x)-224*x^4+4032*x^3-28512*x^2)/(x^8-84*x^7+2430*x^6-26244*x^5+59049*x^4),x, algorithm="fricas")

[Out]

4*((x^2 - 54*x + 729)*log(-x + 3)^2 + 16*x^2 - 8*(x^2 - 27*x)*log(-x + 3))/(x^5 - 54*x^4 + 729*x^3)

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giac [B]  time = 0.21, size = 56, normalized size = 2.55 \begin {gather*} -\frac {32}{729} \, {\left (\frac {1}{x - 27} - \frac {x + 27}{x^{2}}\right )} \log \left (-x + 3\right ) - \frac {64 \, {\left (x - 54\right )}}{729 \, {\left (x^{2} - 54 \, x + 729\right )}} + \frac {64}{729 \, x} + \frac {4 \, \log \left (-x + 3\right )^{2}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x^4+1008*x^3-29160*x^2+314928*x-708588)*log(3-x)^2+(104*x^4-5256*x^3+77112*x^2-297432*x)*log(3
-x)-224*x^4+4032*x^3-28512*x^2)/(x^8-84*x^7+2430*x^6-26244*x^5+59049*x^4),x, algorithm="giac")

[Out]

-32/729*(1/(x - 27) - (x + 27)/x^2)*log(-x + 3) - 64/729*(x - 54)/(x^2 - 54*x + 729) + 64/729/x + 4*log(-x + 3
)^2/x^3

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maple [A]  time = 0.11, size = 41, normalized size = 1.86

method	result	size
risch	\(\frac {4 \ln \left (3-x \right )^{2}}{x^{3}}-\frac {32 \ln \left (3-x \right )}{x^{2} \left (x -27\right )}+\frac {64}{\left (x -27\right )^{2} x}\)	\(41\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-12*x^4+1008*x^3-29160*x^2+314928*x-708588)*ln(3-x)^2+(104*x^4-5256*x^3+77112*x^2-297432*x)*ln(3-x)-224*
x^4+4032*x^3-28512*x^2)/(x^8-84*x^7+2430*x^6-26244*x^5+59049*x^4),x,method=_RETURNVERBOSE)

[Out]

4/x^3*ln(3-x)^2-32/x^2/(x-27)*ln(3-x)+64/(x-27)^2/x

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maxima [B]  time = 0.58, size = 56, normalized size = 2.55 \begin {gather*} \frac {4 \, {\left ({\left (x^{2} - 54 \, x + 729\right )} \log \left (-x + 3\right )^{2} + 16 \, x^{2} - 8 \, {\left (x^{2} - 27 \, x\right )} \log \left (-x + 3\right )\right )}}{x^{5} - 54 \, x^{4} + 729 \, x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x^4+1008*x^3-29160*x^2+314928*x-708588)*log(3-x)^2+(104*x^4-5256*x^3+77112*x^2-297432*x)*log(3
-x)-224*x^4+4032*x^3-28512*x^2)/(x^8-84*x^7+2430*x^6-26244*x^5+59049*x^4),x, algorithm="maxima")

[Out]

4*((x^2 - 54*x + 729)*log(-x + 3)^2 + 16*x^2 - 8*(x^2 - 27*x)*log(-x + 3))/(x^5 - 54*x^4 + 729*x^3)

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mupad [B]  time = 0.31, size = 33, normalized size = 1.50 \begin {gather*} \frac {4\,{\left (4\,x+27\,\ln \left (3-x\right )-x\,\ln \left (3-x\right )\right )}^2}{x^3\,{\left (x-27\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(3 - x)^2*(29160*x^2 - 314928*x - 1008*x^3 + 12*x^4 + 708588) + 28512*x^2 - 4032*x^3 + 224*x^4 + log(
3 - x)*(297432*x - 77112*x^2 + 5256*x^3 - 104*x^4))/(59049*x^4 - 26244*x^5 + 2430*x^6 - 84*x^7 + x^8),x)

[Out]

(4*(4*x + 27*log(3 - x) - x*log(3 - x))^2)/(x^3*(x - 27)^2)

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sympy [B]  time = 0.27, size = 39, normalized size = 1.77 \begin {gather*} \frac {64}{x^{3} - 54 x^{2} + 729 x} - \frac {32 \log {\left (3 - x \right )}}{x^{3} - 27 x^{2}} + \frac {4 \log {\left (3 - x \right )}^{2}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x**4+1008*x**3-29160*x**2+314928*x-708588)*ln(3-x)**2+(104*x**4-5256*x**3+77112*x**2-297432*x)
*ln(3-x)-224*x**4+4032*x**3-28512*x**2)/(x**8-84*x**7+2430*x**6-26244*x**5+59049*x**4),x)

[Out]

64/(x**3 - 54*x**2 + 729*x) - 32*log(3 - x)/(x**3 - 27*x**2) + 4*log(3 - x)**2/x**3

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