3.1.18 $\int (-1119744+(-1119744-1306368x)\log (x)+(-1306368x-653184x^2){\log }^2(x)+(-653184x^2-181440x^3){\log }^3(x)+(-181440x^3-30240x^4){\log }^4(x)+(-30240x^4-3024x^5){\log }^5(x)+(-3024x^5-168x^6){\log }^6(x)+(-168x^6-4x^7){\log }^7(x)-4x^7{\log }^8(x))dx$

Optimal. Leaf size=13 $$-\frac{1}{2}(-6-x\log (x){)}^8$$

________________________________________________________________________________________

Rubi [B]  time = 1.11, antiderivative size = 105, normalized size of antiderivative = 8.08, number of steps used = 83, number of rules used = 6, integrand size = 113, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.053, Rules used = {2313, 9, 1593, 2353, 2305, 2304} $$\begin{array}{c}-\frac{1}{2}{x}^8{\log }^8(x)-24x^7{\log }^7(x)-504x^6{\log }^6(x)-6048x^5{\log }^5(x)-45360x^4{\log }^4(x)-217728x^3{\log }^3(x)-326592x^2-653184x^2{\log }^2(x)+653184x^2\log (x)-93312(7x^2+12x)\log (x)+\frac{46656}{7}(7x+12{)}^2-1119744x\end{array}$$

Antiderivative was successfully verified.

[In]

Int[-1119744 + (-1119744 - 1306368*x)*Log[x] + (-1306368*x - 653184*x^2)*Log[x]^2 + (-653184*x^2 - 181440*x^3)
*Log[x]^3 + (-181440*x^3 - 30240*x^4)*Log[x]^4 + (-30240*x^4 - 3024*x^5)*Log[x]^5 + (-3024*x^5 - 168*x^6)*Log[
x]^6 + (-168*x^6 - 4*x^7)*Log[x]^7 - 4*x^7*Log[x]^8,x]

[Out]

-1119744*x - 326592*x^2 + (46656*(12 + 7*x)^2)/7 + 653184*x^2*Log[x] - 93312*(12*x + 7*x^2)*Log[x] - 653184*x^
2*Log[x]^2 - 217728*x^3*Log[x]^3 - 45360*x^4*Log[x]^4 - 6048*x^5*Log[x]^5 - 504*x^6*Log[x]^6 - 24*x^7*Log[x]^7
- (x^8*Log[x]^8)/2

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rule 1593

Int[(u_.)*((a_.)*(x_)^(p_.) + (b_.)*(x_)^(q_.))^(n_.), x_Symbol] :> Int[u*x^(n*p)*(a + b*x^(q - p))^n, x] /; F
reeQ[{a, b, p, q}, x] && IntegerQ[n] && PosQ[q - p]

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 2313

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> With[{u = IntHide[(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]

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
]))

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =-1119744x-4\int x^7{\log }^8(x)dx+\int (-1119744-1306368x)\log (x)dx+\int (-1306368x-653184x^2){\log }^2(x)dx+\int (-653184x^2-181440x^3){\log }^3(x)dx+\int (-181440x^3-30240x^4){\log }^4(x)dx+\int (-30240x^4-3024x^5){\log }^5(x)dx+\int (-3024x^5-168x^6){\log }^6(x)dx+\int (-168x^6-4x^7){\log }^7(x)dx\\ & =-1119744x-93312(12x+7x^2)\log (x)-\frac{1}{2}{x}^8{\log }^8(x)+4\int x^7{\log }^7(x)dx-\int 93312(-12-7x)dx+\int (-1306368-653184x)x{\log }^2(x)dx+\int (-653184-181440x)x^2{\log }^3(x)dx+\int (-181440-30240x)x^3{\log }^4(x)dx+\int (-30240-3024x)x^4{\log }^5(x)dx+\int (-3024-168x)x^5{\log }^6(x)dx+\int (-168-4x)x^6{\log }^7(x)dx\\ & =-1119744x+\frac{46656}{7}(12+7x{)}^2-93312(12x+7x^2)\log (x)+\frac{1}{2}{x}^8{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)-\frac{7}{2}\int x^7{\log }^6(x)dx+\int (-1306368x{\log }^2(x)-653184x^2{\log }^2(x))dx+\int (-653184x^2{\log }^3(x)-181440x^3{\log }^3(x))dx+\int (-181440x^3{\log }^4(x)-30240x^4{\log }^4(x))dx+\int (-30240x^4{\log }^5(x)-3024x^5{\log }^5(x))dx+\int (-3024x^5{\log }^6(x)-168x^6{\log }^6(x))dx+\int (-168x^6{\log }^7(x)-4x^7{\log }^7(x))dx\\ & =-1119744x+\frac{46656}{7}(12+7x{)}^2-93312(12x+7x^2)\log (x)-\frac{7}{16}{x}^8{\log }^6(x)+\frac{1}{2}{x}^8{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)+\frac{21}{8}\int x^7{\log }^5(x)dx-4\int x^7{\log }^7(x)dx-168\int x^6{\log }^6(x)dx-168\int x^6{\log }^7(x)dx-3024\int x^5{\log }^5(x)dx-3024\int x^5{\log }^6(x)dx-30240\int x^4{\log }^4(x)dx-30240\int x^4{\log }^5(x)dx-181440\int x^3{\log }^3(x)dx-181440\int x^3{\log }^4(x)dx-653184\int x^2{\log }^2(x)dx-653184\int x^2{\log }^3(x)dx-1306368\int x{\log }^2(x)dx\\ & =-1119744x+\frac{46656}{7}(12+7x{)}^2-93312(12x+7x^2)\log (x)-653184x^2{\log }^2(x)-217728x^3{\log }^2(x)-217728x^3{\log }^3(x)-45360x^4{\log }^3(x)-45360x^4{\log }^4(x)-6048x^5{\log }^4(x)-6048x^5{\log }^5(x)-504x^6{\log }^5(x)+\frac{21}{64}{x}^8{\log }^5(x)-504x^6{\log }^6(x)-24x^7{\log }^6(x)-\frac{7}{16}{x}^8{\log }^6(x)-24x^7{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)-\frac{105}{64}\int x^7{\log }^4(x)dx+\frac{7}{2}\int x^7{\log }^6(x)dx+144\int x^6{\log }^5(x)dx+168\int x^6{\log }^6(x)dx+2520\int x^5{\log }^4(x)dx+3024\int x^5{\log }^5(x)dx+24192\int x^4{\log }^3(x)dx+30240\int x^4{\log }^4(x)dx+136080\int x^3{\log }^2(x)dx+181440\int x^3{\log }^3(x)dx+435456\int x^2\log (x)dx+653184\int x^2{\log }^2(x)dx+1306368\int x\log (x)dx\\ & =-1119744x-326592x^2-48384x^3+\frac{46656}{7}(12+7x{)}^2+653184x^2\log (x)+145152x^3\log (x)-93312(12x+7x^2)\log (x)-653184x^2{\log }^2(x)+34020x^4{\log }^2(x)-217728x^3{\log }^3(x)+\frac{24192}{5}{x}^5{\log }^3(x)-45360x^4{\log }^4(x)+420x^6{\log }^4(x)-\frac{105}{512}{x}^8{\log }^4(x)-6048x^5{\log }^5(x)+\frac{144}{7}{x}^7{\log }^5(x)+\frac{21}{64}{x}^8{\log }^5(x)-504x^6{\log }^6(x)-24x^7{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)+\frac{105}{128}\int x^7{\log }^3(x)dx-\frac{21}{8}\int x^7{\log }^5(x)dx-\frac{720}{7}\int x^6{\log }^4(x)dx-144\int x^6{\log }^5(x)dx-1680\int x^5{\log }^3(x)dx-2520\int x^5{\log }^4(x)dx-\frac{72576}{5}\int x^4{\log }^2(x)dx-24192\int x^4{\log }^3(x)dx-68040\int x^3\log (x)dx-136080\int x^3{\log }^2(x)dx-435456\int x^2\log (x)dx\\ & =-1119744x-326592x^2+\frac{8505x^4}{2}+\frac{46656}{7}(12+7x{)}^2+653184x^2\log (x)-17010x^4\log (x)-93312(12x+7x^2)\log (x)-653184x^2{\log }^2(x)-\frac{72576}{25}{x}^5{\log }^2(x)-217728x^3{\log }^3(x)-280x^6{\log }^3(x)+\frac{105x^8{\log }^3(x)}{1024}-45360x^4{\log }^4(x)-\frac{720}{49}{x}^7{\log }^4(x)-\frac{105}{512}{x}^8{\log }^4(x)-6048x^5{\log }^5(x)-504x^6{\log }^6(x)-24x^7{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)-\frac{315\int x^7{\log }^2(x)dx}{1024}+\frac{105}{64}\int x^7{\log }^4(x)dx+\frac{2880}{49}\int x^6{\log }^3(x)dx+\frac{720}{7}\int x^6{\log }^4(x)dx+840\int x^5{\log }^2(x)dx+1680\int x^5{\log }^3(x)dx+\frac{145152}{25}\int x^4\log (x)dx+\frac{72576}{5}\int x^4{\log }^2(x)dx+68040\int x^3\log (x)dx\\ & =-1119744x-326592x^2-\frac{145152x^5}{625}+\frac{46656}{7}(12+7x{)}^2+653184x^2\log (x)[phone]\frac{\mathrm{}}{\mathrm{}}{x}^5\log (x)-93312(12x+7x^2)\log (x)-653184x^2{\log }^2(x)+140x^6{\log }^2(x)-\frac{315x^8{\log }^2(x)}{8192}-217728x^3{\log }^3(x)+\frac{2880}{343}{x}^7{\log }^3(x)+\frac{105x^8{\log }^3(x)}{1024}-45360x^4{\log }^4(x)-6048x^5{\log }^5(x)-504x^6{\log }^6(x)-24x^7{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)+\frac{315\int x^7\log (x)dx}{4096}-\frac{105}{128}\int x^7{\log }^3(x)dx-\frac{8640}{343}\int x^6{\log }^2(x)dx-\frac{2880}{49}\int x^6{\log }^3(x)dx-280\int x^5\log (x)dx-840\int x^5{\log }^2(x)dx-\frac{145152}{25}\int x^4\log (x)dx\\ & =-1119744x-326592x^2+\frac{70x^6}{9}-\frac{315x^8}{262144}+\frac{46656}{7}(12+7x{)}^2+653184x^2\log (x)-\frac{140}{3}{x}^6\log (x)+\frac{315x^8\log (x)}{32768}-93312(12x+7x^2)\log (x)-653184x^2{\log }^2(x)-\frac{8640x^7{\log }^2(x)}{2401}-\frac{315x^8{\log }^2(x)}{8192}-217728x^3{\log }^3(x)-45360x^4{\log }^4(x)-6048x^5{\log }^5(x)-504x^6{\log }^6(x)-24x^7{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)+\frac{315\int x^7{\log }^2(x)dx}{1024}+\frac{17280\int x^6\log (x)dx}{2401}+\frac{8640}{343}\int x^6{\log }^2(x)dx+280\int x^5\log (x)dx\\ & =-1119744x-326592x^2-\frac{17280x^7}{117649}-\frac{315x^8}{262144}+\frac{46656}{7}(12+7x{)}^2+653184x^2\log (x)+\frac{17280x^7\log (x)}{16807}+\frac{315x^8\log (x)}{32768}-93312(12x+7x^2)\log (x)-653184x^2{\log }^2(x)-217728x^3{\log }^3(x)-45360x^4{\log }^4(x)-6048x^5{\log }^5(x)-504x^6{\log }^6(x)-24x^7{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)-\frac{315\int x^7\log (x)dx}{4096}-\frac{17280\int x^6\log (x)dx}{2401}\\ & =-1119744x-326592x^2+\frac{46656}{7}(12+7x{)}^2+653184x^2\log (x)-93312(12x+7x^2)\log (x)-653184x^2{\log }^2(x)-217728x^3{\log }^3(x)-45360x^4{\log }^4(x)-6048x^5{\log }^5(x)-504x^6{\log }^6(x)-24x^7{\log }^7(x)-\frac{1}{2}{x}^8{\log }^8(x)\end{array}\end{array}$$

________________________________________________________________________________________

Mathematica [A]  time = 0.01, size = 12, normalized size = 0.92 $$\begin{array}{c}-\frac{1}{2}(6+x\log (x){)}^8\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[-1119744 + (-1119744 - 1306368*x)*Log[x] + (-1306368*x - 653184*x^2)*Log[x]^2 + (-653184*x^2 - 18144
0*x^3)*Log[x]^3 + (-181440*x^3 - 30240*x^4)*Log[x]^4 + (-30240*x^4 - 3024*x^5)*Log[x]^5 + (-3024*x^5 - 168*x^6
)*Log[x]^6 + (-168*x^6 - 4*x^7)*Log[x]^7 - 4*x^7*Log[x]^8,x]

[Out]

-1/2*(6 + x*Log[x])^8

________________________________________________________________________________________

fricas [B]  time = 0.50, size = 69, normalized size = 5.31 $$\begin{array}{c}-\frac{1}{2}{x}^8\log (x{)}^8-24x^7\log (x{)}^7-504x^6\log (x{)}^6-6048x^5\log (x{)}^5-45360x^4\log (x{)}^4-217728x^3\log (x{)}^3-653184x^2\log (x{)}^2-1119744x\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^7*log(x)^8+(-4*x^7-168*x^6)*log(x)^7+(-168*x^6-3024*x^5)*log(x)^6+(-3024*x^5-30240*x^4)*log(x)^
5+(-30240*x^4-181440*x^3)*log(x)^4+(-181440*x^3-653184*x^2)*log(x)^3+(-653184*x^2-1306368*x)*log(x)^2+(-130636
8*x-1119744)*log(x)-1119744,x, algorithm="fricas")

[Out]

-1/2*x^8*log(x)^8 - 24*x^7*log(x)^7 - 504*x^6*log(x)^6 - 6048*x^5*log(x)^5 - 45360*x^4*log(x)^4 - 217728*x^3*l
og(x)^3 - 653184*x^2*log(x)^2 - 1119744*x*log(x)

________________________________________________________________________________________

giac [B]  time = 0.14, size = 69, normalized size = 5.31 $$\begin{array}{c}-\frac{1}{2}{x}^8\log (x{)}^8-24x^7\log (x{)}^7-504x^6\log (x{)}^6-6048x^5\log (x{)}^5-45360x^4\log (x{)}^4-217728x^3\log (x{)}^3-653184x^2\log (x{)}^2-1119744x\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^7*log(x)^8+(-4*x^7-168*x^6)*log(x)^7+(-168*x^6-3024*x^5)*log(x)^6+(-3024*x^5-30240*x^4)*log(x)^
5+(-30240*x^4-181440*x^3)*log(x)^4+(-181440*x^3-653184*x^2)*log(x)^3+(-653184*x^2-1306368*x)*log(x)^2+(-130636
8*x-1119744)*log(x)-1119744,x, algorithm="giac")

[Out]

-1/2*x^8*log(x)^8 - 24*x^7*log(x)^7 - 504*x^6*log(x)^6 - 6048*x^5*log(x)^5 - 45360*x^4*log(x)^4 - 217728*x^3*l
og(x)^3 - 653184*x^2*log(x)^2 - 1119744*x*log(x)

________________________________________________________________________________________

maple [B]  time = 0.06, size = 70, normalized size = 5.38

method	result	size
default	$-6048x^5\ln (x{)}^5-504x^6\ln (x{)}^6-24x^7\ln (x{)}^7-653184x^2\ln (x{)}^2-217728x^3\ln (x{)}^3-1119744x\ln (x)-45360x^4\ln (x{)}^4-\frac{x^8\ln (x{)}^8}{2}$	$70$
risch	$-6048x^5\ln (x{)}^5-504x^6\ln (x{)}^6-24x^7\ln (x{)}^7-653184x^2\ln (x{)}^2-217728x^3\ln (x{)}^3-1119744x\ln (x)-45360x^4\ln (x{)}^4-\frac{x^8\ln (x{)}^8}{2}$	$70$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4*x^7*ln(x)^8+(-4*x^7-168*x^6)*ln(x)^7+(-168*x^6-3024*x^5)*ln(x)^6+(-3024*x^5-30240*x^4)*ln(x)^5+(-30240*
x^4-181440*x^3)*ln(x)^4+(-181440*x^3-653184*x^2)*ln(x)^3+(-653184*x^2-1306368*x)*ln(x)^2+(-1306368*x-1119744)*
ln(x)-1119744,x,method=_RETURNVERBOSE)

[Out]

-6048*x^5*ln(x)^5-504*x^6*ln(x)^6-24*x^7*ln(x)^7-653184*x^2*ln(x)^2-217728*x^3*ln(x)^3-1119744*x*ln(x)-45360*x
^4*ln(x)^4-1/2*x^8*ln(x)^8

________________________________________________________________________________________

maxima [B]  time = 0.52, size = 456, normalized size = 35.08 $$\begin{array}{c}-\frac{1}{262144}(131072\log (x{)}^8-131072\log (x{)}^7+114688\log (x{)}^6-86016\log (x{)}^5+53760\log (x{)}^4-26880\log (x{)}^3+10080\log (x{)}^2-2520\log (x)+315)x^8-\frac{1}{262144}(131072\log (x{)}^7-114688\log (x{)}^6+86016\log (x{)}^5-53760\log (x{)}^4+26880\log (x{)}^3-10080\log (x{)}^2+2520\log (x)-315)x^8-\frac{24}{117649}(117649\log (x{)}^7-117649\log (x{)}^6+100842\log (x{)}^5-72030\log (x{)}^4+41160\log (x{)}^3-17640\log (x{)}^2+5040\log (x)-720)x^7-\frac{24}{117649}(117649\log (x{)}^6-100842\log (x{)}^5+72030\log (x{)}^4-41160\log (x{)}^3+17640\log (x{)}^2-5040\log (x)+720)x^7-\frac{14}{9}(324\log (x{)}^6-324\log (x{)}^5+270\log (x{)}^4-180\log (x{)}^3+90\log (x{)}^2-30\log (x)+5)x^6-\frac{14}{9}(324\log (x{)}^5-270\log (x{)}^4+180\log (x{)}^3-90\log (x{)}^2+30\log (x)-5)x^6-\frac{6048}{625}(625\log (x{)}^5-625\log (x{)}^4+500\log (x{)}^3-300\log (x{)}^2+120\log (x)-24)x^5-\frac{6048}{625}(625\log (x{)}^4-500\log (x{)}^3+300\log (x{)}^2-120\log (x)+24)x^5-\frac{2835}{2}(32\log (x{)}^4-32\log (x{)}^3+24\log (x{)}^2-12\log (x)+3)x^4-\frac{2835}{2}(32\log (x{)}^3-24\log (x{)}^2+12\log (x)-3)x^4-24192(9\log (x{)}^3-9\log (x{)}^2+6\log (x)-2)x^3-24192(9\log (x{)}^2-6\log (x)+2)x^3-326592(2\log (x{)}^2-2\log (x)+1)x^2+326592x^2-93312(7x^2+12x)\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^7*log(x)^8+(-4*x^7-168*x^6)*log(x)^7+(-168*x^6-3024*x^5)*log(x)^6+(-3024*x^5-30240*x^4)*log(x)^
5+(-30240*x^4-181440*x^3)*log(x)^4+(-181440*x^3-653184*x^2)*log(x)^3+(-653184*x^2-1306368*x)*log(x)^2+(-130636
8*x-1119744)*log(x)-1119744,x, algorithm="maxima")

[Out]

-1/262144*(131072*log(x)^8 - 131072*log(x)^7 + 114688*log(x)^6 - 86016*log(x)^5 + 53760*log(x)^4 - 26880*log(x
)^3 + 10080*log(x)^2 - 2520*log(x) + 315)*x^8 - 1/262144*(131072*log(x)^7 - 114688*log(x)^6 + 86016*log(x)^5 -
53760*log(x)^4 + 26880*log(x)^3 - 10080*log(x)^2 + 2520*log(x) - 315)*x^8 - 24/117649*(117649*log(x)^7 - 1176
49*log(x)^6 + 100842*log(x)^5 - 72030*log(x)^4 + 41160*log(x)^3 - 17640*log(x)^2 + 5040*log(x) - 720)*x^7 - 24
/117649*(117649*log(x)^6 - 100842*log(x)^5 + 72030*log(x)^4 - 41160*log(x)^3 + 17640*log(x)^2 - 5040*log(x) +
720)*x^7 - 14/9*(324*log(x)^6 - 324*log(x)^5 + 270*log(x)^4 - 180*log(x)^3 + 90*log(x)^2 - 30*log(x) + 5)*x^6
- 14/9*(324*log(x)^5 - 270*log(x)^4 + 180*log(x)^3 - 90*log(x)^2 + 30*log(x) - 5)*x^6 - 6048/625*(625*log(x)^5
- 625*log(x)^4 + 500*log(x)^3 - 300*log(x)^2 + 120*log(x) - 24)*x^5 - 6048/625*(625*log(x)^4 - 500*log(x)^3 +
300*log(x)^2 - 120*log(x) + 24)*x^5 - 2835/2*(32*log(x)^4 - 32*log(x)^3 + 24*log(x)^2 - 12*log(x) + 3)*x^4 -
2835/2*(32*log(x)^3 - 24*log(x)^2 + 12*log(x) - 3)*x^4 - 24192*(9*log(x)^3 - 9*log(x)^2 + 6*log(x) - 2)*x^3 -
24192*(9*log(x)^2 - 6*log(x) + 2)*x^3 - 326592*(2*log(x)^2 - 2*log(x) + 1)*x^2 + 326592*x^2 - 93312*(7*x^2 + 1
2*x)*log(x)

________________________________________________________________________________________

mupad [B]  time = 0.34, size = 69, normalized size = 5.31 $$\begin{array}{c}-\frac{x^8{\ln (x)}^8}{2}-24x^7{\ln (x)}^7-504x^6{\ln (x)}^6-6048x^5{\ln (x)}^5-45360x^4{\ln (x)}^4-217728x^3{\ln (x)}^3-653184x^2{\ln (x)}^2-1119744x\ln (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- log(x)^2*(1306368*x + 653184*x^2) - log(x)^7*(168*x^6 + 4*x^7) - log(x)^6*(3024*x^5 + 168*x^6) - log(x)^
5*(30240*x^4 + 3024*x^5) - log(x)^4*(181440*x^3 + 30240*x^4) - log(x)^3*(653184*x^2 + 181440*x^3) - 4*x^7*log(
x)^8 - log(x)*(1306368*x + 1119744) - 1119744,x)

[Out]

- 653184*x^2*log(x)^2 - 217728*x^3*log(x)^3 - 45360*x^4*log(x)^4 - 6048*x^5*log(x)^5 - 504*x^6*log(x)^6 - 24*x
^7*log(x)^7 - (x^8*log(x)^8)/2 - 1119744*x*log(x)

________________________________________________________________________________________

sympy [B]  time = 0.21, size = 78, normalized size = 6.00 $$\begin{array}{c}-\frac{x^8\log {(x)}^8}{2}-24x^7\log {(x)}^7-504x^6\log {(x)}^6-6048x^5\log {(x)}^5-45360x^4\log {(x)}^4-217728x^3\log {(x)}^3-653184x^2\log {(x)}^2-1119744x\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x**7*ln(x)**8+(-4*x**7-168*x**6)*ln(x)**7+(-168*x**6-3024*x**5)*ln(x)**6+(-3024*x**5-30240*x**4)*
ln(x)**5+(-30240*x**4-181440*x**3)*ln(x)**4+(-181440*x**3-653184*x**2)*ln(x)**3+(-653184*x**2-1306368*x)*ln(x)
**2+(-1306368*x-1119744)*ln(x)-1119744,x)

[Out]

-x**8*log(x)**8/2 - 24*x**7*log(x)**7 - 504*x**6*log(x)**6 - 6048*x**5*log(x)**5 - 45360*x**4*log(x)**4 - 2177
28*x**3*log(x)**3 - 653184*x**2*log(x)**2 - 1119744*x*log(x)

________________________________________________________________________________________