3.46.86 \(\int \frac {-1875 x^3-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}-2 x^3 \log (3)+(11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}) \log (x)+(-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8) \log ^2(x)+(15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6) \log ^3(x)+(-15000+18000 x-7200 x^2+960 x^3) \log ^4(x)}{6 x^5} \, dx\)

Optimal. Leaf size=39 \[ -x+\frac {\log (3)}{3 x}+(-5+2 x)^4 \left (x+\frac {\frac {x}{2}-\log (x)}{x}\right )^4 \]

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Rubi [B]  time = 1.18, antiderivative size = 261, normalized size of antiderivative = 6.69, number of steps used = 75, number of rules used = 12, integrand size = 213, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {6, 12, 14, 2357, 2295, 2304, 2301, 2296, 2305, 2302, 30, 2353} \begin {gather*} 16 x^8-128 x^7+304 x^6-64 x^6 \log (x)-32 x^5+544 x^5 \log (x)-554 x^4+\frac {625 \log ^4(x)}{x^4}+96 x^4 \log ^2(x)-1488 x^4 \log (x)+40 x^3-\frac {1000 \log ^4(x)}{x^3}-\frac {1250 \log ^3(x)}{x^3}-864 x^3 \log ^2(x)+872 x^3 \log (x)+475 x^2+\frac {600 \log ^4(x)}{x^2}-64 x^2 \log ^3(x)-\frac {500 \log ^3(x)}{x^2}+2664 x^2 \log ^2(x)+\frac {1875 \log ^2(x)}{2 x^2}+1780 x^2 \log (x)+249 x-\frac {625}{2 x}+16 \log ^4(x)-\frac {160 \log ^4(x)}{x}+608 x \log ^3(x)-2080 \log ^3(x)+\frac {2800 \log ^3(x)}{x}-2640 x \log ^2(x)-1350 \log ^2(x)+\frac {2250 \log ^2(x)}{x}-1050 x \log (x)-1375 \log (x)-\frac {625 \log (x)}{2 x}+\frac {1875+\log (9)}{6 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1875*x^3 - 8250*x^4 - 4806*x^5 + 16380*x^6 + 5952*x^7 - 22224*x^8 + 2304*x^9 + 10560*x^10 - 5376*x^11 +
768*x^12 - 2*x^3*Log[3] + (11250*x^2 + 28875*x^3 - 16200*x^4 - 37980*x^5 + 53328*x^6 + 5328*x^7 - 34560*x^8 +
16320*x^9 - 2304*x^10)*Log[x] + (-22500*x - 20250*x^2 + 36900*x^3 - 37440*x^4 - 4896*x^5 + 30816*x^6 - 15552*x
^7 + 2304*x^8)*Log[x]^2 + (15000 - 1500*x + 20400*x^2 - 20640*x^3 + 384*x^4 + 3648*x^5 - 768*x^6)*Log[x]^3 + (
-15000 + 18000*x - 7200*x^2 + 960*x^3)*Log[x]^4)/(6*x^5),x]

[Out]

-625/(2*x) + 249*x + 475*x^2 + 40*x^3 - 554*x^4 - 32*x^5 + 304*x^6 - 128*x^7 + 16*x^8 + (1875 + Log[9])/(6*x)
- 1375*Log[x] - (625*Log[x])/(2*x) - 1050*x*Log[x] + 1780*x^2*Log[x] + 872*x^3*Log[x] - 1488*x^4*Log[x] + 544*
x^5*Log[x] - 64*x^6*Log[x] - 1350*Log[x]^2 + (1875*Log[x]^2)/(2*x^2) + (2250*Log[x]^2)/x - 2640*x*Log[x]^2 + 2
664*x^2*Log[x]^2 - 864*x^3*Log[x]^2 + 96*x^4*Log[x]^2 - 2080*Log[x]^3 - (1250*Log[x]^3)/x^3 - (500*Log[x]^3)/x
^2 + (2800*Log[x]^3)/x + 608*x*Log[x]^3 - 64*x^2*Log[x]^3 + 16*Log[x]^4 + (625*Log[x]^4)/x^4 - (1000*Log[x]^4)
/x^3 + (600*Log[x]^4)/x^2 - (160*Log[x]^4)/x

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

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

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -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 2353

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol]
:> With[{u = ExpandIntegrand[(a + b*Log[c*x^n])^p, (f*x)^m*(d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[
{a, b, c, d, e, f, m, n, p, q, r}, x] && IntegerQ[q] && (GtQ[q, 0] || (IGtQ[p, 0] && IntegerQ[m] && IntegerQ[r
]))

Rule 2357

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}+x^3 (-1875-2 \log (3))+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{6 x^5} \, dx\\ &=\frac {1}{6} \int \frac {-8250 x^4-4806 x^5+16380 x^6+5952 x^7-22224 x^8+2304 x^9+10560 x^{10}-5376 x^{11}+768 x^{12}+x^3 (-1875-2 \log (3))+\left (11250 x^2+28875 x^3-16200 x^4-37980 x^5+53328 x^6+5328 x^7-34560 x^8+16320 x^9-2304 x^{10}\right ) \log (x)+\left (-22500 x-20250 x^2+36900 x^3-37440 x^4-4896 x^5+30816 x^6-15552 x^7+2304 x^8\right ) \log ^2(x)+\left (15000-1500 x+20400 x^2-20640 x^3+384 x^4+3648 x^5-768 x^6\right ) \log ^3(x)+\left (-15000+18000 x-7200 x^2+960 x^3\right ) \log ^4(x)}{x^5} \, dx\\ &=\frac {1}{6} \int \left (\frac {-8250 x-4806 x^2+16380 x^3+5952 x^4-22224 x^5+2304 x^6+10560 x^7-5376 x^8+768 x^9-1875 \left (1+\frac {2 \log (3)}{1875}\right )}{x^2}-\frac {3 (-5+2 x)^3 (1+2 x)^2 \left (30-7 x-14 x^2+24 x^3\right ) \log (x)}{x^3}+\frac {18 (-5+2 x)^3 (1+2 x) \left (10+x+2 x^2+8 x^3\right ) \log ^2(x)}{x^4}-\frac {12 (-5+2 x)^3 \left (10+11 x+22 x^2+8 x^3\right ) \log ^3(x)}{x^5}+\frac {120 (-5+2 x)^3 \log ^4(x)}{x^5}\right ) \, dx\\ &=\frac {1}{6} \int \frac {-8250 x-4806 x^2+16380 x^3+5952 x^4-22224 x^5+2304 x^6+10560 x^7-5376 x^8+768 x^9-1875 \left (1+\frac {2 \log (3)}{1875}\right )}{x^2} \, dx-\frac {1}{2} \int \frac {(-5+2 x)^3 (1+2 x)^2 \left (30-7 x-14 x^2+24 x^3\right ) \log (x)}{x^3} \, dx-2 \int \frac {(-5+2 x)^3 \left (10+11 x+22 x^2+8 x^3\right ) \log ^3(x)}{x^5} \, dx+3 \int \frac {(-5+2 x)^3 (1+2 x) \left (10+x+2 x^2+8 x^3\right ) \log ^2(x)}{x^4} \, dx+20 \int \frac {(-5+2 x)^3 \log ^4(x)}{x^5} \, dx\\ &=\frac {1}{6} \int \left (-4806-\frac {8250}{x}+16380 x+5952 x^2-22224 x^3+2304 x^4+10560 x^5-5376 x^6+768 x^7+\frac {-1875-\log (9)}{x^2}\right ) \, dx-\frac {1}{2} \int \left (12660 \log (x)-\frac {3750 \log (x)}{x^3}-\frac {9625 \log (x)}{x^2}+\frac {5400 \log (x)}{x}-17776 x \log (x)-1776 x^2 \log (x)+11520 x^3 \log (x)-5440 x^4 \log (x)+768 x^5 \log (x)\right ) \, dx-2 \int \left (-304 \log ^3(x)-\frac {1250 \log ^3(x)}{x^5}+\frac {125 \log ^3(x)}{x^4}-\frac {1700 \log ^3(x)}{x^3}+\frac {1720 \log ^3(x)}{x^2}-\frac {32 \log ^3(x)}{x}+64 x \log ^3(x)\right ) \, dx+3 \int \left (-272 \log ^2(x)-\frac {1250 \log ^2(x)}{x^4}-\frac {1125 \log ^2(x)}{x^3}+\frac {2050 \log ^2(x)}{x^2}-\frac {2080 \log ^2(x)}{x}+1712 x \log ^2(x)-864 x^2 \log ^2(x)+128 x^3 \log ^2(x)\right ) \, dx+20 \int \left (-\frac {125 \log ^4(x)}{x^5}+\frac {150 \log ^4(x)}{x^4}-\frac {60 \log ^4(x)}{x^3}+\frac {8 \log ^4(x)}{x^2}\right ) \, dx\\ &=-801 x+1365 x^2+\frac {992 x^3}{3}-926 x^4+\frac {384 x^5}{5}+\frac {880 x^6}{3}-128 x^7+16 x^8+\frac {1875+\log (9)}{6 x}-1375 \log (x)+64 \int \frac {\log ^3(x)}{x} \, dx-128 \int x \log ^3(x) \, dx+160 \int \frac {\log ^4(x)}{x^2} \, dx-250 \int \frac {\log ^3(x)}{x^4} \, dx-384 \int x^5 \log (x) \, dx+384 \int x^3 \log ^2(x) \, dx+608 \int \log ^3(x) \, dx-816 \int \log ^2(x) \, dx+888 \int x^2 \log (x) \, dx-1200 \int \frac {\log ^4(x)}{x^3} \, dx+1875 \int \frac {\log (x)}{x^3} \, dx+2500 \int \frac {\log ^3(x)}{x^5} \, dx-2500 \int \frac {\log ^4(x)}{x^5} \, dx-2592 \int x^2 \log ^2(x) \, dx-2700 \int \frac {\log (x)}{x} \, dx+2720 \int x^4 \log (x) \, dx+3000 \int \frac {\log ^4(x)}{x^4} \, dx-3375 \int \frac {\log ^2(x)}{x^3} \, dx+3400 \int \frac {\log ^3(x)}{x^3} \, dx-3440 \int \frac {\log ^3(x)}{x^2} \, dx-3750 \int \frac {\log ^2(x)}{x^4} \, dx+\frac {9625}{2} \int \frac {\log (x)}{x^2} \, dx+5136 \int x \log ^2(x) \, dx-5760 \int x^3 \log (x) \, dx+6150 \int \frac {\log ^2(x)}{x^2} \, dx-6240 \int \frac {\log ^2(x)}{x} \, dx-6330 \int \log (x) \, dx+8888 \int x \log (x) \, dx\\ &=-\frac {1875}{4 x^2}-\frac {9625}{2 x}+5529 x-857 x^2+232 x^3-566 x^4-32 x^5+304 x^6-128 x^7+16 x^8+\frac {1875+\log (9)}{6 x}-1375 \log (x)-\frac {1875 \log (x)}{2 x^2}-\frac {9625 \log (x)}{2 x}-6330 x \log (x)+4444 x^2 \log (x)+296 x^3 \log (x)-1440 x^4 \log (x)+544 x^5 \log (x)-64 x^6 \log (x)-1350 \log ^2(x)+\frac {1250 \log ^2(x)}{x^3}+\frac {3375 \log ^2(x)}{2 x^2}-\frac {6150 \log ^2(x)}{x}-816 x \log ^2(x)+2568 x^2 \log ^2(x)-864 x^3 \log ^2(x)+96 x^4 \log ^2(x)-\frac {625 \log ^3(x)}{x^4}+\frac {250 \log ^3(x)}{3 x^3}-\frac {1700 \log ^3(x)}{x^2}+\frac {3440 \log ^3(x)}{x}+608 x \log ^3(x)-64 x^2 \log ^3(x)+\frac {625 \log ^4(x)}{x^4}-\frac {1000 \log ^4(x)}{x^3}+\frac {600 \log ^4(x)}{x^2}-\frac {160 \log ^4(x)}{x}+64 \operatorname {Subst}\left (\int x^3 \, dx,x,\log (x)\right )-192 \int x^3 \log (x) \, dx+192 \int x \log ^2(x) \, dx-250 \int \frac {\log ^2(x)}{x^4} \, dx+640 \int \frac {\log ^3(x)}{x^2} \, dx+1632 \int \log (x) \, dx+1728 \int x^2 \log (x) \, dx-1824 \int \log ^2(x) \, dx+1875 \int \frac {\log ^2(x)}{x^5} \, dx-2400 \int \frac {\log ^3(x)}{x^3} \, dx-2500 \int \frac {\log (x)}{x^4} \, dx-2500 \int \frac {\log ^3(x)}{x^5} \, dx-3375 \int \frac {\log (x)}{x^3} \, dx+4000 \int \frac {\log ^3(x)}{x^4} \, dx+5100 \int \frac {\log ^2(x)}{x^3} \, dx-5136 \int x \log (x) \, dx-6240 \operatorname {Subst}\left (\int x^2 \, dx,x,\log (x)\right )-10320 \int \frac {\log ^2(x)}{x^2} \, dx+12300 \int \frac {\log (x)}{x^2} \, dx\\ &=\frac {2500}{9 x^3}+\frac {375}{x^2}-\frac {34225}{2 x}+3897 x+427 x^2+40 x^3-554 x^4-32 x^5+304 x^6-128 x^7+16 x^8+\frac {1875+\log (9)}{6 x}-1375 \log (x)+\frac {2500 \log (x)}{3 x^3}+\frac {750 \log (x)}{x^2}-\frac {34225 \log (x)}{2 x}-4698 x \log (x)+1876 x^2 \log (x)+872 x^3 \log (x)-1488 x^4 \log (x)+544 x^5 \log (x)-64 x^6 \log (x)-1350 \log ^2(x)-\frac {1875 \log ^2(x)}{4 x^4}+\frac {4000 \log ^2(x)}{3 x^3}-\frac {1725 \log ^2(x)}{2 x^2}+\frac {4170 \log ^2(x)}{x}-2640 x \log ^2(x)+2664 x^2 \log ^2(x)-864 x^3 \log ^2(x)+96 x^4 \log ^2(x)-2080 \log ^3(x)-\frac {1250 \log ^3(x)}{x^3}-\frac {500 \log ^3(x)}{x^2}+\frac {2800 \log ^3(x)}{x}+608 x \log ^3(x)-64 x^2 \log ^3(x)+16 \log ^4(x)+\frac {625 \log ^4(x)}{x^4}-\frac {1000 \log ^4(x)}{x^3}+\frac {600 \log ^4(x)}{x^2}-\frac {160 \log ^4(x)}{x}-\frac {500}{3} \int \frac {\log (x)}{x^4} \, dx-192 \int x \log (x) \, dx+\frac {1875}{2} \int \frac {\log (x)}{x^5} \, dx-1875 \int \frac {\log ^2(x)}{x^5} \, dx+1920 \int \frac {\log ^2(x)}{x^2} \, dx-3600 \int \frac {\log ^2(x)}{x^3} \, dx+3648 \int \log (x) \, dx+4000 \int \frac {\log ^2(x)}{x^4} \, dx+5100 \int \frac {\log (x)}{x^3} \, dx-20640 \int \frac {\log (x)}{x^2} \, dx\\ &=-\frac {1875}{32 x^4}+\frac {8000}{27 x^3}-\frac {900}{x^2}+\frac {7055}{2 x}+249 x+475 x^2+40 x^3-554 x^4-32 x^5+304 x^6-128 x^7+16 x^8+\frac {1875+\log (9)}{6 x}-1375 \log (x)-\frac {1875 \log (x)}{8 x^4}+\frac {8000 \log (x)}{9 x^3}-\frac {1800 \log (x)}{x^2}+\frac {7055 \log (x)}{2 x}-1050 x \log (x)+1780 x^2 \log (x)+872 x^3 \log (x)-1488 x^4 \log (x)+544 x^5 \log (x)-64 x^6 \log (x)-1350 \log ^2(x)+\frac {1875 \log ^2(x)}{2 x^2}+\frac {2250 \log ^2(x)}{x}-2640 x \log ^2(x)+2664 x^2 \log ^2(x)-864 x^3 \log ^2(x)+96 x^4 \log ^2(x)-2080 \log ^3(x)-\frac {1250 \log ^3(x)}{x^3}-\frac {500 \log ^3(x)}{x^2}+\frac {2800 \log ^3(x)}{x}+608 x \log ^3(x)-64 x^2 \log ^3(x)+16 \log ^4(x)+\frac {625 \log ^4(x)}{x^4}-\frac {1000 \log ^4(x)}{x^3}+\frac {600 \log ^4(x)}{x^2}-\frac {160 \log ^4(x)}{x}-\frac {1875}{2} \int \frac {\log (x)}{x^5} \, dx+\frac {8000}{3} \int \frac {\log (x)}{x^4} \, dx-3600 \int \frac {\log (x)}{x^3} \, dx+3840 \int \frac {\log (x)}{x^2} \, dx\\ &=-\frac {625}{2 x}+249 x+475 x^2+40 x^3-554 x^4-32 x^5+304 x^6-128 x^7+16 x^8+\frac {1875+\log (9)}{6 x}-1375 \log (x)-\frac {625 \log (x)}{2 x}-1050 x \log (x)+1780 x^2 \log (x)+872 x^3 \log (x)-1488 x^4 \log (x)+544 x^5 \log (x)-64 x^6 \log (x)-1350 \log ^2(x)+\frac {1875 \log ^2(x)}{2 x^2}+\frac {2250 \log ^2(x)}{x}-2640 x \log ^2(x)+2664 x^2 \log ^2(x)-864 x^3 \log ^2(x)+96 x^4 \log ^2(x)-2080 \log ^3(x)-\frac {1250 \log ^3(x)}{x^3}-\frac {500 \log ^3(x)}{x^2}+\frac {2800 \log ^3(x)}{x}+608 x \log ^3(x)-64 x^2 \log ^3(x)+16 \log ^4(x)+\frac {625 \log ^4(x)}{x^4}-\frac {1000 \log ^4(x)}{x^3}+\frac {600 \log ^4(x)}{x^2}-\frac {160 \log ^4(x)}{x}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.07, size = 252, normalized size = 6.46 \begin {gather*} 249 x+475 x^2+40 x^3-554 x^4-32 x^5+304 x^6-128 x^7+16 x^8+\frac {\log (9)}{6 x}-1375 \log (x)-\frac {625 \log (x)}{2 x}-1050 x \log (x)+1780 x^2 \log (x)+872 x^3 \log (x)-1488 x^4 \log (x)+544 x^5 \log (x)-64 x^6 \log (x)-1350 \log ^2(x)+\frac {1875 \log ^2(x)}{2 x^2}+\frac {2250 \log ^2(x)}{x}-2640 x \log ^2(x)+2664 x^2 \log ^2(x)-864 x^3 \log ^2(x)+96 x^4 \log ^2(x)-2080 \log ^3(x)-\frac {1250 \log ^3(x)}{x^3}-\frac {500 \log ^3(x)}{x^2}+\frac {2800 \log ^3(x)}{x}+608 x \log ^3(x)-64 x^2 \log ^3(x)+16 \log ^4(x)+\frac {625 \log ^4(x)}{x^4}-\frac {1000 \log ^4(x)}{x^3}+\frac {600 \log ^4(x)}{x^2}-\frac {160 \log ^4(x)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1875*x^3 - 8250*x^4 - 4806*x^5 + 16380*x^6 + 5952*x^7 - 22224*x^8 + 2304*x^9 + 10560*x^10 - 5376*x
^11 + 768*x^12 - 2*x^3*Log[3] + (11250*x^2 + 28875*x^3 - 16200*x^4 - 37980*x^5 + 53328*x^6 + 5328*x^7 - 34560*
x^8 + 16320*x^9 - 2304*x^10)*Log[x] + (-22500*x - 20250*x^2 + 36900*x^3 - 37440*x^4 - 4896*x^5 + 30816*x^6 - 1
5552*x^7 + 2304*x^8)*Log[x]^2 + (15000 - 1500*x + 20400*x^2 - 20640*x^3 + 384*x^4 + 3648*x^5 - 768*x^6)*Log[x]
^3 + (-15000 + 18000*x - 7200*x^2 + 960*x^3)*Log[x]^4)/(6*x^5),x]

[Out]

249*x + 475*x^2 + 40*x^3 - 554*x^4 - 32*x^5 + 304*x^6 - 128*x^7 + 16*x^8 + Log[9]/(6*x) - 1375*Log[x] - (625*L
og[x])/(2*x) - 1050*x*Log[x] + 1780*x^2*Log[x] + 872*x^3*Log[x] - 1488*x^4*Log[x] + 544*x^5*Log[x] - 64*x^6*Lo
g[x] - 1350*Log[x]^2 + (1875*Log[x]^2)/(2*x^2) + (2250*Log[x]^2)/x - 2640*x*Log[x]^2 + 2664*x^2*Log[x]^2 - 864
*x^3*Log[x]^2 + 96*x^4*Log[x]^2 - 2080*Log[x]^3 - (1250*Log[x]^3)/x^3 - (500*Log[x]^3)/x^2 + (2800*Log[x]^3)/x
+ 608*x*Log[x]^3 - 64*x^2*Log[x]^3 + 16*Log[x]^4 + (625*Log[x]^4)/x^4 - (1000*Log[x]^4)/x^3 + (600*Log[x]^4)/
x^2 - (160*Log[x]^4)/x

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fricas [B]  time = 0.66, size = 201, normalized size = 5.15 \begin {gather*} \frac {96 \, x^{12} - 768 \, x^{11} + 1824 \, x^{10} - 192 \, x^{9} - 3324 \, x^{8} + 240 \, x^{7} + 2850 \, x^{6} + 1494 \, x^{5} + 6 \, {\left (16 \, x^{4} - 160 \, x^{3} + 600 \, x^{2} - 1000 \, x + 625\right )} \log \relax (x)^{4} + 2 \, x^{3} \log \relax (3) - 12 \, {\left (32 \, x^{6} - 304 \, x^{5} + 1040 \, x^{4} - 1400 \, x^{3} + 250 \, x^{2} + 625 \, x\right )} \log \relax (x)^{3} + 9 \, {\left (64 \, x^{8} - 576 \, x^{7} + 1776 \, x^{6} - 1760 \, x^{5} - 900 \, x^{4} + 1500 \, x^{3} + 625 \, x^{2}\right )} \log \relax (x)^{2} - 3 \, {\left (128 \, x^{10} - 1088 \, x^{9} + 2976 \, x^{8} - 1744 \, x^{7} - 3560 \, x^{6} + 2100 \, x^{5} + 2750 \, x^{4} + 625 \, x^{3}\right )} \log \relax (x)}{6 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*((960*x^3-7200*x^2+18000*x-15000)*log(x)^4+(-768*x^6+3648*x^5+384*x^4-20640*x^3+20400*x^2-1500*x
+15000)*log(x)^3+(2304*x^8-15552*x^7+30816*x^6-4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*log(x)^2+(-2304
*x^10+16320*x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+11250*x^2)*log(x)-2*x^3*log(3)+768*
x^12-5376*x^11+10560*x^10+2304*x^9-22224*x^8+5952*x^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x, algorithm="
fricas")

[Out]

1/6*(96*x^12 - 768*x^11 + 1824*x^10 - 192*x^9 - 3324*x^8 + 240*x^7 + 2850*x^6 + 1494*x^5 + 6*(16*x^4 - 160*x^3
+ 600*x^2 - 1000*x + 625)*log(x)^4 + 2*x^3*log(3) - 12*(32*x^6 - 304*x^5 + 1040*x^4 - 1400*x^3 + 250*x^2 + 62
5*x)*log(x)^3 + 9*(64*x^8 - 576*x^7 + 1776*x^6 - 1760*x^5 - 900*x^4 + 1500*x^3 + 625*x^2)*log(x)^2 - 3*(128*x^
10 - 1088*x^9 + 2976*x^8 - 1744*x^7 - 3560*x^6 + 2100*x^5 + 2750*x^4 + 625*x^3)*log(x))/x^4

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {768 \, x^{12} - 5376 \, x^{11} + 10560 \, x^{10} + 2304 \, x^{9} - 22224 \, x^{8} + 5952 \, x^{7} + 16380 \, x^{6} - 4806 \, x^{5} + 120 \, {\left (8 \, x^{3} - 60 \, x^{2} + 150 \, x - 125\right )} \log \relax (x)^{4} - 8250 \, x^{4} - 2 \, x^{3} \log \relax (3) - 12 \, {\left (64 \, x^{6} - 304 \, x^{5} - 32 \, x^{4} + 1720 \, x^{3} - 1700 \, x^{2} + 125 \, x - 1250\right )} \log \relax (x)^{3} - 1875 \, x^{3} + 18 \, {\left (128 \, x^{8} - 864 \, x^{7} + 1712 \, x^{6} - 272 \, x^{5} - 2080 \, x^{4} + 2050 \, x^{3} - 1125 \, x^{2} - 1250 \, x\right )} \log \relax (x)^{2} - 3 \, {\left (768 \, x^{10} - 5440 \, x^{9} + 11520 \, x^{8} - 1776 \, x^{7} - 17776 \, x^{6} + 12660 \, x^{5} + 5400 \, x^{4} - 9625 \, x^{3} - 3750 \, x^{2}\right )} \log \relax (x)}{6 \, x^{5}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*((960*x^3-7200*x^2+18000*x-15000)*log(x)^4+(-768*x^6+3648*x^5+384*x^4-20640*x^3+20400*x^2-1500*x
+15000)*log(x)^3+(2304*x^8-15552*x^7+30816*x^6-4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*log(x)^2+(-2304
*x^10+16320*x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+11250*x^2)*log(x)-2*x^3*log(3)+768*
x^12-5376*x^11+10560*x^10+2304*x^9-22224*x^8+5952*x^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x, algorithm="
giac")

[Out]

integrate(1/6*(768*x^12 - 5376*x^11 + 10560*x^10 + 2304*x^9 - 22224*x^8 + 5952*x^7 + 16380*x^6 - 4806*x^5 + 12
0*(8*x^3 - 60*x^2 + 150*x - 125)*log(x)^4 - 8250*x^4 - 2*x^3*log(3) - 12*(64*x^6 - 304*x^5 - 32*x^4 + 1720*x^3
- 1700*x^2 + 125*x - 1250)*log(x)^3 - 1875*x^3 + 18*(128*x^8 - 864*x^7 + 1712*x^6 - 272*x^5 - 2080*x^4 + 2050
*x^3 - 1125*x^2 - 1250*x)*log(x)^2 - 3*(768*x^10 - 5440*x^9 + 11520*x^8 - 1776*x^7 - 17776*x^6 + 12660*x^5 + 5
400*x^4 - 9625*x^3 - 3750*x^2)*log(x))/x^5, x)

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maple [B]  time = 0.05, size = 197, normalized size = 5.05

method	result	size
risch	\(\frac {\left (16 x^{4}-160 x^{3}+600 x^{2}-1000 x +625\right ) \ln \relax (x )^{4}}{x^{4}}-\frac {2 \left (32 x^{5}-304 x^{4}+1040 x^{3}-1400 x^{2}+250 x +625\right ) \ln \relax (x )^{3}}{x^{3}}+\frac {3 \left (64 x^{6}-576 x^{5}+1776 x^{4}-1760 x^{3}-900 x^{2}+1500 x +625\right ) \ln \relax (x )^{2}}{2 x^{2}}-\frac {\left (128 x^{7}-1088 x^{6}+2976 x^{5}-1744 x^{4}-3560 x^{3}+2100 x^{2}+625\right ) \ln \relax (x )}{2 x}-\frac {-48 x^{9}+384 x^{8}-912 x^{7}+96 x^{6}+1662 x^{5}-120 x^{4}-1425 x^{3}+4125 x \ln \relax (x )-747 x^{2}-\ln \relax (3)}{3 x}\)	\(197\)
default	\(249 x +1780 x^{2} \ln \relax (x )+608 x \ln \relax (x )^{3}+2664 x^{2} \ln \relax (x )^{2}-\frac {625 \ln \relax (x )}{2 x}-128 x^{7}+16 x^{8}+16 \ln \relax (x )^{4}-2080 \ln \relax (x )^{3}-1375 \ln \relax (x )-1350 \ln \relax (x )^{2}+304 x^{6}-32 x^{5}-554 x^{4}+40 x^{3}+475 x^{2}+872 x^{3} \ln \relax (x )-64 x^{6} \ln \relax (x )+\frac {2250 \ln \relax (x )^{2}}{x}+544 x^{5} \ln \relax (x )+96 x^{4} \ln \relax (x )^{2}-1488 x^{4} \ln \relax (x )-2640 x \ln \relax (x )^{2}-1050 x \ln \relax (x )+\frac {1875 \ln \relax (x )^{2}}{2 x^{2}}-64 x^{2} \ln \relax (x )^{3}-864 x^{3} \ln \relax (x )^{2}+\frac {\ln \relax (3)}{3 x}-\frac {1000 \ln \relax (x )^{4}}{x^{3}}-\frac {500 \ln \relax (x )^{3}}{x^{2}}+\frac {600 \ln \relax (x )^{4}}{x^{2}}+\frac {625 \ln \relax (x )^{4}}{x^{4}}-\frac {1250 \ln \relax (x )^{3}}{x^{3}}-\frac {160 \ln \relax (x )^{4}}{x}+\frac {2800 \ln \relax (x )^{3}}{x}\)	\(247\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/6*((960*x^3-7200*x^2+18000*x-15000)*ln(x)^4+(-768*x^6+3648*x^5+384*x^4-20640*x^3+20400*x^2-1500*x+15000)
*ln(x)^3+(2304*x^8-15552*x^7+30816*x^6-4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*ln(x)^2+(-2304*x^10+163
20*x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+11250*x^2)*ln(x)-2*x^3*ln(3)+768*x^12-5376*x
^11+10560*x^10+2304*x^9-22224*x^8+5952*x^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x,method=_RETURNVERBOSE)

[Out]

(16*x^4-160*x^3+600*x^2-1000*x+625)/x^4*ln(x)^4-2*(32*x^5-304*x^4+1040*x^3-1400*x^2+250*x+625)/x^3*ln(x)^3+3/2
*(64*x^6-576*x^5+1776*x^4-1760*x^3-900*x^2+1500*x+625)/x^2*ln(x)^2-1/2*(128*x^7-1088*x^6+2976*x^5-1744*x^4-356
0*x^3+2100*x^2+625)/x*ln(x)-1/3*(-48*x^9+384*x^8-912*x^7+96*x^6+1662*x^5-120*x^4-1425*x^3+4125*x*ln(x)-747*x^2
-ln(3))/x

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maxima [B]  time = 0.38, size = 491, normalized size = 12.59 \begin {gather*} 16 \, x^{8} - 128 \, x^{7} - 64 \, x^{6} \log \relax (x) + 304 \, x^{6} + 544 \, x^{5} \log \relax (x) + 12 \, {\left (8 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )} x^{4} - 32 \, x^{5} - 1440 \, x^{4} \log \relax (x) - 96 \, {\left (9 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 2\right )} x^{3} - 566 \, x^{4} + 296 \, x^{3} \log \relax (x) + 16 \, \log \relax (x)^{4} - 16 \, {\left (4 \, \log \relax (x)^{3} - 6 \, \log \relax (x)^{2} + 6 \, \log \relax (x) - 3\right )} x^{2} + 1284 \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} + 232 \, x^{3} + 4444 \, x^{2} \log \relax (x) - 2080 \, \log \relax (x)^{3} + 608 \, {\left (\log \relax (x)^{3} - 3 \, \log \relax (x)^{2} + 6 \, \log \relax (x) - 6\right )} x - 816 \, {\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x - 857 \, x^{2} - 6330 \, x \log \relax (x) - 1350 \, \log \relax (x)^{2} + 5529 \, x - \frac {160 \, {\left (\log \relax (x)^{4} + 4 \, \log \relax (x)^{3} + 12 \, \log \relax (x)^{2} + 24 \, \log \relax (x) + 24\right )}}{x} + \frac {3440 \, {\left (\log \relax (x)^{3} + 3 \, \log \relax (x)^{2} + 6 \, \log \relax (x) + 6\right )}}{x} - \frac {6150 \, {\left (\log \relax (x)^{2} + 2 \, \log \relax (x) + 2\right )}}{x} + \frac {\log \relax (3)}{3 \, x} - \frac {9625 \, \log \relax (x)}{2 \, x} + \frac {300 \, {\left (2 \, \log \relax (x)^{4} + 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} + 6 \, \log \relax (x) + 3\right )}}{x^{2}} - \frac {425 \, {\left (4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} + 6 \, \log \relax (x) + 3\right )}}{x^{2}} + \frac {3375 \, {\left (2 \, \log \relax (x)^{2} + 2 \, \log \relax (x) + 1\right )}}{4 \, x^{2}} - \frac {4500}{x} - \frac {1875 \, \log \relax (x)}{2 \, x^{2}} - \frac {1000 \, {\left (27 \, \log \relax (x)^{4} + 36 \, \log \relax (x)^{3} + 36 \, \log \relax (x)^{2} + 24 \, \log \relax (x) + 8\right )}}{27 \, x^{3}} + \frac {250 \, {\left (9 \, \log \relax (x)^{3} + 9 \, \log \relax (x)^{2} + 6 \, \log \relax (x) + 2\right )}}{27 \, x^{3}} + \frac {1250 \, {\left (9 \, \log \relax (x)^{2} + 6 \, \log \relax (x) + 2\right )}}{9 \, x^{3}} - \frac {1875}{4 \, x^{2}} + \frac {625 \, {\left (32 \, \log \relax (x)^{4} + 32 \, \log \relax (x)^{3} + 24 \, \log \relax (x)^{2} + 12 \, \log \relax (x) + 3\right )}}{32 \, x^{4}} - \frac {625 \, {\left (32 \, \log \relax (x)^{3} + 24 \, \log \relax (x)^{2} + 12 \, \log \relax (x) + 3\right )}}{32 \, x^{4}} - 1375 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*((960*x^3-7200*x^2+18000*x-15000)*log(x)^4+(-768*x^6+3648*x^5+384*x^4-20640*x^3+20400*x^2-1500*x
+15000)*log(x)^3+(2304*x^8-15552*x^7+30816*x^6-4896*x^5-37440*x^4+36900*x^3-20250*x^2-22500*x)*log(x)^2+(-2304
*x^10+16320*x^9-34560*x^8+5328*x^7+53328*x^6-37980*x^5-16200*x^4+28875*x^3+11250*x^2)*log(x)-2*x^3*log(3)+768*
x^12-5376*x^11+10560*x^10+2304*x^9-22224*x^8+5952*x^7+16380*x^6-4806*x^5-8250*x^4-1875*x^3)/x^5,x, algorithm="
maxima")

[Out]

16*x^8 - 128*x^7 - 64*x^6*log(x) + 304*x^6 + 544*x^5*log(x) + 12*(8*log(x)^2 - 4*log(x) + 1)*x^4 - 32*x^5 - 14
40*x^4*log(x) - 96*(9*log(x)^2 - 6*log(x) + 2)*x^3 - 566*x^4 + 296*x^3*log(x) + 16*log(x)^4 - 16*(4*log(x)^3 -
6*log(x)^2 + 6*log(x) - 3)*x^2 + 1284*(2*log(x)^2 - 2*log(x) + 1)*x^2 + 232*x^3 + 4444*x^2*log(x) - 2080*log(
x)^3 + 608*(log(x)^3 - 3*log(x)^2 + 6*log(x) - 6)*x - 816*(log(x)^2 - 2*log(x) + 2)*x - 857*x^2 - 6330*x*log(x
) - 1350*log(x)^2 + 5529*x - 160*(log(x)^4 + 4*log(x)^3 + 12*log(x)^2 + 24*log(x) + 24)/x + 3440*(log(x)^3 + 3
*log(x)^2 + 6*log(x) + 6)/x - 6150*(log(x)^2 + 2*log(x) + 2)/x + 1/3*log(3)/x - 9625/2*log(x)/x + 300*(2*log(x
)^4 + 4*log(x)^3 + 6*log(x)^2 + 6*log(x) + 3)/x^2 - 425*(4*log(x)^3 + 6*log(x)^2 + 6*log(x) + 3)/x^2 + 3375/4*
(2*log(x)^2 + 2*log(x) + 1)/x^2 - 4500/x - 1875/2*log(x)/x^2 - 1000/27*(27*log(x)^4 + 36*log(x)^3 + 36*log(x)^
2 + 24*log(x) + 8)/x^3 + 250/27*(9*log(x)^3 + 9*log(x)^2 + 6*log(x) + 2)/x^3 + 1250/9*(9*log(x)^2 + 6*log(x) +
2)/x^3 - 1875/4/x^2 + 625/32*(32*log(x)^4 + 32*log(x)^3 + 24*log(x)^2 + 12*log(x) + 3)/x^4 - 625/32*(32*log(x
)^3 + 24*log(x)^2 + 12*log(x) + 3)/x^4 - 1375*log(x)

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mupad [B]  time = 5.97, size = 246, normalized size = 6.31 \begin {gather*} 249\,x-1375\,\ln \relax (x)-\frac {625\,\ln \relax (x)}{2\,x}-2640\,x\,{\ln \relax (x)}^2+1780\,x^2\,\ln \relax (x)+608\,x\,{\ln \relax (x)}^3+872\,x^3\,\ln \relax (x)-1488\,x^4\,\ln \relax (x)+544\,x^5\,\ln \relax (x)-64\,x^6\,\ln \relax (x)-1350\,{\ln \relax (x)}^2-2080\,{\ln \relax (x)}^3+16\,{\ln \relax (x)}^4+\frac {2250\,{\ln \relax (x)}^2}{x}+\frac {2800\,{\ln \relax (x)}^3}{x}+\frac {1875\,{\ln \relax (x)}^2}{2\,x^2}+2664\,x^2\,{\ln \relax (x)}^2-\frac {160\,{\ln \relax (x)}^4}{x}-\frac {500\,{\ln \relax (x)}^3}{x^2}-64\,x^2\,{\ln \relax (x)}^3-864\,x^3\,{\ln \relax (x)}^2+\frac {600\,{\ln \relax (x)}^4}{x^2}-\frac {1250\,{\ln \relax (x)}^3}{x^3}+96\,x^4\,{\ln \relax (x)}^2-\frac {1000\,{\ln \relax (x)}^4}{x^3}+\frac {625\,{\ln \relax (x)}^4}{x^4}+\frac {\ln \relax (3)}{3\,x}-1050\,x\,\ln \relax (x)+475\,x^2+40\,x^3-554\,x^4-32\,x^5+304\,x^6-128\,x^7+16\,x^8 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((log(x)^4*(18000*x - 7200*x^2 + 960*x^3 - 15000))/6 - (log(x)^2*(22500*x + 20250*x^2 - 36900*x^3 + 37440*
x^4 + 4896*x^5 - 30816*x^6 + 15552*x^7 - 2304*x^8))/6 + (log(x)*(11250*x^2 + 28875*x^3 - 16200*x^4 - 37980*x^5
+ 53328*x^6 + 5328*x^7 - 34560*x^8 + 16320*x^9 - 2304*x^10))/6 - (x^3*log(3))/3 - (625*x^3)/2 - 1375*x^4 - 80
1*x^5 + 2730*x^6 + 992*x^7 - 3704*x^8 + 384*x^9 + 1760*x^10 - 896*x^11 + 128*x^12 + (log(x)^3*(20400*x^2 - 150
0*x - 20640*x^3 + 384*x^4 + 3648*x^5 - 768*x^6 + 15000))/6)/x^5,x)

[Out]

249*x - 1375*log(x) - (625*log(x))/(2*x) - 2640*x*log(x)^2 + 1780*x^2*log(x) + 608*x*log(x)^3 + 872*x^3*log(x)
- 1488*x^4*log(x) + 544*x^5*log(x) - 64*x^6*log(x) - 1350*log(x)^2 - 2080*log(x)^3 + 16*log(x)^4 + (2250*log(
x)^2)/x + (2800*log(x)^3)/x + (1875*log(x)^2)/(2*x^2) + 2664*x^2*log(x)^2 - (160*log(x)^4)/x - (500*log(x)^3)/
x^2 - 64*x^2*log(x)^3 - 864*x^3*log(x)^2 + (600*log(x)^4)/x^2 - (1250*log(x)^3)/x^3 + 96*x^4*log(x)^2 - (1000*
log(x)^4)/x^3 + (625*log(x)^4)/x^4 + log(3)/(3*x) - 1050*x*log(x) + 475*x^2 + 40*x^3 - 554*x^4 - 32*x^5 + 304*
x^6 - 128*x^7 + 16*x^8

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sympy [B]  time = 0.59, size = 192, normalized size = 4.92 \begin {gather*} 16 x^{8} - 128 x^{7} + 304 x^{6} - 32 x^{5} - 554 x^{4} + 40 x^{3} + 475 x^{2} + 249 x - 1375 \log {\relax (x )} + \frac {\left (- 128 x^{7} + 1088 x^{6} - 2976 x^{5} + 1744 x^{4} + 3560 x^{3} - 2100 x^{2} - 625\right ) \log {\relax (x )}}{2 x} + \frac {\log {\relax (3 )}}{3 x} + \frac {\left (192 x^{6} - 1728 x^{5} + 5328 x^{4} - 5280 x^{3} - 2700 x^{2} + 4500 x + 1875\right ) \log {\relax (x )}^{2}}{2 x^{2}} + \frac {\left (- 64 x^{5} + 608 x^{4} - 2080 x^{3} + 2800 x^{2} - 500 x - 1250\right ) \log {\relax (x )}^{3}}{x^{3}} + \frac {\left (16 x^{4} - 160 x^{3} + 600 x^{2} - 1000 x + 625\right ) \log {\relax (x )}^{4}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*((960*x**3-7200*x**2+18000*x-15000)*ln(x)**4+(-768*x**6+3648*x**5+384*x**4-20640*x**3+20400*x**2
-1500*x+15000)*ln(x)**3+(2304*x**8-15552*x**7+30816*x**6-4896*x**5-37440*x**4+36900*x**3-20250*x**2-22500*x)*l
n(x)**2+(-2304*x**10+16320*x**9-34560*x**8+5328*x**7+53328*x**6-37980*x**5-16200*x**4+28875*x**3+11250*x**2)*l
n(x)-2*x**3*ln(3)+768*x**12-5376*x**11+10560*x**10+2304*x**9-22224*x**8+5952*x**7+16380*x**6-4806*x**5-8250*x*
*4-1875*x**3)/x**5,x)

[Out]

16*x**8 - 128*x**7 + 304*x**6 - 32*x**5 - 554*x**4 + 40*x**3 + 475*x**2 + 249*x - 1375*log(x) + (-128*x**7 + 1
088*x**6 - 2976*x**5 + 1744*x**4 + 3560*x**3 - 2100*x**2 - 625)*log(x)/(2*x) + log(3)/(3*x) + (192*x**6 - 1728
*x**5 + 5328*x**4 - 5280*x**3 - 2700*x**2 + 4500*x + 1875)*log(x)**2/(2*x**2) + (-64*x**5 + 608*x**4 - 2080*x*
*3 + 2800*x**2 - 500*x - 1250)*log(x)**3/x**3 + (16*x**4 - 160*x**3 + 600*x**2 - 1000*x + 625)*log(x)**4/x**4

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