3.54.92 \(\int \frac {-2 x^3+x^5+(2 x^3-x^5) \log (\frac {x}{3})+(320-240 x-160 x^2+62 x^3-20 x^4+29 x^5+10 x^6) \log ^2(\frac {x}{3})+(-2 x^5 \log (\frac {x}{3})+(160 x^2-240 x^3+10 x^4+58 x^5+10 x^6) \log ^2(\frac {x}{3})) \log (\frac {x^3+(-80+120 x-5 x^2-29 x^3-5 x^4) \log (\frac {x}{3})}{x^2 \log (\frac {x}{3})})}{-x^4 \log (\frac {x}{3})+(80 x-120 x^2+5 x^3+29 x^4+5 x^5) \log ^2(\frac {x}{3})} \, dx\)

Optimal. Leaf size=31 \[ \left (-2+x^2\right ) \log \left (x-5 \left (3-\frac {4}{x}+x\right )^2+\frac {x}{\log \left (\frac {x}{3}\right )}\right ) \]

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Rubi [F]  time = 15.07, 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*} \int \frac {-2 x^3+x^5+\left (2 x^3-x^5\right ) \log \left (\frac {x}{3}\right )+\left (320-240 x-160 x^2+62 x^3-20 x^4+29 x^5+10 x^6\right ) \log ^2\left (\frac {x}{3}\right )+\left (-2 x^5 \log \left (\frac {x}{3}\right )+\left (160 x^2-240 x^3+10 x^4+58 x^5+10 x^6\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log \left (\frac {x^3+\left (-80+120 x-5 x^2-29 x^3-5 x^4\right ) \log \left (\frac {x}{3}\right )}{x^2 \log \left (\frac {x}{3}\right )}\right )}{-x^4 \log \left (\frac {x}{3}\right )+\left (80 x-120 x^2+5 x^3+29 x^4+5 x^5\right ) \log ^2\left (\frac {x}{3}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2*x^3 + x^5 + (2*x^3 - x^5)*Log[x/3] + (320 - 240*x - 160*x^2 + 62*x^3 - 20*x^4 + 29*x^5 + 10*x^6)*Log[x
/3]^2 + (-2*x^5*Log[x/3] + (160*x^2 - 240*x^3 + 10*x^4 + 58*x^5 + 10*x^6)*Log[x/3]^2)*Log[(x^3 + (-80 + 120*x
- 5*x^2 - 29*x^3 - 5*x^4)*Log[x/3])/(x^2*Log[x/3])])/(-(x^4*Log[x/3]) + (80*x - 120*x^2 + 5*x^3 + 29*x^4 + 5*x
^5)*Log[x/3]^2),x]

[Out]

(-29*x)/5 + x^2 - 9*ExpIntegralEi[2*Log[x/3]] + 4*Log[x] + (591*Log[80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4])/100
+ 2*Log[Log[x/3]] + (7066*Defer[Int][(80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4)^(-1), x])/5 - (10951*Defer[Int][x/(
80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4), x])/10 - (29917*Defer[Int][x^2/(80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4), x]
)/100 - (3150096*Defer[Int][1/((-80 + 120*x - 5*x^2 - 29*x^3 - 5*x^4)*(x^3 - (80 - 120*x + 5*x^2 + 29*x^3 + 5*
x^4)*Log[x/3])), x])/125 + (5666264*Defer[Int][x/((-80 + 120*x - 5*x^2 - 29*x^3 - 5*x^4)*(x^3 - (80 - 120*x +
5*x^2 + 29*x^3 + 5*x^4)*Log[x/3])), x])/125 - (1844961*Defer[Int][x^2/((-80 + 120*x - 5*x^2 - 29*x^3 - 5*x^4)*
(x^3 - (80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4)*Log[x/3])), x])/125 - (3202449*Defer[Int][x^3/((-80 + 120*x - 5*x
^2 - 29*x^3 - 5*x^4)*(x^3 - (80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4)*Log[x/3])), x])/625 + (346881*Defer[Int][(-x
^3 + (80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4)*Log[x/3])^(-1), x])/625 - (3014*Defer[Int][x/(-x^3 + (80 - 120*x +
5*x^2 + 29*x^3 + 5*x^4)*Log[x/3]), x])/125 - (3709*Defer[Int][x^2/(-x^3 + (80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4
)*Log[x/3]), x])/25 - (54*Defer[Int][x^3/(-x^3 + (80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4)*Log[x/3]), x])/5 + 30*D
efer[Int][x^4/(-x^3 + (80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4)*Log[x/3]), x] + 5*Defer[Int][x^5/(-x^3 + (80 - 120
*x + 5*x^2 + 29*x^3 + 5*x^4)*Log[x/3]), x] - 160*Defer[Int][(-x^4 + x*(80 - 120*x + 5*x^2 + 29*x^3 + 5*x^4)*Lo
g[x/3])^(-1), x] + 2*Defer[Int][x*Log[-5 - 80/x^2 + 120/x - 29*x - 5*x^2 + x/Log[x/3]], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {\left (-2+x^2\right ) \left (x^3-x^3 \log \left (\frac {x}{3}\right )-160 \log ^2\left (\frac {x}{3}\right )+120 x \log ^2\left (\frac {x}{3}\right )+29 x^3 \log ^2\left (\frac {x}{3}\right )+10 x^4 \log ^2\left (\frac {x}{3}\right )\right )}{x \log \left (\frac {x}{3}\right ) \left (-x^3+80 \log \left (\frac {x}{3}\right )-120 x \log \left (\frac {x}{3}\right )+5 x^2 \log \left (\frac {x}{3}\right )+29 x^3 \log \left (\frac {x}{3}\right )+5 x^4 \log \left (\frac {x}{3}\right )\right )}+2 x \log \left (-5-\frac {80}{x^2}+\frac {120}{x}-29 x-5 x^2+\frac {x}{\log \left (\frac {x}{3}\right )}\right )\right ) \, dx\\ &=2 \int x \log \left (-5-\frac {80}{x^2}+\frac {120}{x}-29 x-5 x^2+\frac {x}{\log \left (\frac {x}{3}\right )}\right ) \, dx+\int \frac {\left (-2+x^2\right ) \left (x^3-x^3 \log \left (\frac {x}{3}\right )-160 \log ^2\left (\frac {x}{3}\right )+120 x \log ^2\left (\frac {x}{3}\right )+29 x^3 \log ^2\left (\frac {x}{3}\right )+10 x^4 \log ^2\left (\frac {x}{3}\right )\right )}{x \log \left (\frac {x}{3}\right ) \left (-x^3+80 \log \left (\frac {x}{3}\right )-120 x \log \left (\frac {x}{3}\right )+5 x^2 \log \left (\frac {x}{3}\right )+29 x^3 \log \left (\frac {x}{3}\right )+5 x^4 \log \left (\frac {x}{3}\right )\right )} \, dx\\ &=2 \int x \log \left (-5-\frac {80}{x^2}+\frac {120}{x}-29 x-5 x^2+\frac {x}{\log \left (\frac {x}{3}\right )}\right ) \, dx+\int \frac {\left (2-x^2\right ) \left (x^3-x^3 \log \left (\frac {x}{3}\right )+\left (-160+120 x+29 x^3+10 x^4\right ) \log ^2\left (\frac {x}{3}\right )\right )}{x \log \left (\frac {x}{3}\right ) \left (x^3-\left (80-120 x+5 x^2+29 x^3+5 x^4\right ) \log \left (\frac {x}{3}\right )\right )} \, dx\\ &=2 \int x \log \left (-5-\frac {80}{x^2}+\frac {120}{x}-29 x-5 x^2+\frac {x}{\log \left (\frac {x}{3}\right )}\right ) \, dx+\int \left (\frac {\left (-2+x^2\right ) \left (-160+120 x+29 x^3+10 x^4\right )}{x \left (80-120 x+5 x^2+29 x^3+5 x^4\right )}+\frac {2-x^2}{x \log \left (\frac {x}{3}\right )}+\frac {\left (-2+x^2\right ) \left (80-120 x+5 x^2+29 x^3+5 x^4\right )}{x \left (-x^3+80 \log \left (\frac {x}{3}\right )-120 x \log \left (\frac {x}{3}\right )+5 x^2 \log \left (\frac {x}{3}\right )+29 x^3 \log \left (\frac {x}{3}\right )+5 x^4 \log \left (\frac {x}{3}\right )\right )}+\frac {5 x^2 \left (96-96 x-46 x^2+48 x^3-3 x^4+x^6\right )}{\left (80-120 x+5 x^2+29 x^3+5 x^4\right ) \left (-x^3+80 \log \left (\frac {x}{3}\right )-120 x \log \left (\frac {x}{3}\right )+5 x^2 \log \left (\frac {x}{3}\right )+29 x^3 \log \left (\frac {x}{3}\right )+5 x^4 \log \left (\frac {x}{3}\right )\right )}\right ) \, dx\\ &=2 \int x \log \left (-5-\frac {80}{x^2}+\frac {120}{x}-29 x-5 x^2+\frac {x}{\log \left (\frac {x}{3}\right )}\right ) \, dx+5 \int \frac {x^2 \left (96-96 x-46 x^2+48 x^3-3 x^4+x^6\right )}{\left (80-120 x+5 x^2+29 x^3+5 x^4\right ) \left (-x^3+80 \log \left (\frac {x}{3}\right )-120 x \log \left (\frac {x}{3}\right )+5 x^2 \log \left (\frac {x}{3}\right )+29 x^3 \log \left (\frac {x}{3}\right )+5 x^4 \log \left (\frac {x}{3}\right )\right )} \, dx+\int \frac {\left (-2+x^2\right ) \left (-160+120 x+29 x^3+10 x^4\right )}{x \left (80-120 x+5 x^2+29 x^3+5 x^4\right )} \, dx+\int \frac {2-x^2}{x \log \left (\frac {x}{3}\right )} \, dx+\int \frac {\left (-2+x^2\right ) \left (80-120 x+5 x^2+29 x^3+5 x^4\right )}{x \left (-x^3+80 \log \left (\frac {x}{3}\right )-120 x \log \left (\frac {x}{3}\right )+5 x^2 \log \left (\frac {x}{3}\right )+29 x^3 \log \left (\frac {x}{3}\right )+5 x^4 \log \left (\frac {x}{3}\right )\right )} \, dx\\ &=2 \int x \log \left (-5-\frac {80}{x^2}+\frac {120}{x}-29 x-5 x^2+\frac {x}{\log \left (\frac {x}{3}\right )}\right ) \, dx+5 \int \frac {x^2 \left (-96+96 x+46 x^2-48 x^3+3 x^4-x^6\right )}{\left (80-120 x+5 x^2+29 x^3+5 x^4\right ) \left (x^3-\left (80-120 x+5 x^2+29 x^3+5 x^4\right ) \log \left (\frac {x}{3}\right )\right )} \, dx+\int \left (-\frac {29}{5}+\frac {4}{x}+2 x+\frac {3520-5180 x+1075 x^2+591 x^3}{5 \left (80-120 x+5 x^2+29 x^3+5 x^4\right )}\right ) \, dx+\int \left (\frac {2}{x \log \left (\frac {x}{3}\right )}-\frac {x}{\log \left (\frac {x}{3}\right )}\right ) \, dx+\int \frac {\left (2-x^2\right ) \left (80-120 x+5 x^2+29 x^3+5 x^4\right )}{x^4-x \left (80-120 x+5 x^2+29 x^3+5 x^4\right ) \log \left (\frac {x}{3}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.17, size = 112, normalized size = 3.61 \begin {gather*} 4 \log \left (\frac {x}{3}\right )+x^2 \log \left (-5-\frac {80}{x^2}+\frac {120}{x}-29 x-5 x^2+\frac {x}{\log \left (\frac {x}{3}\right )}\right )+2 \log \left (\log \left (\frac {x}{3}\right )\right )-2 \log \left (-x^3+80 \log \left (\frac {x}{3}\right )-120 x \log \left (\frac {x}{3}\right )+5 x^2 \log \left (\frac {x}{3}\right )+29 x^3 \log \left (\frac {x}{3}\right )+5 x^4 \log \left (\frac {x}{3}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x^3 + x^5 + (2*x^3 - x^5)*Log[x/3] + (320 - 240*x - 160*x^2 + 62*x^3 - 20*x^4 + 29*x^5 + 10*x^6)
*Log[x/3]^2 + (-2*x^5*Log[x/3] + (160*x^2 - 240*x^3 + 10*x^4 + 58*x^5 + 10*x^6)*Log[x/3]^2)*Log[(x^3 + (-80 +
120*x - 5*x^2 - 29*x^3 - 5*x^4)*Log[x/3])/(x^2*Log[x/3])])/(-(x^4*Log[x/3]) + (80*x - 120*x^2 + 5*x^3 + 29*x^4
+ 5*x^5)*Log[x/3]^2),x]

[Out]

4*Log[x/3] + x^2*Log[-5 - 80/x^2 + 120/x - 29*x - 5*x^2 + x/Log[x/3]] + 2*Log[Log[x/3]] - 2*Log[-x^3 + 80*Log[
x/3] - 120*x*Log[x/3] + 5*x^2*Log[x/3] + 29*x^3*Log[x/3] + 5*x^4*Log[x/3]]

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fricas [A]  time = 0.48, size = 47, normalized size = 1.52 \begin {gather*} {\left (x^{2} - 2\right )} \log \left (\frac {x^{3} - {\left (5 \, x^{4} + 29 \, x^{3} + 5 \, x^{2} - 120 \, x + 80\right )} \log \left (\frac {1}{3} \, x\right )}{x^{2} \log \left (\frac {1}{3} \, x\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x^6+58*x^5+10*x^4-240*x^3+160*x^2)*log(1/3*x)^2-2*x^5*log(1/3*x))*log(((-5*x^4-29*x^3-5*x^2+12
0*x-80)*log(1/3*x)+x^3)/x^2/log(1/3*x))+(10*x^6+29*x^5-20*x^4+62*x^3-160*x^2-240*x+320)*log(1/3*x)^2+(-x^5+2*x
^3)*log(1/3*x)+x^5-2*x^3)/((5*x^5+29*x^4+5*x^3-120*x^2+80*x)*log(1/3*x)^2-x^4*log(1/3*x)),x, algorithm="fricas
")

[Out]

(x^2 - 2)*log((x^3 - (5*x^4 + 29*x^3 + 5*x^2 - 120*x + 80)*log(1/3*x))/(x^2*log(1/3*x)))

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giac [B]  time = 2.38, size = 148, normalized size = 4.77 \begin {gather*} x^{2} \log \left (-5 \, x^{4} \log \left (\frac {1}{3} \, x\right ) - 29 \, x^{3} \log \left (\frac {1}{3} \, x\right ) + x^{3} - 5 \, x^{2} \log \left (\frac {1}{3} \, x\right ) + 120 \, x \log \left (\frac {1}{3} \, x\right ) - 80 \, \log \left (\frac {1}{3} \, x\right )\right ) - 2 \, x^{2} \log \relax (x) - x^{2} \log \left (\log \left (\frac {1}{3} \, x\right )\right ) - 2 \, \log \left (5 \, x^{4} \log \relax (3) - 5 \, x^{4} \log \relax (x) + 29 \, x^{3} \log \relax (3) - 29 \, x^{3} \log \relax (x) + x^{3} + 5 \, x^{2} \log \relax (3) - 5 \, x^{2} \log \relax (x) - 120 \, x \log \relax (3) + 120 \, x \log \relax (x) + 80 \, \log \relax (3) - 80 \, \log \relax (x)\right ) + 4 \, \log \relax (x) + 2 \, \log \left (\log \relax (3) - \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x^6+58*x^5+10*x^4-240*x^3+160*x^2)*log(1/3*x)^2-2*x^5*log(1/3*x))*log(((-5*x^4-29*x^3-5*x^2+12
0*x-80)*log(1/3*x)+x^3)/x^2/log(1/3*x))+(10*x^6+29*x^5-20*x^4+62*x^3-160*x^2-240*x+320)*log(1/3*x)^2+(-x^5+2*x
^3)*log(1/3*x)+x^5-2*x^3)/((5*x^5+29*x^4+5*x^3-120*x^2+80*x)*log(1/3*x)^2-x^4*log(1/3*x)),x, algorithm="giac")

[Out]

x^2*log(-5*x^4*log(1/3*x) - 29*x^3*log(1/3*x) + x^3 - 5*x^2*log(1/3*x) + 120*x*log(1/3*x) - 80*log(1/3*x)) - 2
*x^2*log(x) - x^2*log(log(1/3*x)) - 2*log(5*x^4*log(3) - 5*x^4*log(x) + 29*x^3*log(3) - 29*x^3*log(x) + x^3 +
5*x^2*log(3) - 5*x^2*log(x) - 120*x*log(3) + 120*x*log(x) + 80*log(3) - 80*log(x)) + 4*log(x) + 2*log(log(3) -
log(x))

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maple [F]  time = 0.18, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (10 x^{6}+58 x^{5}+10 x^{4}-240 x^{3}+160 x^{2}\right ) \ln \left (\frac {x}{3}\right )^{2}-2 x^{5} \ln \left (\frac {x}{3}\right )\right ) \ln \left (\frac {\left (-5 x^{4}-29 x^{3}-5 x^{2}+120 x -80\right ) \ln \left (\frac {x}{3}\right )+x^{3}}{x^{2} \ln \left (\frac {x}{3}\right )}\right )+\left (10 x^{6}+29 x^{5}-20 x^{4}+62 x^{3}-160 x^{2}-240 x +320\right ) \ln \left (\frac {x}{3}\right )^{2}+\left (-x^{5}+2 x^{3}\right ) \ln \left (\frac {x}{3}\right )+x^{5}-2 x^{3}}{\left (5 x^{5}+29 x^{4}+5 x^{3}-120 x^{2}+80 x \right ) \ln \left (\frac {x}{3}\right )^{2}-x^{4} \ln \left (\frac {x}{3}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((10*x^6+58*x^5+10*x^4-240*x^3+160*x^2)*ln(1/3*x)^2-2*x^5*ln(1/3*x))*ln(((-5*x^4-29*x^3-5*x^2+120*x-80)*l
n(1/3*x)+x^3)/x^2/ln(1/3*x))+(10*x^6+29*x^5-20*x^4+62*x^3-160*x^2-240*x+320)*ln(1/3*x)^2+(-x^5+2*x^3)*ln(1/3*x
)+x^5-2*x^3)/((5*x^5+29*x^4+5*x^3-120*x^2+80*x)*ln(1/3*x)^2-x^4*ln(1/3*x)),x)

[Out]

int((((10*x^6+58*x^5+10*x^4-240*x^3+160*x^2)*ln(1/3*x)^2-2*x^5*ln(1/3*x))*ln(((-5*x^4-29*x^3-5*x^2+120*x-80)*l
n(1/3*x)+x^3)/x^2/ln(1/3*x))+(10*x^6+29*x^5-20*x^4+62*x^3-160*x^2-240*x+320)*ln(1/3*x)^2+(-x^5+2*x^3)*ln(1/3*x
)+x^5-2*x^3)/((5*x^5+29*x^4+5*x^3-120*x^2+80*x)*ln(1/3*x)^2-x^4*ln(1/3*x)),x)

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maxima [B]  time = 0.54, size = 198, normalized size = 6.39 \begin {gather*} x^{2} \log \left (5 \, x^{4} \log \relax (3) + x^{3} {\left (29 \, \log \relax (3) + 1\right )} + 5 \, x^{2} \log \relax (3) - 120 \, x \log \relax (3) - {\left (5 \, x^{4} + 29 \, x^{3} + 5 \, x^{2} - 120 \, x + 80\right )} \log \relax (x) + 80 \, \log \relax (3)\right ) - 2 \, x^{2} \log \relax (x) - {\left (x^{2} - 2\right )} \log \left (-\log \relax (3) + \log \relax (x)\right ) - 2 \, \log \left (5 \, x^{4} + 29 \, x^{3} + 5 \, x^{2} - 120 \, x + 80\right ) + 4 \, \log \relax (x) - 2 \, \log \left (-\frac {5 \, x^{4} \log \relax (3) + x^{3} {\left (29 \, \log \relax (3) + 1\right )} + 5 \, x^{2} \log \relax (3) - 120 \, x \log \relax (3) - {\left (5 \, x^{4} + 29 \, x^{3} + 5 \, x^{2} - 120 \, x + 80\right )} \log \relax (x) + 80 \, \log \relax (3)}{5 \, x^{4} + 29 \, x^{3} + 5 \, x^{2} - 120 \, x + 80}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x^6+58*x^5+10*x^4-240*x^3+160*x^2)*log(1/3*x)^2-2*x^5*log(1/3*x))*log(((-5*x^4-29*x^3-5*x^2+12
0*x-80)*log(1/3*x)+x^3)/x^2/log(1/3*x))+(10*x^6+29*x^5-20*x^4+62*x^3-160*x^2-240*x+320)*log(1/3*x)^2+(-x^5+2*x
^3)*log(1/3*x)+x^5-2*x^3)/((5*x^5+29*x^4+5*x^3-120*x^2+80*x)*log(1/3*x)^2-x^4*log(1/3*x)),x, algorithm="maxima
")

[Out]

x^2*log(5*x^4*log(3) + x^3*(29*log(3) + 1) + 5*x^2*log(3) - 120*x*log(3) - (5*x^4 + 29*x^3 + 5*x^2 - 120*x + 8
0)*log(x) + 80*log(3)) - 2*x^2*log(x) - (x^2 - 2)*log(-log(3) + log(x)) - 2*log(5*x^4 + 29*x^3 + 5*x^2 - 120*x
+ 80) + 4*log(x) - 2*log(-(5*x^4*log(3) + x^3*(29*log(3) + 1) + 5*x^2*log(3) - 120*x*log(3) - (5*x^4 + 29*x^3
+ 5*x^2 - 120*x + 80)*log(x) + 80*log(3))/(5*x^4 + 29*x^3 + 5*x^2 - 120*x + 80))

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mupad [B]  time = 4.72, size = 357, normalized size = 11.52 \begin {gather*} 2\,\ln \left (x^4+\frac {29\,x^3}{5}+x^2-24\,x+16\right )+2\,\ln \left (\frac {25600\,\ln \left (\frac {x}{3}\right )-76800\,x\,\ln \left (\frac {x}{3}\right )+100\,x^8\,\ln \relax (x)+60800\,x^2\,\ln \left (\frac {x}{3}\right )+12800\,x^3\,\ln \left (\frac {x}{3}\right )-23580\,x^4\,\ln \left (\frac {x}{3}\right )-3660\,x^5\,\ln \left (\frac {x}{3}\right )+3564\,x^6\,\ln \left (\frac {x}{3}\right )+1180\,x^7\,\ln \left (\frac {x}{3}\right )-100\,x^8\,\ln \relax (3)}{x\,{\left (5\,x^4+29\,x^3+5\,x^2-120\,x+80\right )}^2}\right )-2\,\ln \left (\frac {320\,\ln \relax (3)-320\,\ln \relax (x)-20\,x^2\,\ln \relax (x)-116\,x^3\,\ln \relax (x)-20\,x^4\,\ln \relax (x)-480\,x\,\ln \relax (3)+20\,x^2\,\ln \relax (3)+116\,x^3\,\ln \relax (3)+20\,x^4\,\ln \relax (3)+480\,x\,\ln \relax (x)+4\,x^3}{x\,\left (5\,x^4+29\,x^3+5\,x^2-120\,x+80\right )}\right )-2\,\ln \left (x^8+\frac {59\,x^7}{5}+\frac {891\,x^6}{25}-\frac {183\,x^5}{5}-\frac {1179\,x^4}{5}+128\,x^3+608\,x^2-768\,x+256\right )+4\,\ln \relax (x)+x^2\,\ln \left (\frac {80\,\ln \relax (3)-80\,\ln \relax (x)-5\,x^2\,\ln \relax (x)-29\,x^3\,\ln \relax (x)-5\,x^4\,\ln \relax (x)-120\,x\,\ln \relax (3)+5\,x^2\,\ln \relax (3)+29\,x^3\,\ln \relax (3)+5\,x^4\,\ln \relax (3)+120\,x\,\ln \relax (x)+x^3}{x^2\,\ln \relax (x)-x^2\,\ln \relax (3)}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(-(log(x/3)*(5*x^2 - 120*x + 29*x^3 + 5*x^4 + 80) - x^3)/(x^2*log(x/3)))*(log(x/3)^2*(160*x^2 - 240*x^
3 + 10*x^4 + 58*x^5 + 10*x^6) - 2*x^5*log(x/3)) + log(x/3)^2*(62*x^3 - 160*x^2 - 240*x - 20*x^4 + 29*x^5 + 10*
x^6 + 320) + log(x/3)*(2*x^3 - x^5) - 2*x^3 + x^5)/(log(x/3)^2*(80*x - 120*x^2 + 5*x^3 + 29*x^4 + 5*x^5) - x^4
*log(x/3)),x)

[Out]

2*log(x^2 - 24*x + (29*x^3)/5 + x^4 + 16) + 2*log((25600*log(x/3) - 76800*x*log(x/3) + 100*x^8*log(x) + 60800*
x^2*log(x/3) + 12800*x^3*log(x/3) - 23580*x^4*log(x/3) - 3660*x^5*log(x/3) + 3564*x^6*log(x/3) + 1180*x^7*log(
x/3) - 100*x^8*log(3))/(x*(5*x^2 - 120*x + 29*x^3 + 5*x^4 + 80)^2)) - 2*log((320*log(3) - 320*log(x) - 20*x^2*
log(x) - 116*x^3*log(x) - 20*x^4*log(x) - 480*x*log(3) + 20*x^2*log(3) + 116*x^3*log(3) + 20*x^4*log(3) + 480*
x*log(x) + 4*x^3)/(x*(5*x^2 - 120*x + 29*x^3 + 5*x^4 + 80))) - 2*log(608*x^2 - 768*x + 128*x^3 - (1179*x^4)/5
- (183*x^5)/5 + (891*x^6)/25 + (59*x^7)/5 + x^8 + 256) + 4*log(x) + x^2*log((80*log(3) - 80*log(x) - 5*x^2*log
(x) - 29*x^3*log(x) - 5*x^4*log(x) - 120*x*log(3) + 5*x^2*log(3) + 29*x^3*log(3) + 5*x^4*log(3) + 120*x*log(x)
+ x^3)/(x^2*log(x) - x^2*log(3)))

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sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: PolynomialError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x**6+58*x**5+10*x**4-240*x**3+160*x**2)*ln(1/3*x)**2-2*x**5*ln(1/3*x))*ln(((-5*x**4-29*x**3-5*
x**2+120*x-80)*ln(1/3*x)+x**3)/x**2/ln(1/3*x))+(10*x**6+29*x**5-20*x**4+62*x**3-160*x**2-240*x+320)*ln(1/3*x)*
*2+(-x**5+2*x**3)*ln(1/3*x)+x**5-2*x**3)/((5*x**5+29*x**4+5*x**3-120*x**2+80*x)*ln(1/3*x)**2-x**4*ln(1/3*x)),x
)

[Out]

Exception raised: PolynomialError

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