3.63.61 \(\int \frac {(-36+12 x) \log (x) \log (3 x^2)+(-9+3 x-9 \log (x)) \log ^2(3 x^2)+(-12+7 x-x^2+(-12+x^2) \log (x)) \log ^4(3 x^2)}{81-54 x+9 x^2+(216-198 x+60 x^2-6 x^3) \log ^2(3 x^2)+(144-168 x+73 x^2-14 x^3+x^4) \log ^4(3 x^2)} \, dx\)

Optimal. Leaf size=25 \[ -\frac {x \log (x)}{(-3+x) \left (-4+x-\frac {3}{\log ^2\left (3 x^2\right )}\right )} \]

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Rubi [F]  time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-36 + 12*x)*Log[x]*Log[3*x^2] + (-9 + 3*x - 9*Log[x])*Log[3*x^2]^2 + (-12 + 7*x - x^2 + (-12 + x^2)*Log[
x])*Log[3*x^2]^4)/(81 - 54*x + 9*x^2 + (216 - 198*x + 60*x^2 - 6*x^3)*Log[3*x^2]^2 + (144 - 168*x + 73*x^2 - 1
4*x^3 + x^4)*Log[3*x^2]^4),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.13, size = 34, normalized size = 1.36 \begin {gather*} -\frac {x \log (x) \log ^2\left (3 x^2\right )}{(-3+x) \left (-3+(-4+x) \log ^2\left (3 x^2\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-36 + 12*x)*Log[x]*Log[3*x^2] + (-9 + 3*x - 9*Log[x])*Log[3*x^2]^2 + (-12 + 7*x - x^2 + (-12 + x^2
)*Log[x])*Log[3*x^2]^4)/(81 - 54*x + 9*x^2 + (216 - 198*x + 60*x^2 - 6*x^3)*Log[3*x^2]^2 + (144 - 168*x + 73*x
^2 - 14*x^3 + x^4)*Log[3*x^2]^4),x]

[Out]

-((x*Log[x]*Log[3*x^2]^2)/((-3 + x)*(-3 + (-4 + x)*Log[3*x^2]^2)))

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fricas [B]  time = 0.74, size = 75, normalized size = 3.00 \begin {gather*} -\frac {x \log \relax (3)^{2} \log \relax (x) + 4 \, x \log \relax (3) \log \relax (x)^{2} + 4 \, x \log \relax (x)^{3}}{{\left (x^{2} - 7 \, x + 12\right )} \log \relax (3)^{2} + 4 \, {\left (x^{2} - 7 \, x + 12\right )} \log \relax (3) \log \relax (x) + 4 \, {\left (x^{2} - 7 \, x + 12\right )} \log \relax (x)^{2} - 3 \, x + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-12)*log(x)-x^2+7*x-12)*log(3*x^2)^4+(-9*log(x)+3*x-9)*log(3*x^2)^2+(12*x-36)*log(x)*log(3*x^2
))/((x^4-14*x^3+73*x^2-168*x+144)*log(3*x^2)^4+(-6*x^3+60*x^2-198*x+216)*log(3*x^2)^2+9*x^2-54*x+81),x, algori
thm="fricas")

[Out]

-(x*log(3)^2*log(x) + 4*x*log(3)*log(x)^2 + 4*x*log(x)^3)/((x^2 - 7*x + 12)*log(3)^2 + 4*(x^2 - 7*x + 12)*log(
3)*log(x) + 4*(x^2 - 7*x + 12)*log(x)^2 - 3*x + 9)

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giac [B]  time = 4.13, size = 125, normalized size = 5.00 \begin {gather*} -\frac {3 \, x \log \relax (x)}{x^{3} \log \relax (3)^{2} + 4 \, x^{3} \log \relax (3) \log \relax (x) + 4 \, x^{3} \log \relax (x)^{2} - 11 \, x^{2} \log \relax (3)^{2} - 44 \, x^{2} \log \relax (3) \log \relax (x) - 44 \, x^{2} \log \relax (x)^{2} + 40 \, x \log \relax (3)^{2} + 160 \, x \log \relax (3) \log \relax (x) + 160 \, x \log \relax (x)^{2} - 3 \, x^{2} - 48 \, \log \relax (3)^{2} - 192 \, \log \relax (3) \log \relax (x) - 192 \, \log \relax (x)^{2} + 21 \, x - 36} - \frac {x \log \relax (x)}{x^{2} - 7 \, x + 12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-12)*log(x)-x^2+7*x-12)*log(3*x^2)^4+(-9*log(x)+3*x-9)*log(3*x^2)^2+(12*x-36)*log(x)*log(3*x^2
))/((x^4-14*x^3+73*x^2-168*x+144)*log(3*x^2)^4+(-6*x^3+60*x^2-198*x+216)*log(3*x^2)^2+9*x^2-54*x+81),x, algori
thm="giac")

[Out]

-3*x*log(x)/(x^3*log(3)^2 + 4*x^3*log(3)*log(x) + 4*x^3*log(x)^2 - 11*x^2*log(3)^2 - 44*x^2*log(3)*log(x) - 44
*x^2*log(x)^2 + 40*x*log(3)^2 + 160*x*log(3)*log(x) + 160*x*log(x)^2 - 3*x^2 - 48*log(3)^2 - 192*log(3)*log(x)
- 192*log(x)^2 + 21*x - 36) - x*log(x)/(x^2 - 7*x + 12)

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maple [C]  time = 106.03, size = 498, normalized size = 19.92

method	result	size
risch	\(-\frac {x \ln \relax (x )}{x^{2}-7 x +12}-\frac {12 x \ln \relax (x )}{\left (x^{2}-7 x +12\right ) \left (-12+16 x \ln \relax (3) \ln \relax (x )-16 \ln \relax (3)^{2}-64 \ln \relax (x )^{2}+4 x \ln \relax (3)^{2}-64 \ln \relax (3) \ln \relax (x )+16 x \ln \relax (x )^{2}+4 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}-32 i \ln \relax (3) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-4 i x \ln \relax (3) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-8 i x \ln \relax (x ) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 \pi ^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}-16 \pi ^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-16 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-\pi ^{2} x \mathrm {csgn}\left (i x^{2}\right )^{6}-64 i \ln \relax (x ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+16 i \ln \relax (3) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-\pi ^{2} x \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+4 \pi ^{2} x \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-6 \pi ^{2} x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+4 \pi ^{2} x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}+24 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}-8 i x \ln \relax (x ) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+16 i x \ln \relax (x ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-4 i x \ln \relax (3) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+8 i x \ln \relax (3) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+16 i \ln \relax (3) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+32 i \ln \relax (x ) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+32 i \ln \relax (x ) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )\right )}\)	\(498\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^2-12)*ln(x)-x^2+7*x-12)*ln(3*x^2)^4+(-9*ln(x)+3*x-9)*ln(3*x^2)^2+(12*x-36)*ln(x)*ln(3*x^2))/((x^4-14*
x^3+73*x^2-168*x+144)*ln(3*x^2)^4+(-6*x^3+60*x^2-198*x+216)*ln(3*x^2)^2+9*x^2-54*x+81),x,method=_RETURNVERBOSE
)

[Out]

-x/(x^2-7*x+12)*ln(x)-12*x/(x^2-7*x+12)*ln(x)/(-12+16*x*ln(3)*ln(x)+4*Pi^2*csgn(I*x)^4*csgn(I*x^2)^2-16*Pi^2*c
sgn(I*x)^3*csgn(I*x^2)^3+24*Pi^2*csgn(I*x)^2*csgn(I*x^2)^4-16*Pi^2*csgn(I*x)*csgn(I*x^2)^5-16*ln(3)^2-64*ln(x)
^2+4*x*ln(3)^2-64*ln(3)*ln(x)+16*x*ln(x)^2+4*Pi^2*csgn(I*x^2)^6-Pi^2*x*csgn(I*x^2)^6-8*I*x*ln(x)*Pi*csgn(I*x)^
2*csgn(I*x^2)+16*I*x*ln(x)*Pi*csgn(I*x)*csgn(I*x^2)^2-4*I*x*ln(3)*Pi*csgn(I*x)^2*csgn(I*x^2)+8*I*x*ln(3)*Pi*cs
gn(I*x)*csgn(I*x^2)^2+16*I*ln(3)*Pi*csgn(I*x)^2*csgn(I*x^2)-32*I*ln(3)*Pi*csgn(I*x)*csgn(I*x^2)^2-4*I*x*ln(3)*
Pi*csgn(I*x^2)^3-64*I*ln(x)*Pi*csgn(I*x)*csgn(I*x^2)^2+16*I*ln(3)*Pi*csgn(I*x^2)^3+32*I*ln(x)*Pi*csgn(I*x^2)^3
-Pi^2*x*csgn(I*x)^4*csgn(I*x^2)^2+4*Pi^2*x*csgn(I*x)^3*csgn(I*x^2)^3-6*Pi^2*x*csgn(I*x)^2*csgn(I*x^2)^4+4*Pi^2
*x*csgn(I*x)*csgn(I*x^2)^5+32*I*ln(x)*Pi*csgn(I*x)^2*csgn(I*x^2)-8*I*x*ln(x)*Pi*csgn(I*x^2)^3)

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maxima [B]  time = 0.63, size = 140, normalized size = 5.60 \begin {gather*} -\frac {4 \, {\left (x^{2} - 4 \, x\right )} \log \relax (x)^{3} + 4 \, {\left (x^{2} \log \relax (3) - 4 \, x \log \relax (3)\right )} \log \relax (x)^{2} + {\left (x^{2} \log \relax (3)^{2} - 4 \, x \log \relax (3)^{2}\right )} \log \relax (x)}{x^{3} \log \relax (3)^{2} - {\left (11 \, \log \relax (3)^{2} + 3\right )} x^{2} + 4 \, {\left (x^{3} - 11 \, x^{2} + 40 \, x - 48\right )} \log \relax (x)^{2} + {\left (40 \, \log \relax (3)^{2} + 21\right )} x - 48 \, \log \relax (3)^{2} + 4 \, {\left (x^{3} \log \relax (3) - 11 \, x^{2} \log \relax (3) + 40 \, x \log \relax (3) - 48 \, \log \relax (3)\right )} \log \relax (x) - 36} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-12)*log(x)-x^2+7*x-12)*log(3*x^2)^4+(-9*log(x)+3*x-9)*log(3*x^2)^2+(12*x-36)*log(x)*log(3*x^2
))/((x^4-14*x^3+73*x^2-168*x+144)*log(3*x^2)^4+(-6*x^3+60*x^2-198*x+216)*log(3*x^2)^2+9*x^2-54*x+81),x, algori
thm="maxima")

[Out]

-(4*(x^2 - 4*x)*log(x)^3 + 4*(x^2*log(3) - 4*x*log(3))*log(x)^2 + (x^2*log(3)^2 - 4*x*log(3)^2)*log(x))/(x^3*l
og(3)^2 - (11*log(3)^2 + 3)*x^2 + 4*(x^3 - 11*x^2 + 40*x - 48)*log(x)^2 + (40*log(3)^2 + 21)*x - 48*log(3)^2 +
4*(x^3*log(3) - 11*x^2*log(3) + 40*x*log(3) - 48*log(3))*log(x) - 36)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\left (7\,x+\ln \relax (x)\,\left (x^2-12\right )-x^2-12\right )\,{\ln \left (3\,x^2\right )}^4+\left (3\,x-9\,\ln \relax (x)-9\right )\,{\ln \left (3\,x^2\right )}^2+\ln \relax (x)\,\left (12\,x-36\right )\,\ln \left (3\,x^2\right )}{9\,x^2-{\ln \left (3\,x^2\right )}^2\,\left (6\,x^3-60\,x^2+198\,x-216\right )-54\,x+{\ln \left (3\,x^2\right )}^4\,\left (x^4-14\,x^3+73\,x^2-168\,x+144\right )+81} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(3*x^2)^4*(7*x + log(x)*(x^2 - 12) - x^2 - 12) - log(3*x^2)^2*(9*log(x) - 3*x + 9) + log(3*x^2)*log(x)
*(12*x - 36))/(9*x^2 - log(3*x^2)^2*(198*x - 60*x^2 + 6*x^3 - 216) - 54*x + log(3*x^2)^4*(73*x^2 - 168*x - 14*
x^3 + x^4 + 144) + 81),x)

[Out]

int((log(3*x^2)^4*(7*x + log(x)*(x^2 - 12) - x^2 - 12) - log(3*x^2)^2*(9*log(x) - 3*x + 9) + log(3*x^2)*log(x)
*(12*x - 36))/(9*x^2 - log(3*x^2)^2*(198*x - 60*x^2 + 6*x^3 - 216) - 54*x + log(3*x^2)^4*(73*x^2 - 168*x - 14*
x^3 + x^4 + 144) + 81), x)

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sympy [B]  time = 0.85, size = 117, normalized size = 4.68 \begin {gather*} - \frac {3 x \log {\relax (x )}}{x^{3} \log {\relax (3 )}^{2} - 11 x^{2} \log {\relax (3 )}^{2} - 3 x^{2} + 21 x + 40 x \log {\relax (3 )}^{2} + \left (4 x^{3} - 44 x^{2} + 160 x - 192\right ) \log {\relax (x )}^{2} + \left (4 x^{3} \log {\relax (3 )} - 44 x^{2} \log {\relax (3 )} + 160 x \log {\relax (3 )} - 192 \log {\relax (3 )}\right ) \log {\relax (x )} - 48 \log {\relax (3 )}^{2} - 36} - \frac {x \log {\relax (x )}}{x^{2} - 7 x + 12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**2-12)*ln(x)-x**2+7*x-12)*ln(3*x**2)**4+(-9*ln(x)+3*x-9)*ln(3*x**2)**2+(12*x-36)*ln(x)*ln(3*x**
2))/((x**4-14*x**3+73*x**2-168*x+144)*ln(3*x**2)**4+(-6*x**3+60*x**2-198*x+216)*ln(3*x**2)**2+9*x**2-54*x+81),
x)

[Out]

-3*x*log(x)/(x**3*log(3)**2 - 11*x**2*log(3)**2 - 3*x**2 + 21*x + 40*x*log(3)**2 + (4*x**3 - 44*x**2 + 160*x -
192)*log(x)**2 + (4*x**3*log(3) - 44*x**2*log(3) + 160*x*log(3) - 192*log(3))*log(x) - 48*log(3)**2 - 36) - x
*log(x)/(x**2 - 7*x + 12)

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