3.69.84 \(\int \frac {200 x+120 x^2-22 x^3-12 x^4+2 x^5+(-60 x^2+22 x^3+18 x^4-4 x^5) \log (x)+(-400 x-360 x^2+88 x^3+60 x^4-12 x^5) \log ^2(x)+(-200 x-180 x^2+44 x^3+30 x^4-6 x^5) \log ^3(x)}{3 \log ^3(x)} \, dx\)

Optimal. Leaf size=28 \[ 3 \left (1-\frac {1}{9} (-5+x)^2 (2+x)^2 \left (x+\frac {x}{\log (x)}\right )^2\right ) \]

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Rubi [B]  time = 1.94, antiderivative size = 122, normalized size of antiderivative = 4.36, number of steps used = 54, number of rules used = 8, integrand size = 114, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {12, 6688, 6742, 1590, 2356, 2306, 2309, 2178} \begin {gather*} -\frac {x^6}{3 \log ^2(x)}-\frac {2 x^6}{3 \log (x)}+\frac {2 x^5}{\log ^2(x)}+\frac {4 x^5}{\log (x)}+\frac {11 x^4}{3 \log ^2(x)}+\frac {22 x^4}{3 \log (x)}-\frac {20 x^3}{\log ^2(x)}-\frac {40 x^3}{\log (x)}-\frac {1}{3} (5-x)^2 (x+2)^2 x^2-\frac {100 x^2}{3 \log ^2(x)}-\frac {200 x^2}{3 \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(200*x + 120*x^2 - 22*x^3 - 12*x^4 + 2*x^5 + (-60*x^2 + 22*x^3 + 18*x^4 - 4*x^5)*Log[x] + (-400*x - 360*x^
2 + 88*x^3 + 60*x^4 - 12*x^5)*Log[x]^2 + (-200*x - 180*x^2 + 44*x^3 + 30*x^4 - 6*x^5)*Log[x]^3)/(3*Log[x]^3),x
]

[Out]

-1/3*((5 - x)^2*x^2*(2 + x)^2) - (100*x^2)/(3*Log[x]^2) - (20*x^3)/Log[x]^2 + (11*x^4)/(3*Log[x]^2) + (2*x^5)/
Log[x]^2 - x^6/(3*Log[x]^2) - (200*x^2)/(3*Log[x]) - (40*x^3)/Log[x] + (22*x^4)/(3*Log[x]) + (4*x^5)/Log[x] -
(2*x^6)/(3*Log[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 1590

Int[(Pp_)*(Qq_)^(m_.)*(Rr_)^(n_.), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x], r = Expon[Rr, x]}, S
imp[(Coeff[Pp, x, p]*x^(p - q - r + 1)*Qq^(m + 1)*Rr^(n + 1))/((p + m*q + n*r + 1)*Coeff[Qq, x, q]*Coeff[Rr, x
, r]), x] /; NeQ[p + m*q + n*r + 1, 0] && EqQ[(p + m*q + n*r + 1)*Coeff[Qq, x, q]*Coeff[Rr, x, r]*Pp, Coeff[Pp
, x, p]*x^(p - q - r)*((p - q - r + 1)*Qq*Rr + (m + 1)*x*Rr*D[Qq, x] + (n + 1)*x*Qq*D[Rr, x])]] /; FreeQ[{m, n
}, x] && PolyQ[Pp, x] && PolyQ[Qq, x] && PolyQ[Rr, x] && NeQ[m, -1] && NeQ[n, -1]

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral
Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !$UseGamma === True

Rule 2306

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log
[c*x^n])^(p + 1))/(b*d*n*(p + 1)), x] - Dist[(m + 1)/(b*n*(p + 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] && LtQ[p, -1]

Rule 2309

Int[((a_.) + Log[(c_.)*(x_)]*(b_.))^(p_)*(x_)^(m_.), x_Symbol] :> Dist[1/c^(m + 1), Subst[Int[E^((m + 1)*x)*(a
+ b*x)^p, x], x, Log[c*x]], x] /; FreeQ[{a, b, c, p}, x] && IntegerQ[m]

Rule 2356

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Polyx*(a + b*Log[c*
x^n])^p, x], x] /; FreeQ[{a, b, c, n, p}, x] && PolynomialQ[Polyx, x]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {200 x+120 x^2-22 x^3-12 x^4+2 x^5+\left (-60 x^2+22 x^3+18 x^4-4 x^5\right ) \log (x)+\left (-400 x-360 x^2+88 x^3+60 x^4-12 x^5\right ) \log ^2(x)+\left (-200 x-180 x^2+44 x^3+30 x^4-6 x^5\right ) \log ^3(x)}{\log ^3(x)} \, dx\\ &=\frac {1}{3} \int \frac {2 x \left (10+3 x-x^2\right ) (1+\log (x)) \left (10+3 x-x^2+\left (-10-6 x+3 x^2\right ) \log (x)+\left (-10-6 x+3 x^2\right ) \log ^2(x)\right )}{\log ^3(x)} \, dx\\ &=\frac {2}{3} \int \frac {x \left (10+3 x-x^2\right ) (1+\log (x)) \left (10+3 x-x^2+\left (-10-6 x+3 x^2\right ) \log (x)+\left (-10-6 x+3 x^2\right ) \log ^2(x)\right )}{\log ^3(x)} \, dx\\ &=\frac {2}{3} \int \left (-\left ((-5+x) x (2+x) \left (-10-6 x+3 x^2\right )\right )+\frac {x \left (-10-3 x+x^2\right )^2}{\log ^3(x)}-\frac {x^2 \left (30-11 x-9 x^2+2 x^3\right )}{\log ^2(x)}-\frac {2 (-5+x) x (2+x) \left (-10-6 x+3 x^2\right )}{\log (x)}\right ) \, dx\\ &=-\left (\frac {2}{3} \int (-5+x) x (2+x) \left (-10-6 x+3 x^2\right ) \, dx\right )+\frac {2}{3} \int \frac {x \left (-10-3 x+x^2\right )^2}{\log ^3(x)} \, dx-\frac {2}{3} \int \frac {x^2 \left (30-11 x-9 x^2+2 x^3\right )}{\log ^2(x)} \, dx-\frac {4}{3} \int \frac {(-5+x) x (2+x) \left (-10-6 x+3 x^2\right )}{\log (x)} \, dx\\ &=-\frac {1}{3} (5-x)^2 x^2 (2+x)^2+\frac {2}{3} \int \left (\frac {100 x}{\log ^3(x)}+\frac {60 x^2}{\log ^3(x)}-\frac {11 x^3}{\log ^3(x)}-\frac {6 x^4}{\log ^3(x)}+\frac {x^5}{\log ^3(x)}\right ) \, dx-\frac {2}{3} \int \left (\frac {30 x^2}{\log ^2(x)}-\frac {11 x^3}{\log ^2(x)}-\frac {9 x^4}{\log ^2(x)}+\frac {2 x^5}{\log ^2(x)}\right ) \, dx-\frac {4}{3} \int \left (\frac {100 x}{\log (x)}+\frac {90 x^2}{\log (x)}-\frac {22 x^3}{\log (x)}-\frac {15 x^4}{\log (x)}+\frac {3 x^5}{\log (x)}\right ) \, dx\\ &=-\frac {1}{3} (5-x)^2 x^2 (2+x)^2+\frac {2}{3} \int \frac {x^5}{\log ^3(x)} \, dx-\frac {4}{3} \int \frac {x^5}{\log ^2(x)} \, dx-4 \int \frac {x^4}{\log ^3(x)} \, dx-4 \int \frac {x^5}{\log (x)} \, dx+6 \int \frac {x^4}{\log ^2(x)} \, dx-\frac {22}{3} \int \frac {x^3}{\log ^3(x)} \, dx+\frac {22}{3} \int \frac {x^3}{\log ^2(x)} \, dx-20 \int \frac {x^2}{\log ^2(x)} \, dx+20 \int \frac {x^4}{\log (x)} \, dx+\frac {88}{3} \int \frac {x^3}{\log (x)} \, dx+40 \int \frac {x^2}{\log ^3(x)} \, dx+\frac {200}{3} \int \frac {x}{\log ^3(x)} \, dx-120 \int \frac {x^2}{\log (x)} \, dx-\frac {400}{3} \int \frac {x}{\log (x)} \, dx\\ &=-\frac {1}{3} (5-x)^2 x^2 (2+x)^2-\frac {100 x^2}{3 \log ^2(x)}-\frac {20 x^3}{\log ^2(x)}+\frac {11 x^4}{3 \log ^2(x)}+\frac {2 x^5}{\log ^2(x)}-\frac {x^6}{3 \log ^2(x)}+\frac {20 x^3}{\log (x)}-\frac {22 x^4}{3 \log (x)}-\frac {6 x^5}{\log (x)}+\frac {4 x^6}{3 \log (x)}+2 \int \frac {x^5}{\log ^2(x)} \, dx-4 \operatorname {Subst}\left (\int \frac {e^{6 x}}{x} \, dx,x,\log (x)\right )-8 \int \frac {x^5}{\log (x)} \, dx-10 \int \frac {x^4}{\log ^2(x)} \, dx-\frac {44}{3} \int \frac {x^3}{\log ^2(x)} \, dx+20 \operatorname {Subst}\left (\int \frac {e^{5 x}}{x} \, dx,x,\log (x)\right )+\frac {88}{3} \int \frac {x^3}{\log (x)} \, dx+\frac {88}{3} \operatorname {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )+30 \int \frac {x^4}{\log (x)} \, dx+60 \int \frac {x^2}{\log ^2(x)} \, dx-60 \int \frac {x^2}{\log (x)} \, dx+\frac {200}{3} \int \frac {x}{\log ^2(x)} \, dx-120 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-\frac {400}{3} \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=-\frac {1}{3} (5-x)^2 x^2 (2+x)^2-\frac {400}{3} \text {Ei}(2 \log (x))-120 \text {Ei}(3 \log (x))+\frac {88}{3} \text {Ei}(4 \log (x))+20 \text {Ei}(5 \log (x))-4 \text {Ei}(6 \log (x))-\frac {100 x^2}{3 \log ^2(x)}-\frac {20 x^3}{\log ^2(x)}+\frac {11 x^4}{3 \log ^2(x)}+\frac {2 x^5}{\log ^2(x)}-\frac {x^6}{3 \log ^2(x)}-\frac {200 x^2}{3 \log (x)}-\frac {40 x^3}{\log (x)}+\frac {22 x^4}{3 \log (x)}+\frac {4 x^5}{\log (x)}-\frac {2 x^6}{3 \log (x)}-8 \operatorname {Subst}\left (\int \frac {e^{6 x}}{x} \, dx,x,\log (x)\right )+12 \int \frac {x^5}{\log (x)} \, dx+\frac {88}{3} \operatorname {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )+30 \operatorname {Subst}\left (\int \frac {e^{5 x}}{x} \, dx,x,\log (x)\right )-50 \int \frac {x^4}{\log (x)} \, dx-\frac {176}{3} \int \frac {x^3}{\log (x)} \, dx-60 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )+\frac {400}{3} \int \frac {x}{\log (x)} \, dx+180 \int \frac {x^2}{\log (x)} \, dx\\ &=-\frac {1}{3} (5-x)^2 x^2 (2+x)^2-\frac {400}{3} \text {Ei}(2 \log (x))-180 \text {Ei}(3 \log (x))+\frac {176}{3} \text {Ei}(4 \log (x))+50 \text {Ei}(5 \log (x))-12 \text {Ei}(6 \log (x))-\frac {100 x^2}{3 \log ^2(x)}-\frac {20 x^3}{\log ^2(x)}+\frac {11 x^4}{3 \log ^2(x)}+\frac {2 x^5}{\log ^2(x)}-\frac {x^6}{3 \log ^2(x)}-\frac {200 x^2}{3 \log (x)}-\frac {40 x^3}{\log (x)}+\frac {22 x^4}{3 \log (x)}+\frac {4 x^5}{\log (x)}-\frac {2 x^6}{3 \log (x)}+12 \operatorname {Subst}\left (\int \frac {e^{6 x}}{x} \, dx,x,\log (x)\right )-50 \operatorname {Subst}\left (\int \frac {e^{5 x}}{x} \, dx,x,\log (x)\right )-\frac {176}{3} \operatorname {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )+\frac {400}{3} \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )+180 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )\\ &=-\frac {1}{3} (5-x)^2 x^2 (2+x)^2-\frac {100 x^2}{3 \log ^2(x)}-\frac {20 x^3}{\log ^2(x)}+\frac {11 x^4}{3 \log ^2(x)}+\frac {2 x^5}{\log ^2(x)}-\frac {x^6}{3 \log ^2(x)}-\frac {200 x^2}{3 \log (x)}-\frac {40 x^3}{\log (x)}+\frac {22 x^4}{3 \log (x)}+\frac {4 x^5}{\log (x)}-\frac {2 x^6}{3 \log (x)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.22, size = 27, normalized size = 0.96 \begin {gather*} -\frac {x^2 \left (-10-3 x+x^2\right )^2 (1+\log (x))^2}{3 \log ^2(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(200*x + 120*x^2 - 22*x^3 - 12*x^4 + 2*x^5 + (-60*x^2 + 22*x^3 + 18*x^4 - 4*x^5)*Log[x] + (-400*x -
360*x^2 + 88*x^3 + 60*x^4 - 12*x^5)*Log[x]^2 + (-200*x - 180*x^2 + 44*x^3 + 30*x^4 - 6*x^5)*Log[x]^3)/(3*Log[x
]^3),x]

[Out]

-1/3*(x^2*(-10 - 3*x + x^2)^2*(1 + Log[x])^2)/Log[x]^2

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fricas [B]  time = 1.00, size = 87, normalized size = 3.11 \begin {gather*} -\frac {x^{6} - 6 \, x^{5} - 11 \, x^{4} + 60 \, x^{3} + {\left (x^{6} - 6 \, x^{5} - 11 \, x^{4} + 60 \, x^{3} + 100 \, x^{2}\right )} \log \relax (x)^{2} + 100 \, x^{2} + 2 \, {\left (x^{6} - 6 \, x^{5} - 11 \, x^{4} + 60 \, x^{3} + 100 \, x^{2}\right )} \log \relax (x)}{3 \, \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-6*x^5+30*x^4+44*x^3-180*x^2-200*x)*log(x)^3+(-12*x^5+60*x^4+88*x^3-360*x^2-400*x)*log(x)^2+(-
4*x^5+18*x^4+22*x^3-60*x^2)*log(x)+2*x^5-12*x^4-22*x^3+120*x^2+200*x)/log(x)^3,x, algorithm="fricas")

[Out]

-1/3*(x^6 - 6*x^5 - 11*x^4 + 60*x^3 + (x^6 - 6*x^5 - 11*x^4 + 60*x^3 + 100*x^2)*log(x)^2 + 100*x^2 + 2*(x^6 -
6*x^5 - 11*x^4 + 60*x^3 + 100*x^2)*log(x))/log(x)^2

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giac [B]  time = 0.17, size = 116, normalized size = 4.14 \begin {gather*} -\frac {1}{3} \, x^{6} + 2 \, x^{5} - \frac {2 \, x^{6}}{3 \, \log \relax (x)} + \frac {11}{3} \, x^{4} - \frac {x^{6}}{3 \, \log \relax (x)^{2}} + \frac {4 \, x^{5}}{\log \relax (x)} - 20 \, x^{3} + \frac {2 \, x^{5}}{\log \relax (x)^{2}} + \frac {22 \, x^{4}}{3 \, \log \relax (x)} - \frac {100}{3} \, x^{2} + \frac {11 \, x^{4}}{3 \, \log \relax (x)^{2}} - \frac {40 \, x^{3}}{\log \relax (x)} - \frac {20 \, x^{3}}{\log \relax (x)^{2}} - \frac {200 \, x^{2}}{3 \, \log \relax (x)} - \frac {100 \, x^{2}}{3 \, \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-6*x^5+30*x^4+44*x^3-180*x^2-200*x)*log(x)^3+(-12*x^5+60*x^4+88*x^3-360*x^2-400*x)*log(x)^2+(-
4*x^5+18*x^4+22*x^3-60*x^2)*log(x)+2*x^5-12*x^4-22*x^3+120*x^2+200*x)/log(x)^3,x, algorithm="giac")

[Out]

-1/3*x^6 + 2*x^5 - 2/3*x^6/log(x) + 11/3*x^4 - 1/3*x^6/log(x)^2 + 4*x^5/log(x) - 20*x^3 + 2*x^5/log(x)^2 + 22/
3*x^4/log(x) - 100/3*x^2 + 11/3*x^4/log(x)^2 - 40*x^3/log(x) - 20*x^3/log(x)^2 - 200/3*x^2/log(x) - 100/3*x^2/
log(x)^2

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maple [B]  time = 0.03, size = 84, normalized size = 3.00

method	result	size
risch	\(-\frac {x^{6}}{3}+2 x^{5}+\frac {11 x^{4}}{3}-20 x^{3}-\frac {100 x^{2}}{3}-\frac {x^{2} \left (2 x^{4} \ln \relax (x )+x^{4}-12 x^{3} \ln \relax (x )-6 x^{3}-22 x^{2} \ln \relax (x )-11 x^{2}+120 x \ln \relax (x )+60 x +200 \ln \relax (x )+100\right )}{3 \ln \relax (x )^{2}}\)	\(84\)
norman	\(\frac {-\frac {100 x^{2}}{3}-20 x^{3}+\frac {11 x^{4}}{3}+2 x^{5}-\frac {x^{6}}{3}-\frac {200 x^{2} \ln \relax (x )}{3}-\frac {100 x^{2} \ln \relax (x )^{2}}{3}-40 x^{3} \ln \relax (x )-20 x^{3} \ln \relax (x )^{2}+\frac {22 x^{4} \ln \relax (x )}{3}+\frac {11 x^{4} \ln \relax (x )^{2}}{3}+4 x^{5} \ln \relax (x )+2 x^{5} \ln \relax (x )^{2}-\frac {2 x^{6} \ln \relax (x )}{3}-\frac {x^{6} \ln \relax (x )^{2}}{3}}{\ln \relax (x )^{2}}\)	\(112\)
default	\(-\frac {200 x^{2}}{3 \ln \relax (x )}-\frac {x^{6}}{3}+2 x^{5}+\frac {11 x^{4}}{3}-20 x^{3}-\frac {100 x^{2}}{3}-\frac {100 x^{2}}{3 \ln \relax (x )^{2}}+\frac {22 x^{4}}{3 \ln \relax (x )}-\frac {40 x^{3}}{\ln \relax (x )}+\frac {11 x^{4}}{3 \ln \relax (x )^{2}}-\frac {20 x^{3}}{\ln \relax (x )^{2}}+\frac {4 x^{5}}{\ln \relax (x )}+\frac {2 x^{5}}{\ln \relax (x )^{2}}-\frac {2 x^{6}}{3 \ln \relax (x )}-\frac {x^{6}}{3 \ln \relax (x )^{2}}\)	\(117\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3*((-6*x^5+30*x^4+44*x^3-180*x^2-200*x)*ln(x)^3+(-12*x^5+60*x^4+88*x^3-360*x^2-400*x)*ln(x)^2+(-4*x^5+18
*x^4+22*x^3-60*x^2)*ln(x)+2*x^5-12*x^4-22*x^3+120*x^2+200*x)/ln(x)^3,x,method=_RETURNVERBOSE)

[Out]

-1/3*x^6+2*x^5+11/3*x^4-20*x^3-100/3*x^2-1/3*x^2*(2*x^4*ln(x)+x^4-12*x^3*ln(x)-6*x^3-22*x^2*ln(x)-11*x^2+120*x
*ln(x)+60*x+200*ln(x)+100)/ln(x)^2

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maxima [C]  time = 0.43, size = 133, normalized size = 4.75 \begin {gather*} -\frac {1}{3} \, x^{6} + 2 \, x^{5} + \frac {11}{3} \, x^{4} - 20 \, x^{3} - \frac {100}{3} \, x^{2} - 4 \, {\rm Ei}\left (6 \, \log \relax (x)\right ) + 20 \, {\rm Ei}\left (5 \, \log \relax (x)\right ) + \frac {88}{3} \, {\rm Ei}\left (4 \, \log \relax (x)\right ) - 120 \, {\rm Ei}\left (3 \, \log \relax (x)\right ) - \frac {400}{3} \, {\rm Ei}\left (2 \, \log \relax (x)\right ) - 60 \, \Gamma \left (-1, -3 \, \log \relax (x)\right ) + \frac {88}{3} \, \Gamma \left (-1, -4 \, \log \relax (x)\right ) + 30 \, \Gamma \left (-1, -5 \, \log \relax (x)\right ) - 8 \, \Gamma \left (-1, -6 \, \log \relax (x)\right ) - \frac {800}{3} \, \Gamma \left (-2, -2 \, \log \relax (x)\right ) - 360 \, \Gamma \left (-2, -3 \, \log \relax (x)\right ) + \frac {352}{3} \, \Gamma \left (-2, -4 \, \log \relax (x)\right ) + 100 \, \Gamma \left (-2, -5 \, \log \relax (x)\right ) - 24 \, \Gamma \left (-2, -6 \, \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-6*x^5+30*x^4+44*x^3-180*x^2-200*x)*log(x)^3+(-12*x^5+60*x^4+88*x^3-360*x^2-400*x)*log(x)^2+(-
4*x^5+18*x^4+22*x^3-60*x^2)*log(x)+2*x^5-12*x^4-22*x^3+120*x^2+200*x)/log(x)^3,x, algorithm="maxima")

[Out]

-1/3*x^6 + 2*x^5 + 11/3*x^4 - 20*x^3 - 100/3*x^2 - 4*Ei(6*log(x)) + 20*Ei(5*log(x)) + 88/3*Ei(4*log(x)) - 120*
Ei(3*log(x)) - 400/3*Ei(2*log(x)) - 60*gamma(-1, -3*log(x)) + 88/3*gamma(-1, -4*log(x)) + 30*gamma(-1, -5*log(
x)) - 8*gamma(-1, -6*log(x)) - 800/3*gamma(-2, -2*log(x)) - 360*gamma(-2, -3*log(x)) + 352/3*gamma(-2, -4*log(
x)) + 100*gamma(-2, -5*log(x)) - 24*gamma(-2, -6*log(x))

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mupad [B]  time = 4.21, size = 27, normalized size = 0.96 \begin {gather*} -\frac {x^2\,{\left (\ln \relax (x)+1\right )}^2\,{\left (-x^2+3\,x+10\right )}^2}{3\,{\ln \relax (x)}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((log(x)*(60*x^2 - 22*x^3 - 18*x^4 + 4*x^5))/3 - (200*x)/3 + (log(x)^3*(200*x + 180*x^2 - 44*x^3 - 30*x^4
+ 6*x^5))/3 + (log(x)^2*(400*x + 360*x^2 - 88*x^3 - 60*x^4 + 12*x^5))/3 - 40*x^2 + (22*x^3)/3 + 4*x^4 - (2*x^
5)/3)/log(x)^3,x)

[Out]

-(x^2*(log(x) + 1)^2*(3*x - x^2 + 10)^2)/(3*log(x)^2)

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sympy [B]  time = 0.19, size = 87, normalized size = 3.11 \begin {gather*} - \frac {x^{6}}{3} + 2 x^{5} + \frac {11 x^{4}}{3} - 20 x^{3} - \frac {100 x^{2}}{3} + \frac {- x^{6} + 6 x^{5} + 11 x^{4} - 60 x^{3} - 100 x^{2} + \left (- 2 x^{6} + 12 x^{5} + 22 x^{4} - 120 x^{3} - 200 x^{2}\right ) \log {\relax (x )}}{3 \log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-6*x**5+30*x**4+44*x**3-180*x**2-200*x)*ln(x)**3+(-12*x**5+60*x**4+88*x**3-360*x**2-400*x)*ln(
x)**2+(-4*x**5+18*x**4+22*x**3-60*x**2)*ln(x)+2*x**5-12*x**4-22*x**3+120*x**2+200*x)/ln(x)**3,x)

[Out]

-x**6/3 + 2*x**5 + 11*x**4/3 - 20*x**3 - 100*x**2/3 + (-x**6 + 6*x**5 + 11*x**4 - 60*x**3 - 100*x**2 + (-2*x**
6 + 12*x**5 + 22*x**4 - 120*x**3 - 200*x**2)*log(x))/(3*log(x)**2)

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