3.86.78 \(\int \frac {-36-12 x^2 \log ^2(3)+(-36 x \log (3)-4 x^3 \log ^3(3)) \log (4)+(-24-12 x^2 \log ^2(3)) \log ^2(4)-12 x \log (3) \log ^3(4)-4 \log ^4(4)+(-12-4 x^2 \log ^2(3)-8 x \log (3) \log (4)-4 \log ^2(4)) \log (x)+(24+4 x^2 \log ^2(3)+12 x \log (3) \log (4)+8 \log ^2(4)) \log ^2(x)+4 \log ^3(x)-4 \log ^4(x)}{x^5} \, dx\)

Optimal. Leaf size=23 \[ \frac {\left (3+(x \log (3)+\log (4))^2-\log ^2(x)\right )^2}{x^4} \]

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Rubi [B]  time = 0.44, antiderivative size = 153, normalized size of antiderivative = 6.65, number of steps used = 24, number of rules used = 4, integrand size = 132, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {14, 2357, 2304, 2305} \begin {gather*} \frac {\log ^4(x)}{x^4}-\frac {2 \left (3+\log ^2(4)\right ) \log ^2(x)}{x^4}+\frac {\left (3+\log ^2(4)\right )^2}{x^4}-\frac {4 \log (4) \log (27) \log ^2(x)}{3 x^3}+\frac {4 \log (3) \log (4) \left (3+\log ^2(4)\right )}{x^3}-\frac {8 \log (4) \log (27) \log (x)}{9 x^3}+\frac {4 \log (4) \log (9) \log (x)}{3 x^3}-\frac {8 \log (4) \log (27)}{27 x^3}+\frac {4 \log (4) \log (9)}{9 x^3}-\frac {2 \log ^2(3) \log ^2(x)}{x^2}+\frac {6 \log ^2(3) \left (1+\log ^2(4)\right )}{x^2}+\frac {4 \log ^3(3) \log (4)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-36 - 12*x^2*Log[3]^2 + (-36*x*Log[3] - 4*x^3*Log[3]^3)*Log[4] + (-24 - 12*x^2*Log[3]^2)*Log[4]^2 - 12*x*
Log[3]*Log[4]^3 - 4*Log[4]^4 + (-12 - 4*x^2*Log[3]^2 - 8*x*Log[3]*Log[4] - 4*Log[4]^2)*Log[x] + (24 + 4*x^2*Lo
g[3]^2 + 12*x*Log[3]*Log[4] + 8*Log[4]^2)*Log[x]^2 + 4*Log[x]^3 - 4*Log[x]^4)/x^5,x]

[Out]

(4*Log[3]^3*Log[4])/x + (6*Log[3]^2*(1 + Log[4]^2))/x^2 + (4*Log[3]*Log[4]*(3 + Log[4]^2))/x^3 + (3 + Log[4]^2
)^2/x^4 + (4*Log[4]*Log[9])/(9*x^3) - (8*Log[4]*Log[27])/(27*x^3) + (4*Log[4]*Log[9]*Log[x])/(3*x^3) - (8*Log[
4]*Log[27]*Log[x])/(9*x^3) - (2*Log[3]^2*Log[x]^2)/x^2 - (2*(3 + Log[4]^2)*Log[x]^2)/x^4 - (4*Log[4]*Log[27]*L
og[x]^2)/(3*x^3) + Log[x]^4/x^4

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 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 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 \left (\frac {4 \left (-x^3 \log ^3(3) \log (4)-3 x^2 \log ^2(3) \left (1+\log ^2(4)\right )-3 x \log (3) \log (4) \left (3+\log ^2(4)\right )-\left (3+\log ^2(4)\right )^2\right )}{x^5}-\frac {4 \left (3+x^2 \log ^2(3)+\log ^2(4)+x \log (4) \log (9)\right ) \log (x)}{x^5}+\frac {4 \left (x^2 \log ^2(3)+2 \left (3+\log ^2(4)\right )+x \log (4) \log (27)\right ) \log ^2(x)}{x^5}+\frac {4 \log ^3(x)}{x^5}-\frac {4 \log ^4(x)}{x^5}\right ) \, dx\\ &=4 \int \frac {-x^3 \log ^3(3) \log (4)-3 x^2 \log ^2(3) \left (1+\log ^2(4)\right )-3 x \log (3) \log (4) \left (3+\log ^2(4)\right )-\left (3+\log ^2(4)\right )^2}{x^5} \, dx-4 \int \frac {\left (3+x^2 \log ^2(3)+\log ^2(4)+x \log (4) \log (9)\right ) \log (x)}{x^5} \, dx+4 \int \frac {\left (x^2 \log ^2(3)+2 \left (3+\log ^2(4)\right )+x \log (4) \log (27)\right ) \log ^2(x)}{x^5} \, dx+4 \int \frac {\log ^3(x)}{x^5} \, dx-4 \int \frac {\log ^4(x)}{x^5} \, dx\\ &=-\frac {\log ^3(x)}{x^4}+\frac {\log ^4(x)}{x^4}+3 \int \frac {\log ^2(x)}{x^5} \, dx+4 \int \left (-\frac {\log ^3(3) \log (4)}{x^2}-\frac {3 \log ^2(3) \left (1+\log ^2(4)\right )}{x^3}-\frac {3 \log (3) \log (4) \left (3+\log ^2(4)\right )}{x^4}-\frac {\left (3+\log ^2(4)\right )^2}{x^5}\right ) \, dx-4 \int \frac {\log ^3(x)}{x^5} \, dx-4 \int \left (\frac {\log ^2(3) \log (x)}{x^3}+\frac {\left (3+\log ^2(4)\right ) \log (x)}{x^5}+\frac {\log (4) \log (9) \log (x)}{x^4}\right ) \, dx+4 \int \left (\frac {\log ^2(3) \log ^2(x)}{x^3}+\frac {2 \left (3+\log ^2(4)\right ) \log ^2(x)}{x^5}+\frac {\log (4) \log (27) \log ^2(x)}{x^4}\right ) \, dx\\ &=\frac {4 \log ^3(3) \log (4)}{x}+\frac {6 \log ^2(3) \left (1+\log ^2(4)\right )}{x^2}+\frac {4 \log (3) \log (4) \left (3+\log ^2(4)\right )}{x^3}+\frac {\left (3+\log ^2(4)\right )^2}{x^4}-\frac {3 \log ^2(x)}{4 x^4}+\frac {\log ^4(x)}{x^4}+\frac {3}{2} \int \frac {\log (x)}{x^5} \, dx-3 \int \frac {\log ^2(x)}{x^5} \, dx-\left (4 \log ^2(3)\right ) \int \frac {\log (x)}{x^3} \, dx+\left (4 \log ^2(3)\right ) \int \frac {\log ^2(x)}{x^3} \, dx-\left (4 \left (3+\log ^2(4)\right )\right ) \int \frac {\log (x)}{x^5} \, dx+\left (8 \left (3+\log ^2(4)\right )\right ) \int \frac {\log ^2(x)}{x^5} \, dx-(4 \log (4) \log (9)) \int \frac {\log (x)}{x^4} \, dx+(4 \log (4) \log (27)) \int \frac {\log ^2(x)}{x^4} \, dx\\ &=-\frac {3}{32 x^4}+\frac {\log ^2(3)}{x^2}+\frac {4 \log ^3(3) \log (4)}{x}+\frac {6 \log ^2(3) \left (1+\log ^2(4)\right )}{x^2}+\frac {3+\log ^2(4)}{4 x^4}+\frac {4 \log (3) \log (4) \left (3+\log ^2(4)\right )}{x^3}+\frac {\left (3+\log ^2(4)\right )^2}{x^4}+\frac {4 \log (4) \log (9)}{9 x^3}-\frac {3 \log (x)}{8 x^4}+\frac {2 \log ^2(3) \log (x)}{x^2}+\frac {\left (3+\log ^2(4)\right ) \log (x)}{x^4}+\frac {4 \log (4) \log (9) \log (x)}{3 x^3}-\frac {2 \log ^2(3) \log ^2(x)}{x^2}-\frac {2 \left (3+\log ^2(4)\right ) \log ^2(x)}{x^4}-\frac {4 \log (4) \log (27) \log ^2(x)}{3 x^3}+\frac {\log ^4(x)}{x^4}-\frac {3}{2} \int \frac {\log (x)}{x^5} \, dx+\left (4 \log ^2(3)\right ) \int \frac {\log (x)}{x^3} \, dx+\left (4 \left (3+\log ^2(4)\right )\right ) \int \frac {\log (x)}{x^5} \, dx+\frac {1}{3} (8 \log (4) \log (27)) \int \frac {\log (x)}{x^4} \, dx\\ &=\frac {4 \log ^3(3) \log (4)}{x}+\frac {6 \log ^2(3) \left (1+\log ^2(4)\right )}{x^2}+\frac {4 \log (3) \log (4) \left (3+\log ^2(4)\right )}{x^3}+\frac {\left (3+\log ^2(4)\right )^2}{x^4}+\frac {4 \log (4) \log (9)}{9 x^3}-\frac {8 \log (4) \log (27)}{27 x^3}+\frac {4 \log (4) \log (9) \log (x)}{3 x^3}-\frac {8 \log (4) \log (27) \log (x)}{9 x^3}-\frac {2 \log ^2(3) \log ^2(x)}{x^2}-\frac {2 \left (3+\log ^2(4)\right ) \log ^2(x)}{x^4}-\frac {4 \log (4) \log (27) \log ^2(x)}{3 x^3}+\frac {\log ^4(x)}{x^4}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.05, size = 184, normalized size = 8.00 \begin {gather*} \frac {9}{x^4}+\frac {6 \log ^2(3)}{x^2}+\frac {12 \log (3) \log (4)}{x^3}+\frac {4 \log ^3(3) \log (4)}{x}+\frac {6 \log ^2(4)}{x^4}+\frac {6 \log ^2(3) \log ^2(4)}{x^2}+\frac {\log ^4(4)}{x^4}+\frac {4 \log (4) \log (9)}{9 x^3}-\frac {8 \log (4) \log (27)}{27 x^3}+\frac {4 \log ^3(4) \log (27)}{3 x^3}+\frac {4 \log (4) \log (9) \log (x)}{3 x^3}-\frac {8 \log (4) \log (27) \log (x)}{9 x^3}-\frac {6 \log ^2(x)}{x^4}-\frac {2 \log ^2(3) \log ^2(x)}{x^2}-\frac {2 \log ^2(4) \log ^2(x)}{x^4}-\frac {4 \log (4) \log (27) \log ^2(x)}{3 x^3}+\frac {\log ^4(x)}{x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-36 - 12*x^2*Log[3]^2 + (-36*x*Log[3] - 4*x^3*Log[3]^3)*Log[4] + (-24 - 12*x^2*Log[3]^2)*Log[4]^2 -
12*x*Log[3]*Log[4]^3 - 4*Log[4]^4 + (-12 - 4*x^2*Log[3]^2 - 8*x*Log[3]*Log[4] - 4*Log[4]^2)*Log[x] + (24 + 4*
x^2*Log[3]^2 + 12*x*Log[3]*Log[4] + 8*Log[4]^2)*Log[x]^2 + 4*Log[x]^3 - 4*Log[x]^4)/x^5,x]

[Out]

9/x^4 + (6*Log[3]^2)/x^2 + (12*Log[3]*Log[4])/x^3 + (4*Log[3]^3*Log[4])/x + (6*Log[4]^2)/x^4 + (6*Log[3]^2*Log
[4]^2)/x^2 + Log[4]^4/x^4 + (4*Log[4]*Log[9])/(9*x^3) - (8*Log[4]*Log[27])/(27*x^3) + (4*Log[4]^3*Log[27])/(3*
x^3) + (4*Log[4]*Log[9]*Log[x])/(3*x^3) - (8*Log[4]*Log[27]*Log[x])/(9*x^3) - (6*Log[x]^2)/x^4 - (2*Log[3]^2*L
og[x]^2)/x^2 - (2*Log[4]^2*Log[x]^2)/x^4 - (4*Log[4]*Log[27]*Log[x]^2)/(3*x^3) + Log[x]^4/x^4

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fricas [B]  time = 1.05, size = 98, normalized size = 4.26 \begin {gather*} \frac {8 \, x^{3} \log \relax (3)^{3} \log \relax (2) + 16 \, \log \relax (2)^{4} + \log \relax (x)^{4} + 6 \, {\left (4 \, x^{2} \log \relax (2)^{2} + x^{2}\right )} \log \relax (3)^{2} - 2 \, {\left (x^{2} \log \relax (3)^{2} + 4 \, x \log \relax (3) \log \relax (2) + 4 \, \log \relax (2)^{2} + 3\right )} \log \relax (x)^{2} + 8 \, {\left (4 \, x \log \relax (2)^{3} + 3 \, x \log \relax (2)\right )} \log \relax (3) + 24 \, \log \relax (2)^{2} + 9}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*log(x)^4+4*log(x)^3+(32*log(2)^2+24*x*log(2)*log(3)+4*x^2*log(3)^2+24)*log(x)^2+(-16*log(2)^2-16
*x*log(2)*log(3)-4*x^2*log(3)^2-12)*log(x)-64*log(2)^4-96*x*log(3)*log(2)^3+4*(-12*x^2*log(3)^2-24)*log(2)^2+2
*(-4*x^3*log(3)^3-36*x*log(3))*log(2)-12*x^2*log(3)^2-36)/x^5,x, algorithm="fricas")

[Out]

(8*x^3*log(3)^3*log(2) + 16*log(2)^4 + log(x)^4 + 6*(4*x^2*log(2)^2 + x^2)*log(3)^2 - 2*(x^2*log(3)^2 + 4*x*lo
g(3)*log(2) + 4*log(2)^2 + 3)*log(x)^2 + 8*(4*x*log(2)^3 + 3*x*log(2))*log(3) + 24*log(2)^2 + 9)/x^4

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giac [B]  time = 0.15, size = 108, normalized size = 4.70 \begin {gather*} \frac {\log \relax (x)^{4}}{x^{4}} - \frac {2 \, {\left (x^{2} \log \relax (3)^{2} + 4 \, x \log \relax (3) \log \relax (2) + 4 \, \log \relax (2)^{2} + 3\right )} \log \relax (x)^{2}}{x^{4}} + \frac {8 \, x^{3} \log \relax (3)^{3} \log \relax (2) + 24 \, x^{2} \log \relax (3)^{2} \log \relax (2)^{2} + 32 \, x \log \relax (3) \log \relax (2)^{3} + 6 \, x^{2} \log \relax (3)^{2} + 16 \, \log \relax (2)^{4} + 24 \, x \log \relax (3) \log \relax (2) + 24 \, \log \relax (2)^{2} + 9}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*log(x)^4+4*log(x)^3+(32*log(2)^2+24*x*log(2)*log(3)+4*x^2*log(3)^2+24)*log(x)^2+(-16*log(2)^2-16
*x*log(2)*log(3)-4*x^2*log(3)^2-12)*log(x)-64*log(2)^4-96*x*log(3)*log(2)^3+4*(-12*x^2*log(3)^2-24)*log(2)^2+2
*(-4*x^3*log(3)^3-36*x*log(3))*log(2)-12*x^2*log(3)^2-36)/x^5,x, algorithm="giac")

[Out]

log(x)^4/x^4 - 2*(x^2*log(3)^2 + 4*x*log(3)*log(2) + 4*log(2)^2 + 3)*log(x)^2/x^4 + (8*x^3*log(3)^3*log(2) + 2
4*x^2*log(3)^2*log(2)^2 + 32*x*log(3)*log(2)^3 + 6*x^2*log(3)^2 + 16*log(2)^4 + 24*x*log(3)*log(2) + 24*log(2)
^2 + 9)/x^4

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maple [B]  time = 0.03, size = 109, normalized size = 4.74

method	result	size
risch	\(\frac {\ln \relax (x )^{4}}{x^{4}}-\frac {2 \left (x^{2} \ln \relax (3)^{2}+4 x \ln \relax (2) \ln \relax (3)+4 \ln \relax (2)^{2}+3\right ) \ln \relax (x )^{2}}{x^{4}}+\frac {8 \ln \relax (3)^{3} \ln \relax (2) x^{3}+24 x^{2} \ln \relax (3)^{2} \ln \relax (2)^{2}+32 x \ln \relax (3) \ln \relax (2)^{3}+6 x^{2} \ln \relax (3)^{2}+16 \ln \relax (2)^{4}+24 x \ln \relax (2) \ln \relax (3)+24 \ln \relax (2)^{2}+9}{x^{4}}\)	\(109\)
default	\(\frac {24 \ln \relax (2)^{2}}{x^{4}}+\frac {9}{x^{4}}+\frac {6 \ln \relax (3)^{2}}{x^{2}}+\frac {24 \ln \relax (2) \ln \relax (3)}{x^{3}}+24 \ln \relax (2) \ln \relax (3) \left (-\frac {\ln \relax (x )^{2}}{3 x^{3}}-\frac {2 \ln \relax (x )}{9 x^{3}}-\frac {2}{27 x^{3}}\right )+32 \ln \relax (2)^{2} \left (-\frac {\ln \relax (x )^{2}}{4 x^{4}}-\frac {\ln \relax (x )}{8 x^{4}}-\frac {1}{32 x^{4}}\right )+\frac {16 \ln \relax (2)^{4}}{x^{4}}-16 \ln \relax (2)^{2} \left (-\frac {\ln \relax (x )}{4 x^{4}}-\frac {1}{16 x^{4}}\right )+\frac {32 \ln \relax (2)^{3} \ln \relax (3)}{x^{3}}+\frac {8 \ln \relax (2) \ln \relax (3)^{3}}{x}+\frac {24 \ln \relax (3)^{2} \ln \relax (2)^{2}}{x^{2}}+4 \ln \relax (3)^{2} \left (-\frac {\ln \relax (x )^{2}}{2 x^{2}}-\frac {\ln \relax (x )}{2 x^{2}}-\frac {1}{4 x^{2}}\right )-4 \ln \relax (3)^{2} \left (-\frac {\ln \relax (x )}{2 x^{2}}-\frac {1}{4 x^{2}}\right )+\frac {\ln \relax (x )^{4}}{x^{4}}-\frac {6 \ln \relax (x )^{2}}{x^{4}}-16 \ln \relax (2) \ln \relax (3) \left (-\frac {\ln \relax (x )}{3 x^{3}}-\frac {1}{9 x^{3}}\right )\)	\(236\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*ln(x)^4+4*ln(x)^3+(32*ln(2)^2+24*x*ln(2)*ln(3)+4*x^2*ln(3)^2+24)*ln(x)^2+(-16*ln(2)^2-16*x*ln(2)*ln(3)
-4*x^2*ln(3)^2-12)*ln(x)-64*ln(2)^4-96*x*ln(3)*ln(2)^3+4*(-12*x^2*ln(3)^2-24)*ln(2)^2+2*(-4*x^3*ln(3)^3-36*x*l
n(3))*ln(2)-12*x^2*ln(3)^2-36)/x^5,x,method=_RETURNVERBOSE)

[Out]

1/x^4*ln(x)^4-2*(x^2*ln(3)^2+4*x*ln(2)*ln(3)+4*ln(2)^2+3)/x^4*ln(x)^2+(8*ln(3)^3*ln(2)*x^3+24*x^2*ln(3)^2*ln(2
)^2+32*x*ln(3)*ln(2)^3+6*x^2*ln(3)^2+16*ln(2)^4+24*x*ln(2)*ln(3)+24*ln(2)^2+9)/x^4

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maxima [B]  time = 0.36, size = 265, normalized size = 11.52 \begin {gather*} {\left (\frac {2 \, \log \relax (x)}{x^{2}} + \frac {1}{x^{2}}\right )} \log \relax (3)^{2} + \frac {16}{9} \, {\left (\frac {3 \, \log \relax (x)}{x^{3}} + \frac {1}{x^{3}}\right )} \log \relax (3) \log \relax (2) + \frac {8 \, \log \relax (3)^{3} \log \relax (2)}{x} + {\left (\frac {4 \, \log \relax (x)}{x^{4}} + \frac {1}{x^{4}}\right )} \log \relax (2)^{2} + \frac {24 \, \log \relax (3)^{2} \log \relax (2)^{2}}{x^{2}} - \frac {{\left (2 \, \log \relax (x)^{2} + 2 \, \log \relax (x) + 1\right )} \log \relax (3)^{2}}{x^{2}} + \frac {32 \, \log \relax (3) \log \relax (2)^{3}}{x^{3}} + \frac {6 \, \log \relax (3)^{2}}{x^{2}} - \frac {8 \, {\left (9 \, \log \relax (x)^{2} + 6 \, \log \relax (x) + 2\right )} \log \relax (3) \log \relax (2)}{9 \, x^{3}} + \frac {16 \, \log \relax (2)^{4}}{x^{4}} + \frac {24 \, \log \relax (3) \log \relax (2)}{x^{3}} - \frac {{\left (8 \, \log \relax (x)^{2} + 4 \, \log \relax (x) + 1\right )} \log \relax (2)^{2}}{x^{4}} + \frac {24 \, \log \relax (2)^{2}}{x^{4}} + \frac {32 \, \log \relax (x)^{4} + 32 \, \log \relax (x)^{3} + 24 \, \log \relax (x)^{2} + 12 \, \log \relax (x) + 3}{32 \, x^{4}} - \frac {32 \, \log \relax (x)^{3} + 24 \, \log \relax (x)^{2} + 12 \, \log \relax (x) + 3}{32 \, x^{4}} - \frac {3 \, {\left (8 \, \log \relax (x)^{2} + 4 \, \log \relax (x) + 1\right )}}{4 \, x^{4}} + \frac {3 \, \log \relax (x)}{x^{4}} + \frac {39}{4 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*log(x)^4+4*log(x)^3+(32*log(2)^2+24*x*log(2)*log(3)+4*x^2*log(3)^2+24)*log(x)^2+(-16*log(2)^2-16
*x*log(2)*log(3)-4*x^2*log(3)^2-12)*log(x)-64*log(2)^4-96*x*log(3)*log(2)^3+4*(-12*x^2*log(3)^2-24)*log(2)^2+2
*(-4*x^3*log(3)^3-36*x*log(3))*log(2)-12*x^2*log(3)^2-36)/x^5,x, algorithm="maxima")

[Out]

(2*log(x)/x^2 + 1/x^2)*log(3)^2 + 16/9*(3*log(x)/x^3 + 1/x^3)*log(3)*log(2) + 8*log(3)^3*log(2)/x + (4*log(x)/
x^4 + 1/x^4)*log(2)^2 + 24*log(3)^2*log(2)^2/x^2 - (2*log(x)^2 + 2*log(x) + 1)*log(3)^2/x^2 + 32*log(3)*log(2)
^3/x^3 + 6*log(3)^2/x^2 - 8/9*(9*log(x)^2 + 6*log(x) + 2)*log(3)*log(2)/x^3 + 16*log(2)^4/x^4 + 24*log(3)*log(
2)/x^3 - (8*log(x)^2 + 4*log(x) + 1)*log(2)^2/x^4 + 24*log(2)^2/x^4 + 1/32*(32*log(x)^4 + 32*log(x)^3 + 24*log
(x)^2 + 12*log(x) + 3)/x^4 - 1/32*(32*log(x)^3 + 24*log(x)^2 + 12*log(x) + 3)/x^4 - 3/4*(8*log(x)^2 + 4*log(x)
+ 1)/x^4 + 3*log(x)/x^4 + 39/4/x^4

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mupad [B]  time = 5.59, size = 107, normalized size = 4.65 \begin {gather*} \frac {x\,\left ({\ln \relax (x)}^4+\left (-8\,{\ln \relax (2)}^2-6\right )\,{\ln \relax (x)}^2+{\left (4\,{\ln \relax (2)}^2+3\right )}^2\right )-x^3\,\left (2\,{\ln \relax (3)}^2\,{\ln \relax (x)}^2-6\,{\ln \relax (3)}^2\,\left (4\,{\ln \relax (2)}^2+1\right )\right )-x^2\,\left (8\,\ln \relax (2)\,\ln \relax (3)\,{\ln \relax (x)}^2-8\,\ln \relax (2)\,\ln \relax (3)\,\left (4\,{\ln \relax (2)}^2+3\right )\right )+8\,x^4\,\ln \relax (2)\,{\ln \relax (3)}^3}{x^5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(12*x^2*log(3)^2 - 4*log(x)^3 + 4*log(x)^4 + 2*log(2)*(4*x^3*log(3)^3 + 36*x*log(3)) + log(x)*(4*x^2*log(
3)^2 + 16*log(2)^2 + 16*x*log(2)*log(3) + 12) + 4*log(2)^2*(12*x^2*log(3)^2 + 24) + 64*log(2)^4 - log(x)^2*(4*
x^2*log(3)^2 + 32*log(2)^2 + 24*x*log(2)*log(3) + 24) + 96*x*log(2)^3*log(3) + 36)/x^5,x)

[Out]

(x*(log(x)^4 - log(x)^2*(8*log(2)^2 + 6) + (4*log(2)^2 + 3)^2) - x^3*(2*log(3)^2*log(x)^2 - 6*log(3)^2*(4*log(
2)^2 + 1)) - x^2*(8*log(2)*log(3)*log(x)^2 - 8*log(2)*log(3)*(4*log(2)^2 + 3)) + 8*x^4*log(2)*log(3)^3)/x^5

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sympy [B]  time = 1.15, size = 124, normalized size = 5.39 \begin {gather*} \frac {\left (- 2 x^{2} \log {\relax (3 )}^{2} - 8 x \log {\relax (2 )} \log {\relax (3 )} - 6 - 8 \log {\relax (2 )}^{2}\right ) \log {\relax (x )}^{2}}{x^{4}} - \frac {- 8 x^{3} \log {\relax (2 )} \log {\relax (3 )}^{3} + x^{2} \left (- 24 \log {\relax (2 )}^{2} \log {\relax (3 )}^{2} - 6 \log {\relax (3 )}^{2}\right ) + x \left (- 24 \log {\relax (2 )} \log {\relax (3 )} - 32 \log {\relax (2 )}^{3} \log {\relax (3 )}\right ) - 24 \log {\relax (2 )}^{2} - 9 - 16 \log {\relax (2 )}^{4}}{x^{4}} + \frac {\log {\relax (x )}^{4}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*ln(x)**4+4*ln(x)**3+(32*ln(2)**2+24*x*ln(2)*ln(3)+4*x**2*ln(3)**2+24)*ln(x)**2+(-16*ln(2)**2-16*
x*ln(2)*ln(3)-4*x**2*ln(3)**2-12)*ln(x)-64*ln(2)**4-96*x*ln(3)*ln(2)**3+4*(-12*x**2*ln(3)**2-24)*ln(2)**2+2*(-
4*x**3*ln(3)**3-36*x*ln(3))*ln(2)-12*x**2*ln(3)**2-36)/x**5,x)

[Out]

(-2*x**2*log(3)**2 - 8*x*log(2)*log(3) - 6 - 8*log(2)**2)*log(x)**2/x**4 - (-8*x**3*log(2)*log(3)**3 + x**2*(-
24*log(2)**2*log(3)**2 - 6*log(3)**2) + x*(-24*log(2)*log(3) - 32*log(2)**3*log(3)) - 24*log(2)**2 - 9 - 16*lo
g(2)**4)/x**4 + log(x)**4/x**4

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