3.89.30 \(\int \frac {-60 x^4-36 x^5+40 x^6+e^6 (-12-20 x+8 x^2)+e^3 (72 x^2+56 x^3-48 x^4)+(-240 x^4-160 x^5+144 x^6+e^3 (144 x^2+128 x^3-80 x^4)) \log (3-x)+(-360 x^4-264 x^5+192 x^6+e^3 (72 x^2+72 x^3-32 x^4)) \log ^2(3-x)+(-240 x^4-192 x^5+112 x^6) \log ^3(3-x)+(-60 x^4-52 x^5+24 x^6) \log ^4(3-x)}{-3+x} \, dx\)

Optimal. Leaf size=27 \[ 4 x (1+x) \left (e^3-x^2 (1+\log (3-x))^2\right )^2 \]

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Rubi [B]  time = 4.60, antiderivative size = 1308, normalized size of antiderivative = 48.44, number of steps used = 221, number of rules used = 19, integrand size = 194, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.098, Rules used = {6742, 1850, 2418, 2389, 2295, 2390, 2301, 2395, 43, 2296, 2302, 30, 2401, 2305, 2304, 2398, 2411, 2334, 2416} \begin {gather*} 4 \log ^4(3-x) (3-x)^6+16 \log ^3(3-x) (3-x)^6-8 \log ^2(3-x) (3-x)^6+\frac {8}{3} \log (3-x) (3-x)^6+\frac {4}{3} (3-x)^6-76 \log ^4(3-x) (3-x)^5-304 \log ^3(3-x) (3-x)^5+\frac {912}{5} \log ^2(3-x) (3-x)^5-\frac {1824}{25} \log (3-x) (3-x)^5-\frac {912}{25} (3-x)^5+600 \log ^4(3-x) (3-x)^4+2400 \log ^3(3-x) (3-x)^4-1800 \log ^2(3-x) (3-x)^4+900 \log (3-x) (3-x)^4+\left (18-e^3\right ) (3-x)^4+432 (3-x)^4-2520 \log ^4(3-x) (3-x)^3-10080 \log ^3(3-x) (3-x)^3+10080 \log ^2(3-x) (3-x)^3-6720 \log (3-x) (3-x)^3-\frac {16}{9} \left (72-e^3\right ) (3-x)^3-\frac {64}{3} \left (18-e^3\right ) (3-x)^3-2848 (3-x)^3+5940 \log ^4(3-x) (3-x)^2+23760 \log ^3(3-x) (3-x)^2-33048 \log ^2(3-x) (3-x)^2+33048 \log (3-x) (3-x)^2+36 \left (72-e^3\right ) (3-x)^2+216 \left (18-e^3\right ) (3-x)^2+11340 (3-x)^2-7452 \log ^4(3-x) (3-x)-29808 \log ^3(3-x) (3-x)+58320 \log ^2(3-x) (3-x)-576 \left (27-e^3\right ) \log (3-x) (3-x)-116640 \log (3-x) (3-x)+\frac {8 x^6}{3}-\frac {212 x^5}{25}+12 \left (4-e^3\right ) x^4-\left (36-5 e^3\right ) x^4-\frac {474 x^4}{5}+3888 \log ^4(3-x)-4 \left (36-5 e^3\right ) x^3-\frac {16}{9} \left (108-7 e^3\right ) x^3+\frac {8}{3} \left (72-11 e^3\right ) x^3-\frac {1896 x^3}{5}+15552 \log ^3(3-x)+4 \left (216-24 e^3+e^6\right ) x^2-48 \left (27-e^3\right ) x^2-18 \left (36-5 e^3\right ) x^2-8 \left (108-7 e^3\right ) x^2-\frac {8532 x^2}{5}+32 x^6 \log ^2(3-x)+\frac {312}{5} x^5 \log ^2(3-x)+8 \left (18-e^3\right ) x^4 \log ^2(3-x)+8 \left (72-e^3\right ) x^3 \log ^2(3-x)+216 \left (72-e^3\right ) \log ^2(3-x)+864 \left (27-e^3\right ) \log ^2(3-x)+648 \left (18-e^3\right ) \log ^2(3-x)+\frac {192456}{5} \log ^2(3-x)+4 \left (1296-144 e^3+e^6\right ) x+432 \left (72-e^3\right ) x-864 \left (27-e^3\right ) x+1728 \left (18-e^3\right ) x-108 \left (36-5 e^3\right ) x-48 \left (108-7 e^3\right ) x+\frac {84888 x}{5}+24 x^6 \log (3-x)+\frac {272}{5} x^5 \log (3-x)+4 \left (36-5 e^3\right ) x^4 \log (3-x)+\frac {16}{3} \left (108-7 e^3\right ) x^3 \log (3-x)+96 \left (27-e^3\right ) x^2 \log (3-x)+\frac {16}{15} \left (-10 (3-x)^6+216 (3-x)^5-2025 (3-x)^4+10800 (3-x)^3-36450 (3-x)^2+87480 (3-x)-43740 \log (3-x)\right ) \log (3-x)+\frac {156}{25} \left (4 (3-x)^5-75 (3-x)^4+600 (3-x)^3-2700 (3-x)^2+8100 (3-x)-4860 \log (3-x)\right ) \log (3-x)+4 \left (18-e^3\right ) \left (-(3-x)^4+16 (3-x)^3-108 (3-x)^2+432 (3-x)-324 \log (3-x)\right ) \log (3-x)+\frac {8}{3} \left (72-e^3\right ) \left (2 (3-x)^3-27 (3-x)^2+162 (3-x)-162 \log (3-x)\right ) \log (3-x)-864 \left (27-e^3\right ) \log (3-x)+1728 \left (9-e^3\right ) \log (3-x)-324 \left (36-5 e^3\right ) \log (3-x)-144 \left (108-7 e^3\right ) \log (3-x)-\frac {153576}{5} \log (3-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-60*x^4 - 36*x^5 + 40*x^6 + E^6*(-12 - 20*x + 8*x^2) + E^3*(72*x^2 + 56*x^3 - 48*x^4) + (-240*x^4 - 160*x
^5 + 144*x^6 + E^3*(144*x^2 + 128*x^3 - 80*x^4))*Log[3 - x] + (-360*x^4 - 264*x^5 + 192*x^6 + E^3*(72*x^2 + 72
*x^3 - 32*x^4))*Log[3 - x]^2 + (-240*x^4 - 192*x^5 + 112*x^6)*Log[3 - x]^3 + (-60*x^4 - 52*x^5 + 24*x^6)*Log[3
- x]^4)/(-3 + x),x]

[Out]

11340*(3 - x)^2 + 216*(18 - E^3)*(3 - x)^2 + 36*(72 - E^3)*(3 - x)^2 - 2848*(3 - x)^3 - (64*(18 - E^3)*(3 - x)
^3)/3 - (16*(72 - E^3)*(3 - x)^3)/9 + 432*(3 - x)^4 + (18 - E^3)*(3 - x)^4 - (912*(3 - x)^5)/25 + (4*(3 - x)^6
)/3 + (84888*x)/5 - 48*(108 - 7*E^3)*x - 108*(36 - 5*E^3)*x + 1728*(18 - E^3)*x - 864*(27 - E^3)*x + 432*(72 -
E^3)*x + 4*(1296 - 144*E^3 + E^6)*x - (8532*x^2)/5 - 8*(108 - 7*E^3)*x^2 - 18*(36 - 5*E^3)*x^2 - 48*(27 - E^3
)*x^2 + 4*(216 - 24*E^3 + E^6)*x^2 - (1896*x^3)/5 + (8*(72 - 11*E^3)*x^3)/3 - (16*(108 - 7*E^3)*x^3)/9 - 4*(36
- 5*E^3)*x^3 - (474*x^4)/5 - (36 - 5*E^3)*x^4 + 12*(4 - E^3)*x^4 - (212*x^5)/25 + (8*x^6)/3 - (153576*Log[3 -
x])/5 - 144*(108 - 7*E^3)*Log[3 - x] - 324*(36 - 5*E^3)*Log[3 - x] + 1728*(9 - E^3)*Log[3 - x] - 864*(27 - E^
3)*Log[3 - x] - 116640*(3 - x)*Log[3 - x] - 576*(27 - E^3)*(3 - x)*Log[3 - x] + 33048*(3 - x)^2*Log[3 - x] - 6
720*(3 - x)^3*Log[3 - x] + 900*(3 - x)^4*Log[3 - x] - (1824*(3 - x)^5*Log[3 - x])/25 + (8*(3 - x)^6*Log[3 - x]
)/3 + 96*(27 - E^3)*x^2*Log[3 - x] + (16*(108 - 7*E^3)*x^3*Log[3 - x])/3 + 4*(36 - 5*E^3)*x^4*Log[3 - x] + (27
2*x^5*Log[3 - x])/5 + 24*x^6*Log[3 - x] + (16*(87480*(3 - x) - 36450*(3 - x)^2 + 10800*(3 - x)^3 - 2025*(3 - x
)^4 + 216*(3 - x)^5 - 10*(3 - x)^6 - 43740*Log[3 - x])*Log[3 - x])/15 + (156*(8100*(3 - x) - 2700*(3 - x)^2 +
600*(3 - x)^3 - 75*(3 - x)^4 + 4*(3 - x)^5 - 4860*Log[3 - x])*Log[3 - x])/25 + 4*(18 - E^3)*(432*(3 - x) - 108
*(3 - x)^2 + 16*(3 - x)^3 - (3 - x)^4 - 324*Log[3 - x])*Log[3 - x] + (8*(72 - E^3)*(162*(3 - x) - 27*(3 - x)^2
+ 2*(3 - x)^3 - 162*Log[3 - x])*Log[3 - x])/3 + (192456*Log[3 - x]^2)/5 + 648*(18 - E^3)*Log[3 - x]^2 + 864*(
27 - E^3)*Log[3 - x]^2 + 216*(72 - E^3)*Log[3 - x]^2 + 58320*(3 - x)*Log[3 - x]^2 - 33048*(3 - x)^2*Log[3 - x]
^2 + 10080*(3 - x)^3*Log[3 - x]^2 - 1800*(3 - x)^4*Log[3 - x]^2 + (912*(3 - x)^5*Log[3 - x]^2)/5 - 8*(3 - x)^6
*Log[3 - x]^2 + 8*(72 - E^3)*x^3*Log[3 - x]^2 + 8*(18 - E^3)*x^4*Log[3 - x]^2 + (312*x^5*Log[3 - x]^2)/5 + 32*
x^6*Log[3 - x]^2 + 15552*Log[3 - x]^3 - 29808*(3 - x)*Log[3 - x]^3 + 23760*(3 - x)^2*Log[3 - x]^3 - 10080*(3 -
x)^3*Log[3 - x]^3 + 2400*(3 - x)^4*Log[3 - x]^3 - 304*(3 - x)^5*Log[3 - x]^3 + 16*(3 - x)^6*Log[3 - x]^3 + 38
88*Log[3 - x]^4 - 7452*(3 - x)*Log[3 - x]^4 + 5940*(3 - x)^2*Log[3 - x]^4 - 2520*(3 - x)^3*Log[3 - x]^4 + 600*
(3 - x)^4*Log[3 - x]^4 - 76*(3 - x)^5*Log[3 - x]^4 + 4*(3 - x)^6*Log[3 - x]^4

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

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 1850

Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x^n)^p, x], x] /; FreeQ[
{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p, 0] || EqQ[n, 1])

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 2302

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/(x_), x_Symbol] :> Dist[1/(b*n), Subst[Int[x^p, x], x, a + b*L
og[c*x^n]], x] /; FreeQ[{a, b, c, n, p}, 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 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 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 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 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 {4 \left (3 e^6+5 e^6 x-18 e^3 \left (1+\frac {e^3}{9}\right ) x^2-14 e^3 x^3+15 \left (1+\frac {4 e^3}{5}\right ) x^4+9 x^5-10 x^6\right )}{3-x}+\frac {16 x^2 \left (-9 e^3-8 e^3 x+5 \left (3+e^3\right ) x^2+10 x^3-9 x^4\right ) \log (3-x)}{3-x}+\frac {8 x^2 \left (-9 e^3-9 e^3 x+\left (45+4 e^3\right ) x^2+33 x^3-24 x^4\right ) \log ^2(3-x)}{3-x}+\frac {16 x^4 \left (-15-12 x+7 x^2\right ) \log ^3(3-x)}{-3+x}+4 x^4 (5+6 x) \log ^4(3-x)\right ) \, dx\\ &=4 \int \frac {3 e^6+5 e^6 x-18 e^3 \left (1+\frac {e^3}{9}\right ) x^2-14 e^3 x^3+15 \left (1+\frac {4 e^3}{5}\right ) x^4+9 x^5-10 x^6}{3-x} \, dx+4 \int x^4 (5+6 x) \log ^4(3-x) \, dx+8 \int \frac {x^2 \left (-9 e^3-9 e^3 x+\left (45+4 e^3\right ) x^2+33 x^3-24 x^4\right ) \log ^2(3-x)}{3-x} \, dx+16 \int \frac {x^2 \left (-9 e^3-8 e^3 x+5 \left (3+e^3\right ) x^2+10 x^3-9 x^4\right ) \log (3-x)}{3-x} \, dx+16 \int \frac {x^4 \left (-15-12 x+7 x^2\right ) \log ^3(3-x)}{-3+x} \, dx\\ &=4 \int \left (1296 \left (1+\frac {e^3 \left (-144+e^3\right )}{1296}\right )-\frac {432 \left (-9+e^3\right )}{-3+x}+2 \left (216-24 e^3+e^6\right ) x-2 \left (-72+11 e^3\right ) x^2-12 \left (-4+e^3\right ) x^3+21 x^4+10 x^5\right ) \, dx+4 \int \left (5 x^4 \log ^4(3-x)+6 x^5 \log ^4(3-x)\right ) \, dx+8 \int \left (1944 \log ^2(3-x)+\frac {5832 \log ^2(3-x)}{-3+x}+648 x \log ^2(3-x)-3 \left (-72+e^3\right ) x^2 \log ^2(3-x)-4 \left (-18+e^3\right ) x^3 \log ^2(3-x)+39 x^4 \log ^2(3-x)+24 x^5 \log ^2(3-x)\right ) \, dx+16 \int \left (-36 \left (-27+e^3\right ) \log (3-x)-\frac {108 \left (-27+e^3\right ) \log (3-x)}{-3+x}-12 \left (-27+e^3\right ) x \log (3-x)-\left (-108+7 e^3\right ) x^2 \log (3-x)-\left (-36+5 e^3\right ) x^3 \log (3-x)+17 x^4 \log (3-x)+9 x^5 \log (3-x)\right ) \, dx+16 \int \left (324 \log ^3(3-x)+\frac {972 \log ^3(3-x)}{-3+x}+108 x \log ^3(3-x)+36 x^2 \log ^3(3-x)+12 x^3 \log ^3(3-x)+9 x^4 \log ^3(3-x)+7 x^5 \log ^3(3-x)\right ) \, dx\\ &=4 \left (1296-144 e^3+e^6\right ) x+4 \left (216-24 e^3+e^6\right ) x^2+\frac {8}{3} \left (72-11 e^3\right ) x^3+12 \left (4-e^3\right ) x^4+\frac {84 x^5}{5}+\frac {20 x^6}{3}+1728 \left (9-e^3\right ) \log (3-x)+20 \int x^4 \log ^4(3-x) \, dx+24 \int x^5 \log ^4(3-x) \, dx+112 \int x^5 \log ^3(3-x) \, dx+144 \int x^5 \log (3-x) \, dx+144 \int x^4 \log ^3(3-x) \, dx+192 \int x^5 \log ^2(3-x) \, dx+192 \int x^3 \log ^3(3-x) \, dx+272 \int x^4 \log (3-x) \, dx+312 \int x^4 \log ^2(3-x) \, dx+576 \int x^2 \log ^3(3-x) \, dx+1728 \int x \log ^3(3-x) \, dx+5184 \int x \log ^2(3-x) \, dx+5184 \int \log ^3(3-x) \, dx+15552 \int \log ^2(3-x) \, dx+15552 \int \frac {\log ^3(3-x)}{-3+x} \, dx+46656 \int \frac {\log ^2(3-x)}{-3+x} \, dx+\left (16 \left (108-7 e^3\right )\right ) \int x^2 \log (3-x) \, dx+\left (16 \left (36-5 e^3\right )\right ) \int x^3 \log (3-x) \, dx+\left (32 \left (18-e^3\right )\right ) \int x^3 \log ^2(3-x) \, dx+\left (192 \left (27-e^3\right )\right ) \int x \log (3-x) \, dx+\left (576 \left (27-e^3\right )\right ) \int \log (3-x) \, dx+\left (1728 \left (27-e^3\right )\right ) \int \frac {\log (3-x)}{-3+x} \, dx+\left (24 \left (72-e^3\right )\right ) \int x^2 \log ^2(3-x) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.08, size = 40, normalized size = 1.48 \begin {gather*} 4 x (1+x) \left (-e^3+x^2+2 x^2 \log (3-x)+x^2 \log ^2(3-x)\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-60*x^4 - 36*x^5 + 40*x^6 + E^6*(-12 - 20*x + 8*x^2) + E^3*(72*x^2 + 56*x^3 - 48*x^4) + (-240*x^4 -
160*x^5 + 144*x^6 + E^3*(144*x^2 + 128*x^3 - 80*x^4))*Log[3 - x] + (-360*x^4 - 264*x^5 + 192*x^6 + E^3*(72*x^
2 + 72*x^3 - 32*x^4))*Log[3 - x]^2 + (-240*x^4 - 192*x^5 + 112*x^6)*Log[3 - x]^3 + (-60*x^4 - 52*x^5 + 24*x^6)
*Log[3 - x]^4)/(-3 + x),x]

[Out]

4*x*(1 + x)*(-E^3 + x^2 + 2*x^2*Log[3 - x] + x^2*Log[3 - x]^2)^2

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fricas [B]  time = 0.61, size = 123, normalized size = 4.56 \begin {gather*} 4 \, x^{6} + 4 \, x^{5} + 4 \, {\left (x^{6} + x^{5}\right )} \log \left (-x + 3\right )^{4} + 16 \, {\left (x^{6} + x^{5}\right )} \log \left (-x + 3\right )^{3} + 8 \, {\left (3 \, x^{6} + 3 \, x^{5} - {\left (x^{4} + x^{3}\right )} e^{3}\right )} \log \left (-x + 3\right )^{2} + 4 \, {\left (x^{2} + x\right )} e^{6} - 8 \, {\left (x^{4} + x^{3}\right )} e^{3} + 16 \, {\left (x^{6} + x^{5} - {\left (x^{4} + x^{3}\right )} e^{3}\right )} \log \left (-x + 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^6-52*x^5-60*x^4)*log(3-x)^4+(112*x^6-192*x^5-240*x^4)*log(3-x)^3+((-32*x^4+72*x^3+72*x^2)*exp
(3)+192*x^6-264*x^5-360*x^4)*log(3-x)^2+((-80*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*log(3-x)+(8
*x^2-20*x-12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/(x-3),x, algorithm="fricas")

[Out]

4*x^6 + 4*x^5 + 4*(x^6 + x^5)*log(-x + 3)^4 + 16*(x^6 + x^5)*log(-x + 3)^3 + 8*(3*x^6 + 3*x^5 - (x^4 + x^3)*e^
3)*log(-x + 3)^2 + 4*(x^2 + x)*e^6 - 8*(x^4 + x^3)*e^3 + 16*(x^6 + x^5 - (x^4 + x^3)*e^3)*log(-x + 3)

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giac [B]  time = 0.16, size = 193, normalized size = 7.15 \begin {gather*} 4 \, x^{6} \log \left (-x + 3\right )^{4} + 16 \, x^{6} \log \left (-x + 3\right )^{3} + 4 \, x^{5} \log \left (-x + 3\right )^{4} + 24 \, x^{6} \log \left (-x + 3\right )^{2} + 16 \, x^{5} \log \left (-x + 3\right )^{3} + 16 \, x^{6} \log \left (-x + 3\right ) + 24 \, x^{5} \log \left (-x + 3\right )^{2} - 8 \, x^{4} e^{3} \log \left (-x + 3\right )^{2} + 4 \, x^{6} + 16 \, x^{5} \log \left (-x + 3\right ) - 16 \, x^{4} e^{3} \log \left (-x + 3\right ) - 8 \, x^{3} e^{3} \log \left (-x + 3\right )^{2} + 4 \, x^{5} - 8 \, x^{4} e^{3} - 16 \, x^{3} e^{3} \log \left (-x + 3\right ) - 8 \, x^{3} e^{3} + 4 \, x^{2} e^{6} + 4 \, x e^{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^6-52*x^5-60*x^4)*log(3-x)^4+(112*x^6-192*x^5-240*x^4)*log(3-x)^3+((-32*x^4+72*x^3+72*x^2)*exp
(3)+192*x^6-264*x^5-360*x^4)*log(3-x)^2+((-80*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*log(3-x)+(8
*x^2-20*x-12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/(x-3),x, algorithm="giac")

[Out]

4*x^6*log(-x + 3)^4 + 16*x^6*log(-x + 3)^3 + 4*x^5*log(-x + 3)^4 + 24*x^6*log(-x + 3)^2 + 16*x^5*log(-x + 3)^3
+ 16*x^6*log(-x + 3) + 24*x^5*log(-x + 3)^2 - 8*x^4*e^3*log(-x + 3)^2 + 4*x^6 + 16*x^5*log(-x + 3) - 16*x^4*e
^3*log(-x + 3) - 8*x^3*e^3*log(-x + 3)^2 + 4*x^5 - 8*x^4*e^3 - 16*x^3*e^3*log(-x + 3) - 8*x^3*e^3 + 4*x^2*e^6
+ 4*x*e^6

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maple [B]  time = 0.49, size = 144, normalized size = 5.33

method	result	size
risch	\(\left (4 x^{6}+4 x^{5}\right ) \ln \left (3-x \right )^{4}+\left (16 x^{6}+16 x^{5}\right ) \ln \left (3-x \right )^{3}+\left (24 x^{6}-8 x^{4} {\mathrm e}^{3}+24 x^{5}-8 x^{3} {\mathrm e}^{3}\right ) \ln \left (3-x \right )^{2}+\left (16 x^{6}-16 x^{4} {\mathrm e}^{3}+16 x^{5}-16 x^{3} {\mathrm e}^{3}\right ) \ln \left (3-x \right )+4 x^{6}-8 x^{4} {\mathrm e}^{3}+4 x^{5}+4 x^{2} {\mathrm e}^{6}-8 x^{3} {\mathrm e}^{3}+4 x \,{\mathrm e}^{6}\)	\(144\)
derivativedivides	\(-22356+7452 x +5940 \left (3-x \right )^{2}+3240 \left (3-x \right ) {\mathrm e}^{3}-29808 \left (3-x \right ) \ln \left (3-x \right )+15552 \ln \left (3-x \right )-2520 \left (3-x \right )^{3}+600 \left (3-x \right )^{4}+4 \left (3-x \right )^{6}-76 \left (3-x \right )^{5}+4 \,{\mathrm e}^{6} \left (3-x \right )^{2}-28 \,{\mathrm e}^{6} \left (3-x \right )+4320 \,{\mathrm e}^{3} \left (\left (3-x \right ) \ln \left (3-x \right )-3+x \right )-456 \ln \left (3-x \right )^{2} \left (3-x \right )^{5}+16 \ln \left (3-x \right ) \left (3-x \right )^{6}+5940 \ln \left (3-x \right )^{4} \left (3-x \right )^{2}-10080 \ln \left (3-x \right )^{3} \left (3-x \right )^{3}+3600 \ln \left (3-x \right )^{2} \left (3-x \right )^{4}-304 \ln \left (3-x \right ) \left (3-x \right )^{5}-12 \,{\mathrm e}^{3} \left (3-x \right )^{4}-7452 \ln \left (3-x \right )^{4} \left (3-x \right )+23760 \ln \left (3-x \right )^{3} \left (3-x \right )^{2}-15120 \ln \left (3-x \right )^{2} \left (3-x \right )^{3}+2400 \ln \left (3-x \right ) \left (3-x \right )^{4}+\frac {520 \,{\mathrm e}^{3} \left (3-x \right )^{3}}{3}-29808 \ln \left (3-x \right )^{3} \left (3-x \right )+35640 \ln \left (3-x \right )^{2} \left (3-x \right )^{2}-10080 \ln \left (3-x \right ) \left (3-x \right )^{3}-1008 \,{\mathrm e}^{3} \left (3-x \right )^{2}-44712 \ln \left (3-x \right )^{2} \left (3-x \right )+23760 \ln \left (3-x \right ) \left (3-x \right )^{2}-1728 \,{\mathrm e}^{3} \ln \left (3-x \right )+4 \ln \left (3-x \right )^{4} \left (3-x \right )^{6}-76 \ln \left (3-x \right )^{4} \left (3-x \right )^{5}+16 \ln \left (3-x \right )^{3} \left (3-x \right )^{6}+600 \ln \left (3-x \right )^{4} \left (3-x \right )^{4}-304 \ln \left (3-x \right )^{3} \left (3-x \right )^{5}+24 \ln \left (3-x \right )^{2} \left (3-x \right )^{6}-2520 \ln \left (3-x \right )^{4} \left (3-x \right )^{3}+2400 \ln \left (3-x \right )^{3} \left (3-x \right )^{4}-864 \,{\mathrm e}^{3} \ln \left (3-x \right )^{2}+832 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right ) \left (3-x \right )^{3}}{3}-\frac {\left (3-x \right )^{3}}{9}\right )-3024 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right ) \left (3-x \right )^{2}}{2}-\frac {\left (3-x \right )^{2}}{4}\right )-32 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right )^{2} \left (3-x \right )^{4}}{4}-\frac {\ln \left (3-x \right ) \left (3-x \right )^{4}}{8}+\frac {\left (3-x \right )^{4}}{32}\right )+312 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right )^{2} \left (3-x \right )^{3}}{3}-\frac {2 \ln \left (3-x \right ) \left (3-x \right )^{3}}{9}+\frac {2 \left (3-x \right )^{3}}{27}\right )-80 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right ) \left (3-x \right )^{4}}{4}-\frac {\left (3-x \right )^{4}}{16}\right )-1008 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right )^{2} \left (3-x \right )^{2}}{2}-\frac {\ln \left (3-x \right ) \left (3-x \right )^{2}}{2}+\frac {\left (3-x \right )^{2}}{4}\right )+1080 \,{\mathrm e}^{3} \left (\ln \left (3-x \right )^{2} \left (3-x \right )-2 \left (3-x \right ) \ln \left (3-x \right )+6-2 x \right )+3888 \ln \left (3-x \right )^{4}+15552 \ln \left (3-x \right )^{3}+23328 \ln \left (3-x \right )^{2}\)	\(845\)
default	\(-22356+7452 x +5940 \left (3-x \right )^{2}+3240 \left (3-x \right ) {\mathrm e}^{3}-29808 \left (3-x \right ) \ln \left (3-x \right )+15552 \ln \left (3-x \right )-2520 \left (3-x \right )^{3}+600 \left (3-x \right )^{4}+4 \left (3-x \right )^{6}-76 \left (3-x \right )^{5}+4 \,{\mathrm e}^{6} \left (3-x \right )^{2}-28 \,{\mathrm e}^{6} \left (3-x \right )+4320 \,{\mathrm e}^{3} \left (\left (3-x \right ) \ln \left (3-x \right )-3+x \right )-456 \ln \left (3-x \right )^{2} \left (3-x \right )^{5}+16 \ln \left (3-x \right ) \left (3-x \right )^{6}+5940 \ln \left (3-x \right )^{4} \left (3-x \right )^{2}-10080 \ln \left (3-x \right )^{3} \left (3-x \right )^{3}+3600 \ln \left (3-x \right )^{2} \left (3-x \right )^{4}-304 \ln \left (3-x \right ) \left (3-x \right )^{5}-12 \,{\mathrm e}^{3} \left (3-x \right )^{4}-7452 \ln \left (3-x \right )^{4} \left (3-x \right )+23760 \ln \left (3-x \right )^{3} \left (3-x \right )^{2}-15120 \ln \left (3-x \right )^{2} \left (3-x \right )^{3}+2400 \ln \left (3-x \right ) \left (3-x \right )^{4}+\frac {520 \,{\mathrm e}^{3} \left (3-x \right )^{3}}{3}-29808 \ln \left (3-x \right )^{3} \left (3-x \right )+35640 \ln \left (3-x \right )^{2} \left (3-x \right )^{2}-10080 \ln \left (3-x \right ) \left (3-x \right )^{3}-1008 \,{\mathrm e}^{3} \left (3-x \right )^{2}-44712 \ln \left (3-x \right )^{2} \left (3-x \right )+23760 \ln \left (3-x \right ) \left (3-x \right )^{2}-1728 \,{\mathrm e}^{3} \ln \left (3-x \right )+4 \ln \left (3-x \right )^{4} \left (3-x \right )^{6}-76 \ln \left (3-x \right )^{4} \left (3-x \right )^{5}+16 \ln \left (3-x \right )^{3} \left (3-x \right )^{6}+600 \ln \left (3-x \right )^{4} \left (3-x \right )^{4}-304 \ln \left (3-x \right )^{3} \left (3-x \right )^{5}+24 \ln \left (3-x \right )^{2} \left (3-x \right )^{6}-2520 \ln \left (3-x \right )^{4} \left (3-x \right )^{3}+2400 \ln \left (3-x \right )^{3} \left (3-x \right )^{4}-864 \,{\mathrm e}^{3} \ln \left (3-x \right )^{2}+832 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right ) \left (3-x \right )^{3}}{3}-\frac {\left (3-x \right )^{3}}{9}\right )-3024 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right ) \left (3-x \right )^{2}}{2}-\frac {\left (3-x \right )^{2}}{4}\right )-32 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right )^{2} \left (3-x \right )^{4}}{4}-\frac {\ln \left (3-x \right ) \left (3-x \right )^{4}}{8}+\frac {\left (3-x \right )^{4}}{32}\right )+312 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right )^{2} \left (3-x \right )^{3}}{3}-\frac {2 \ln \left (3-x \right ) \left (3-x \right )^{3}}{9}+\frac {2 \left (3-x \right )^{3}}{27}\right )-80 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right ) \left (3-x \right )^{4}}{4}-\frac {\left (3-x \right )^{4}}{16}\right )-1008 \,{\mathrm e}^{3} \left (\frac {\ln \left (3-x \right )^{2} \left (3-x \right )^{2}}{2}-\frac {\ln \left (3-x \right ) \left (3-x \right )^{2}}{2}+\frac {\left (3-x \right )^{2}}{4}\right )+1080 \,{\mathrm e}^{3} \left (\ln \left (3-x \right )^{2} \left (3-x \right )-2 \left (3-x \right ) \ln \left (3-x \right )+6-2 x \right )+3888 \ln \left (3-x \right )^{4}+15552 \ln \left (3-x \right )^{3}+23328 \ln \left (3-x \right )^{2}\)	\(845\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((24*x^6-52*x^5-60*x^4)*ln(3-x)^4+(112*x^6-192*x^5-240*x^4)*ln(3-x)^3+((-32*x^4+72*x^3+72*x^2)*exp(3)+192*
x^6-264*x^5-360*x^4)*ln(3-x)^2+((-80*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*ln(3-x)+(8*x^2-20*x-
12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/(x-3),x,method=_RETURNVERBOSE)

[Out]

(4*x^6+4*x^5)*ln(3-x)^4+(16*x^6+16*x^5)*ln(3-x)^3+(24*x^6-8*x^4*exp(3)+24*x^5-8*x^3*exp(3))*ln(3-x)^2+(16*x^6-
16*x^4*exp(3)+16*x^5-16*x^3*exp(3))*ln(3-x)+4*x^6-8*x^4*exp(3)+4*x^5+4*x^2*exp(6)-8*x^3*exp(3)+4*x*exp(6)

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maxima [B]  time = 0.43, size = 1389, normalized size = 51.44 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^6-52*x^5-60*x^4)*log(3-x)^4+(112*x^6-192*x^5-240*x^4)*log(3-x)^3+((-32*x^4+72*x^3+72*x^2)*exp
(3)+192*x^6-264*x^5-360*x^4)*log(3-x)^2+((-80*x^4+128*x^3+144*x^2)*exp(3)+144*x^6-160*x^5-240*x^4)*log(3-x)+(8
*x^2-20*x-12)*exp(3)^2+(-48*x^4+56*x^3+72*x^2)*exp(3)+40*x^6-36*x^5-60*x^4)/(x-3),x, algorithm="maxima")

[Out]

2/27*(54*log(-x + 3)^4 - 36*log(-x + 3)^3 + 18*log(-x + 3)^2 - 6*log(-x + 3) + 1)*(x - 3)^6 + 14/27*(36*log(-x
+ 3)^3 - 18*log(-x + 3)^2 + 6*log(-x + 3) - 1)*(x - 3)^6 + 16/9*(18*log(-x + 3)^2 - 6*log(-x + 3) + 1)*(x - 3
)^6 + 76/625*(625*log(-x + 3)^4 - 500*log(-x + 3)^3 + 300*log(-x + 3)^2 - 120*log(-x + 3) + 24)*(x - 3)^5 + 18
24/625*(125*log(-x + 3)^3 - 75*log(-x + 3)^2 + 30*log(-x + 3) - 6)*(x - 3)^5 + 3192/125*(25*log(-x + 3)^2 - 10
*log(-x + 3) + 2)*(x - 3)^5 + 8/3*x^6 + 75/4*(32*log(-x + 3)^4 - 32*log(-x + 3)^3 + 24*log(-x + 3)^2 - 12*log(
-x + 3) + 3)*(x - 3)^4 + 375/4*(32*log(-x + 3)^3 - 24*log(-x + 3)^2 + 12*log(-x + 3) - 3)*(x - 3)^4 + 675*(8*l
og(-x + 3)^2 - 4*log(-x + 3) + 1)*(x - 3)^4 - 212/25*x^5 + 280/3*(27*log(-x + 3)^4 - 36*log(-x + 3)^3 + 36*log
(-x + 3)^2 - 24*log(-x + 3) + 8)*(x - 3)^3 + 4480/3*(9*log(-x + 3)^3 - 9*log(-x + 3)^2 + 6*log(-x + 3) - 2)*(x
- 3)^3 + 2800*(9*log(-x + 3)^2 - 6*log(-x + 3) + 2)*(x - 3)^3 - 414/5*x^4 + 3888*log(-x + 3)^4 + 2970*(2*log(
-x + 3)^4 - 4*log(-x + 3)^3 + 6*log(-x + 3)^2 - 6*log(-x + 3) + 3)*(x - 3)^2 + 8910*(4*log(-x + 3)^3 - 6*log(-
x + 3)^2 + 6*log(-x + 3) - 3)*(x - 3)^2 + 35640*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 - 2616/5*x^3 -
20*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x - 3))*e^3*log(-x + 3) + 64/3*(2*x^3 + 9*x^2 + 54*x + 162*log(x -
3))*e^3*log(-x + 3) + 72*(x^2 + 6*x + 18*log(x - 3))*e^3*log(-x + 3) + 15552*log(-x + 3)^3 + 7452*(log(-x + 3
)^4 - 4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*log(-x + 3) + 24)*(x - 3) + 59616*(log(-x + 3)^3 - 3*log(-x + 3)
^2 + 6*log(-x + 3) - 6)*(x - 3) + 134136*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3) - 18252/5*x^2 + 4*(x^2 +
6*x + 18*log(x - 3))*e^6 - 20*(x + 3*log(x - 3))*e^6 - 1/9*(9*(8*log(-x + 3)^2 - 4*log(-x + 3) + 1)*(x - 3)^4
+ 128*(9*log(-x + 3)^2 - 6*log(-x + 3) + 2)*(x - 3)^3 + 3888*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 +
7776*log(-x + 3)^3 + 31104*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^3 + 2/3*(4*(9*log(-x + 3)^2 - 6*log
(-x + 3) + 2)*(x - 3)^3 + 243*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 + 972*log(-x + 3)^3 + 2916*(log(
-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^3 + 5/3*(3*x^4 + 28*x^3 + 234*x^2 + 1944*log(x - 3)^2 + 2700*x + 810
0*log(x - 3))*e^3 - 12*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x - 3))*e^3 + 18*((2*log(-x + 3)^2 - 2*log(-x +
3) + 1)*(x - 3)^2 + 12*log(-x + 3)^3 + 24*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^3 - 32/9*(4*x^3 + 45
*x^2 + 486*log(x - 3)^2 + 594*x + 1782*log(x - 3))*e^3 + 28/3*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^3 - 36
*(x^2 + 18*log(x - 3)^2 + 18*x + 54*log(x - 3))*e^3 + 36*(x^2 + 6*x + 18*log(x - 3))*e^3 - 12*e^6*log(x - 3) -
23328*log(x - 3)^2 + 12/5*(10*x^6 + 36*x^5 + 135*x^4 + 540*x^3 + 2430*x^2 + 14580*x + 43740*log(x - 3))*log(-
x + 3) - 8*(4*x^5 + 15*x^4 + 60*x^3 + 270*x^2 + 1620*x + 4860*log(x - 3))*log(-x + 3) - 60*(x^4 + 4*x^3 + 18*x
^2 + 108*x + 324*log(x - 3))*log(-x + 3) - 187272/5*x - 561816/5*log(x - 3)

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mupad [B]  time = 5.83, size = 39, normalized size = 1.44 \begin {gather*} 4\,x\,\left (x+1\right )\,{\left (x^2\,{\ln \left (3-x\right )}^2+2\,x^2\,\ln \left (3-x\right )+x^2-{\mathrm {e}}^3\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(6)*(20*x - 8*x^2 + 12) - log(3 - x)^2*(exp(3)*(72*x^2 + 72*x^3 - 32*x^4) - 360*x^4 - 264*x^5 + 192*x
^6) + log(3 - x)^4*(60*x^4 + 52*x^5 - 24*x^6) + log(3 - x)^3*(240*x^4 + 192*x^5 - 112*x^6) - exp(3)*(72*x^2 +
56*x^3 - 48*x^4) - log(3 - x)*(exp(3)*(144*x^2 + 128*x^3 - 80*x^4) - 240*x^4 - 160*x^5 + 144*x^6) + 60*x^4 + 3
6*x^5 - 40*x^6)/(x - 3),x)

[Out]

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

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sympy [B]  time = 0.35, size = 141, normalized size = 5.22 \begin {gather*} 4 x^{6} + 4 x^{5} - 8 x^{4} e^{3} - 8 x^{3} e^{3} + 4 x^{2} e^{6} + 4 x e^{6} + \left (4 x^{6} + 4 x^{5}\right ) \log {\left (3 - x \right )}^{4} + \left (16 x^{6} + 16 x^{5}\right ) \log {\left (3 - x \right )}^{3} + \left (16 x^{6} + 16 x^{5} - 16 x^{4} e^{3} - 16 x^{3} e^{3}\right ) \log {\left (3 - x \right )} + \left (24 x^{6} + 24 x^{5} - 8 x^{4} e^{3} - 8 x^{3} e^{3}\right ) \log {\left (3 - x \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x**6-52*x**5-60*x**4)*ln(3-x)**4+(112*x**6-192*x**5-240*x**4)*ln(3-x)**3+((-32*x**4+72*x**3+72*
x**2)*exp(3)+192*x**6-264*x**5-360*x**4)*ln(3-x)**2+((-80*x**4+128*x**3+144*x**2)*exp(3)+144*x**6-160*x**5-240
*x**4)*ln(3-x)+(8*x**2-20*x-12)*exp(3)**2+(-48*x**4+56*x**3+72*x**2)*exp(3)+40*x**6-36*x**5-60*x**4)/(x-3),x)

[Out]

4*x**6 + 4*x**5 - 8*x**4*exp(3) - 8*x**3*exp(3) + 4*x**2*exp(6) + 4*x*exp(6) + (4*x**6 + 4*x**5)*log(3 - x)**4
+ (16*x**6 + 16*x**5)*log(3 - x)**3 + (16*x**6 + 16*x**5 - 16*x**4*exp(3) - 16*x**3*exp(3))*log(3 - x) + (24*
x**6 + 24*x**5 - 8*x**4*exp(3) - 8*x**3*exp(3))*log(3 - x)**2

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