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

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

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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 {gather*} -\frac {1}{2} x^8 \log ^8(x)-24 x^7 \log ^7(x)-504 x^6 \log ^6(x)-6048 x^5 \log ^5(x)-45360 x^4 \log ^4(x)-217728 x^3 \log ^3(x)-326592 x^2-653184 x^2 \log ^2(x)+653184 x^2 \log (x)-93312 \left (7 x^2+12 x\right ) \log (x)+\frac {46656}{7} (7 x+12)^2-1119744 x \end {gather*}

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 {gather*} \begin {aligned} \text {integral} &=-1119744 x-4 \int x^7 \log ^8(x) \, dx+\int (-1119744-1306368 x) \log (x) \, dx+\int \left (-1306368 x-653184 x^2\right ) \log ^2(x) \, dx+\int \left (-653184 x^2-181440 x^3\right ) \log ^3(x) \, dx+\int \left (-181440 x^3-30240 x^4\right ) \log ^4(x) \, dx+\int \left (-30240 x^4-3024 x^5\right ) \log ^5(x) \, dx+\int \left (-3024 x^5-168 x^6\right ) \log ^6(x) \, dx+\int \left (-168 x^6-4 x^7\right ) \log ^7(x) \, dx\\ &=-1119744 x-93312 \left (12 x+7 x^2\right ) \log (x)-\frac {1}{2} x^8 \log ^8(x)+4 \int x^7 \log ^7(x) \, dx-\int 93312 (-12-7 x) \, dx+\int (-1306368-653184 x) x \log ^2(x) \, dx+\int (-653184-181440 x) x^2 \log ^3(x) \, dx+\int (-181440-30240 x) x^3 \log ^4(x) \, dx+\int (-30240-3024 x) x^4 \log ^5(x) \, dx+\int (-3024-168 x) x^5 \log ^6(x) \, dx+\int (-168-4 x) x^6 \log ^7(x) \, dx\\ &=-1119744 x+\frac {46656}{7} (12+7 x)^2-93312 \left (12 x+7 x^2\right ) \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 \left (-1306368 x \log ^2(x)-653184 x^2 \log ^2(x)\right ) \, dx+\int \left (-653184 x^2 \log ^3(x)-181440 x^3 \log ^3(x)\right ) \, dx+\int \left (-181440 x^3 \log ^4(x)-30240 x^4 \log ^4(x)\right ) \, dx+\int \left (-30240 x^4 \log ^5(x)-3024 x^5 \log ^5(x)\right ) \, dx+\int \left (-3024 x^5 \log ^6(x)-168 x^6 \log ^6(x)\right ) \, dx+\int \left (-168 x^6 \log ^7(x)-4 x^7 \log ^7(x)\right ) \, dx\\ &=-1119744 x+\frac {46656}{7} (12+7 x)^2-93312 \left (12 x+7 x^2\right ) \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\\ &=-1119744 x+\frac {46656}{7} (12+7 x)^2-93312 \left (12 x+7 x^2\right ) \log (x)-653184 x^2 \log ^2(x)-217728 x^3 \log ^2(x)-217728 x^3 \log ^3(x)-45360 x^4 \log ^3(x)-45360 x^4 \log ^4(x)-6048 x^5 \log ^4(x)-6048 x^5 \log ^5(x)-504 x^6 \log ^5(x)+\frac {21}{64} x^8 \log ^5(x)-504 x^6 \log ^6(x)-24 x^7 \log ^6(x)-\frac {7}{16} x^8 \log ^6(x)-24 x^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\\ &=-1119744 x-326592 x^2-48384 x^3+\frac {46656}{7} (12+7 x)^2+653184 x^2 \log (x)+145152 x^3 \log (x)-93312 \left (12 x+7 x^2\right ) \log (x)-653184 x^2 \log ^2(x)+34020 x^4 \log ^2(x)-217728 x^3 \log ^3(x)+\frac {24192}{5} x^5 \log ^3(x)-45360 x^4 \log ^4(x)+420 x^6 \log ^4(x)-\frac {105}{512} x^8 \log ^4(x)-6048 x^5 \log ^5(x)+\frac {144}{7} x^7 \log ^5(x)+\frac {21}{64} x^8 \log ^5(x)-504 x^6 \log ^6(x)-24 x^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\\ &=-1119744 x-326592 x^2+\frac {8505 x^4}{2}+\frac {46656}{7} (12+7 x)^2+653184 x^2 \log (x)-17010 x^4 \log (x)-93312 \left (12 x+7 x^2\right ) \log (x)-653184 x^2 \log ^2(x)-\frac {72576}{25} x^5 \log ^2(x)-217728 x^3 \log ^3(x)-280 x^6 \log ^3(x)+\frac {105 x^8 \log ^3(x)}{1024}-45360 x^4 \log ^4(x)-\frac {720}{49} x^7 \log ^4(x)-\frac {105}{512} x^8 \log ^4(x)-6048 x^5 \log ^5(x)-504 x^6 \log ^6(x)-24 x^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\\ &=-1119744 x-326592 x^2-\frac {145152 x^5}{625}+\frac {46656}{7} (12+7 x)^2+653184 x^2 \log (x)+\frac {145152}{125} x^5 \log (x)-93312 \left (12 x+7 x^2\right ) \log (x)-653184 x^2 \log ^2(x)+140 x^6 \log ^2(x)-\frac {315 x^8 \log ^2(x)}{8192}-217728 x^3 \log ^3(x)+\frac {2880}{343} x^7 \log ^3(x)+\frac {105 x^8 \log ^3(x)}{1024}-45360 x^4 \log ^4(x)-6048 x^5 \log ^5(x)-504 x^6 \log ^6(x)-24 x^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\\ &=-1119744 x-326592 x^2+\frac {70 x^6}{9}-\frac {315 x^8}{262144}+\frac {46656}{7} (12+7 x)^2+653184 x^2 \log (x)-\frac {140}{3} x^6 \log (x)+\frac {315 x^8 \log (x)}{32768}-93312 \left (12 x+7 x^2\right ) \log (x)-653184 x^2 \log ^2(x)-\frac {8640 x^7 \log ^2(x)}{2401}-\frac {315 x^8 \log ^2(x)}{8192}-217728 x^3 \log ^3(x)-45360 x^4 \log ^4(x)-6048 x^5 \log ^5(x)-504 x^6 \log ^6(x)-24 x^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\\ &=-1119744 x-326592 x^2-\frac {17280 x^7}{117649}-\frac {315 x^8}{262144}+\frac {46656}{7} (12+7 x)^2+653184 x^2 \log (x)+\frac {17280 x^7 \log (x)}{16807}+\frac {315 x^8 \log (x)}{32768}-93312 \left (12 x+7 x^2\right ) \log (x)-653184 x^2 \log ^2(x)-217728 x^3 \log ^3(x)-45360 x^4 \log ^4(x)-6048 x^5 \log ^5(x)-504 x^6 \log ^6(x)-24 x^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}\\ &=-1119744 x-326592 x^2+\frac {46656}{7} (12+7 x)^2+653184 x^2 \log (x)-93312 \left (12 x+7 x^2\right ) \log (x)-653184 x^2 \log ^2(x)-217728 x^3 \log ^3(x)-45360 x^4 \log ^4(x)-6048 x^5 \log ^5(x)-504 x^6 \log ^6(x)-24 x^7 \log ^7(x)-\frac {1}{2} x^8 \log ^8(x)\\ \end {aligned} \end {gather*}

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

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

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

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)

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

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)

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

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

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

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

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)

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

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)

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

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)

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