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

Optimal. Leaf size=27 $$4x(1+x){(e^3-x^2(1+\log (3-x){)}^2)}^2$$

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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{array}{c}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+(18-e^3)(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}(72-e^3)(3-x{)}^3-\frac{64}{3}(18-e^3)(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(72-e^3)(3-x{)}^2+216(18-e^3)(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(27-e^3)\log (3-x)(3-x)-116640\log (3-x)(3-x)+\frac{8x^6}{3}-\frac{212x^5}{25}+12(4-e^3)x^4-(36-5e^3)x^4-\frac{474x^4}{5}+3888{\log }^4(3-x)-4(36-5e^3)x^3-\frac{16}{9}(108-7e^3)x^3+\frac{8}{3}(72-11e^3)x^3-\frac{1896x^3}{5}+15552{\log }^3(3-x)+4(216-24e^3+e^6)x^2-48(27-e^3)x^2-18(36-5e^3)x^2-8(108-7e^3)x^2-\frac{8532x^2}{5}+32x^6{\log }^2(3-x)+\frac{312}{5}{x}^5{\log }^2(3-x)+8(18-e^3)x^4{\log }^2(3-x)+8(72-e^3)x^3{\log }^2(3-x)+216(72-e^3){\log }^2(3-x)+864(27-e^3){\log }^2(3-x)+648(18-e^3){\log }^2(3-x)+\frac{192456}{5}{\log }^2(3-x)+4(1296-144e^3+e^6)x+432(72-e^3)x-864(27-e^3)x+1728(18-e^3)x-108(36-5e^3)x-48(108-7e^3)x+\frac{84888x}{5}+24x^6\log (3-x)+\frac{272}{5}{x}^5\log (3-x)+4(36-5e^3)x^4\log (3-x)+\frac{16}{3}(108-7e^3)x^3\log (3-x)+96(27-e^3)x^2\log (3-x)+\frac{16}{15}(-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))\log (3-x)+\frac{156}{25}(4(3-x{)}^5-75(3-x{)}^4+600(3-x{)}^3-2700(3-x{)}^2+8100(3-x)-4860\log (3-x))\log (3-x)+4(18-e^3)(-(3-x{)}^4+16(3-x{)}^3-108(3-x{)}^2+432(3-x)-324\log (3-x))\log (3-x)+\frac{8}{3}(72-e^3)(2(3-x{)}^3-27(3-x{)}^2+162(3-x)-162\log (3-x))\log (3-x)-864(27-e^3)\log (3-x)+1728(9-e^3)\log (3-x)-324(36-5e^3)\log (3-x)-144(108-7e^3)\log (3-x)-\frac{153576}{5}\log (3-x)\end{array}$$

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{array}{c}\begin{array}{rl}\text{integral}& =\int (\frac{4(3e^6+5e^{6}x-18e^3(1+\frac{e^3}{9})x^2-14e^3{x}^3+15(1+\frac{4e^3}{5})x^4+9x^5-10x^6)}{3-x}+\frac{16x^2(-9e^3-8e^{3}x+5(3+e^3)x^2+10x^3-9x^4)\log (3-x)}{3-x}+\frac{8x^2(-9e^3-9e^{3}x+(45+4e^3)x^2+33x^3-24x^4){\log }^2(3-x)}{3-x}+\frac{16x^4(-15-12x+7x^2){\log }^3(3-x)}{-3+x}+4x^4(5+6x){\log }^4(3-x))dx\\ & =4\int \frac{3e^6+5e^{6}x-18e^3(1+\frac{e^3}{9})x^2-14e^3{x}^3+15(1+\frac{4e^3}{5})x^4+9x^5-10x^6}{3-x}dx+4\int x^4(5+6x){\log }^4(3-x)dx+8\int \frac{x^2(-9e^3-9e^{3}x+(45+4e^3)x^2+33x^3-24x^4){\log }^2(3-x)}{3-x}dx+16\int \frac{x^2(-9e^3-8e^{3}x+5(3+e^3)x^2+10x^3-9x^4)\log (3-x)}{3-x}dx+16\int \frac{x^4(-15-12x+7x^2){\log }^3(3-x)}{-3+x}dx\\ & =4\int (1296(1+\frac{e^3(-144+e^3)}{1296})-\frac{432(-9+e^3)}{-3+x}+2(216-24e^3+e^6)x-2(-72+11e^3)x^2-12(-4+e^3)x^3+21x^4+10x^5)dx+4\int (5x^4{\log }^4(3-x)+6x^5{\log }^4(3-x))dx+8\int (1944{\log }^2(3-x)+\frac{5832{\log }^2(3-x)}{-3+x}+648x{\log }^2(3-x)-3(-72+e^3)x^2{\log }^2(3-x)-4(-18+e^3)x^3{\log }^2(3-x)+39x^4{\log }^2(3-x)+24x^5{\log }^2(3-x))dx+16\int (-36(-27+e^3)\log (3-x)-\frac{108(-27+e^3)\log (3-x)}{-3+x}-12(-27+e^3)x\log (3-x)-(-108+7e^3)x^2\log (3-x)-(-36+5e^3)x^3\log (3-x)+17x^4\log (3-x)+9x^5\log (3-x))dx+16\int (324{\log }^3(3-x)+\frac{972{\log }^3(3-x)}{-3+x}+108x{\log }^3(3-x)+36x^2{\log }^3(3-x)+12x^3{\log }^3(3-x)+9x^4{\log }^3(3-x)+7x^5{\log }^3(3-x))dx\\ & =4(1296-144e^3+e^6)x+4(216-24e^3+e^6)x^2+\frac{8}{3}(72-11e^3)x^3+12(4-e^3)x^4+\frac{84x^5}{5}+\frac{20x^6}{3}+1728(9-e^3)\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(108-7e^3)\right)\int x^2\log (3-x)dx+\left(16(36-5e^3)\right)\int x^3\log (3-x)dx+\left(32(18-e^3)\right)\int x^3{\log }^2(3-x)dx+\left(192(27-e^3)\right)\int x\log (3-x)dx+\left(576(27-e^3)\right)\int \log (3-x)dx+\left(1728(27-e^3)\right)\int \frac{\log (3-x)}{-3+x}dx+\left(24(72-e^3)\right)\int x^2{\log }^2(3-x)dx\\ & =\text{Rest of rules removed due to large latex content}\end{array}\end{array}$$

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

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 $$\begin{array}{c}4x^6+4x^5+4(x^6+x^5)\log {(-x+3)}^4+16(x^6+x^5)\log {(-x+3)}^3+8(3x^6+3x^5-(x^4+x^3)e^3)\log {(-x+3)}^2+4(x^2+x)e^6-8(x^4+x^3)e^3+16(x^6+x^5-(x^4+x^3)e^3)\log (-x+3)\end{array}$$

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 $$\begin{array}{c}4x^6\log {(-x+3)}^4+16x^6\log {(-x+3)}^3+4x^5\log {(-x+3)}^4+24x^6\log {(-x+3)}^2+16x^5\log {(-x+3)}^3+16x^6\log (-x+3)+24x^5\log {(-x+3)}^2-8x^4{e}^3\log {(-x+3)}^2+4x^6+16x^5\log (-x+3)-16x^4{e}^3\log (-x+3)-8x^3{e}^3\log {(-x+3)}^2+4x^5-8x^4{e}^3-16x^3{e}^3\log (-x+3)-8x^3{e}^3+4x^2{e}^6+4x{e}^6\end{array}$$

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

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 $$\begin{array}{c}4x(x+1){(x^2{\ln (3-x)}^2+2x^2\ln (3-x)+x^2-{\mathrm{e}}^3)}^2\end{array}$$

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 $$\begin{array}{c}4x^6+4x^5-8x^4{e}^3-8x^3{e}^3+4x^2{e}^6+4x{e}^6+(4x^6+4x^5)\log {(3-x)}^4+(16x^6+16x^5)\log {(3-x)}^3+(16x^6+16x^5-16x^4{e}^3-16x^3{e}^3)\log (3-x)+(24x^6+24x^5-8x^4{e}^3-8x^3{e}^3)\log {(3-x)}^2\end{array}$$

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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