Integrand size = 127, antiderivative size = 28 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\left (3+\frac {1}{25} \left (-\log (4) (x-x \log (-3+x))+\log \left (9 x^2\right )\right )\right )^2 \]
Time = 0.05 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {1}{625} \left (75-x \log (4)+x \log (4) \log (-3+x)+\log \left (9 x^2\right )\right )^2 \]
Integrate[(-900 + 300*x + (462*x - 4*x^2)*Log[4] - 6*x^2*Log[4]^2 + ((-462 *x + 154*x^2)*Log[4] + (12*x^2 - 2*x^3)*Log[4]^2)*Log[-3 + x] + (-6*x^2 + 2*x^3)*Log[4]^2*Log[-3 + x]^2 + (-12 + 4*x + 6*x*Log[4] + (-6*x + 2*x^2)*L og[4]*Log[-3 + x])*Log[9*x^2])/(-1875*x + 625*x^2),x]
Time = 0.66 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {2026, 7239, 27, 7237}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-6 x^2 \log ^2(4)+\left (\left (2 x^2-6 x\right ) \log (4) \log (x-3)+4 x+6 x \log (4)-12\right ) \log \left (9 x^2\right )+\left (462 x-4 x^2\right ) \log (4)+\left (2 x^3-6 x^2\right ) \log ^2(4) \log ^2(x-3)+\left (\left (154 x^2-462 x\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (x-3)+300 x-900}{625 x^2-1875 x} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-6 x^2 \log ^2(4)+\left (\left (2 x^2-6 x\right ) \log (4) \log (x-3)+4 x+6 x \log (4)-12\right ) \log \left (9 x^2\right )+\left (462 x-4 x^2\right ) \log (4)+\left (2 x^3-6 x^2\right ) \log ^2(4) \log ^2(x-3)+\left (\left (154 x^2-462 x\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (x-3)+300 x-900}{x (625 x-1875)}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 (-((x-3) x \log (4) \log (x-3))-x (2+\log (64))+6) \left (\log \left (9 x^2\right )+x \log (4) \log (x-3)-x \log (4)+75\right )}{625 (3-x) x}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{625} \int \frac {((3-x) \log (4) \log (x-3) x-(2+\log (64)) x+6) \left (\log (4) \log (x-3) x-\log (4) x+\log \left (9 x^2\right )+75\right )}{(3-x) x}dx\) |
| \(\Big \downarrow \) 7237 |
| \(\displaystyle \frac {1}{625} \left (\log \left (9 x^2\right )+x \log (4) \log (x-3)-x \log (4)+75\right )^2\) |
Int[(-900 + 300*x + (462*x - 4*x^2)*Log[4] - 6*x^2*Log[4]^2 + ((-462*x + 1 54*x^2)*Log[4] + (12*x^2 - 2*x^3)*Log[4]^2)*Log[-3 + x] + (-6*x^2 + 2*x^3) *Log[4]^2*Log[-3 + x]^2 + (-12 + 4*x + 6*x*Log[4] + (-6*x + 2*x^2)*Log[4]* Log[-3 + x])*Log[9*x^2])/(-1875*x + 625*x^2),x]
3.9.55.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Si mp[q*(y^(m + 1)/(m + 1)), x] /; !FalseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(106\) vs. \(2(25)=50\).
Time = 1.44 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.82
| method | result | size |
| parallelrisch | \(\frac {4 x^{2} \ln \left (2\right )^{2} \ln \left (-3+x \right )^{2}}{625}-\frac {8 \ln \left (2\right )^{2} \ln \left (-3+x \right ) x^{2}}{625}+\frac {4 x^{2} \ln \left (2\right )^{2}}{625}+\frac {4 \ln \left (2\right ) \ln \left (-3+x \right ) \ln \left (9 x^{2}\right ) x}{625}-\frac {4 \ln \left (2\right ) \ln \left (9 x^{2}\right ) x}{625}+\frac {12 \ln \left (2\right ) \ln \left (-3+x \right ) x}{25}-\frac {36 \ln \left (2\right )^{2}}{625}-\frac {12 x \ln \left (2\right )}{25}+\frac {\ln \left (9 x^{2}\right )^{2}}{625}-\frac {72 \ln \left (2\right )}{25}+\frac {6 \ln \left (9 x^{2}\right )}{25}\) | \(107\) |
| default | \(\frac {4 x^{2} \ln \left (2\right )^{2} \ln \left (-3+x \right )^{2}}{625}-\frac {8 \ln \left (2\right )^{2} \ln \left (-3+x \right ) x^{2}}{625}+\frac {4 x^{2} \ln \left (2\right )^{2}}{625}-\frac {108 \ln \left (2\right )^{2}}{625}+\frac {\ln \left (2\right ) \left (924 \ln \left (-3+x \right )-300 x -4 x \ln \left (x^{2}\right )-8 \ln \left (-3+x \right ) x +4 \ln \left (-3+x \right ) \ln \left (x^{2}\right ) x +8 \ln \left (3\right ) \ln \left (-3+x \right ) x -8 x \ln \left (3\right )+24 \ln \left (3\right )+308 \left (-3+x \right ) \ln \left (-3+x \right )+924\right )}{625}+\frac {12 \ln \left (x \right )}{25}+\frac {8 \ln \left (3\right ) \ln \left (x \right )}{625}+\frac {\ln \left (x^{2}\right )^{2}}{625}\) | \(130\) |
| parts | \(\frac {4 \ln \left (2\right ) \left (6 \ln \left (-3+x \right )+\ln \left (-3+x \right ) \ln \left (x^{2}\right ) x +4 x -x \ln \left (x^{2}\right )-2 \ln \left (-3+x \right ) x +2 \ln \left (3\right ) \ln \left (-3+x \right ) x -2 x \ln \left (3\right )+6 \ln \left (3\right )\right )}{625}+\frac {\ln \left (x^{2}\right )^{2}}{625}+\frac {8 \ln \left (3\right ) \ln \left (x \right )}{625}+\frac {8 \ln \left (2\right )^{2} \left (\frac {\left (-3+x \right )^{2} \ln \left (-3+x \right )^{2}}{2}-\frac {\ln \left (-3+x \right ) \left (-3+x \right )^{2}}{2}+\frac {\left (-3+x \right )^{2}}{4}+3 \left (-3+x \right ) \ln \left (-3+x \right )^{2}-6 \left (-3+x \right ) \ln \left (-3+x \right )-18+6 x \right )}{625}-\frac {24 x \ln \left (2\right )^{2}}{625}-\frac {8 x \ln \left (2\right )}{625}+\frac {12 \ln \left (x \right )}{25}-\frac {36 \ln \left (2\right ) \left (2 \ln \left (2\right )-25\right ) \ln \left (-3+x \right )}{625}-\frac {4 \ln \left (2\right ) \left (2 \ln \left (2\right ) \left (\frac {\ln \left (-3+x \right ) \left (-3+x \right )^{2}}{2}-\frac {\left (-3+x \right )^{2}}{4}\right )-9 \ln \left (-3+x \right )^{2} \ln \left (2\right )-77 \left (-3+x \right ) \ln \left (-3+x \right )-231+77 x \right )}{625}\) | \(215\) |
| risch | \(\frac {4 x^{2} \ln \left (2\right )^{2} \ln \left (-3+x \right )^{2}}{625}+\left (\frac {8 x \ln \left (2\right ) \ln \left (x \right )}{625}-\frac {2 i \pi \ln \left (2\right ) x \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )}{625}+\frac {4 i \pi \ln \left (2\right ) x \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}}{625}-\frac {2 i \pi \ln \left (2\right ) x \operatorname {csgn}\left (i x^{2}\right )^{3}}{625}-\frac {8 x^{2} \ln \left (2\right )^{2}}{625}+\frac {8 x \ln \left (2\right ) \ln \left (3\right )}{625}+\frac {12 x \ln \left (2\right )}{25}\right ) \ln \left (-3+x \right )+\frac {4 \ln \left (x \right )^{2}}{625}-\frac {8 x \ln \left (2\right ) \ln \left (x \right )}{625}-\frac {4 i \pi \ln \left (2\right ) x \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}}{625}-\frac {2 i \ln \left (x \right ) \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )}{625}+\frac {2 i \pi \ln \left (2\right ) x \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )}{625}-\frac {2 i \ln \left (x \right ) \pi \operatorname {csgn}\left (i x^{2}\right )^{3}}{625}+\frac {2 i \pi \ln \left (2\right ) x \operatorname {csgn}\left (i x^{2}\right )^{3}}{625}+\frac {4 i \ln \left (x \right ) \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}}{625}+\frac {4 x^{2} \ln \left (2\right )^{2}}{625}-\frac {8 x \ln \left (2\right ) \ln \left (3\right )}{625}-\frac {12 x \ln \left (2\right )}{25}+\frac {12 \ln \left (x \right )}{25}+\frac {8 \ln \left (3\right ) \ln \left (x \right )}{625}\) | \(266\) |
int(((2*(2*x^2-6*x)*ln(2)*ln(-3+x)+12*x*ln(2)+4*x-12)*ln(9*x^2)+4*(2*x^3-6 *x^2)*ln(2)^2*ln(-3+x)^2+(4*(-2*x^3+12*x^2)*ln(2)^2+2*(154*x^2-462*x)*ln(2 ))*ln(-3+x)-24*x^2*ln(2)^2+2*(-4*x^2+462*x)*ln(2)+300*x-900)/(625*x^2-1875 *x),x,method=_RETURNVERBOSE)
4/625*x^2*ln(2)^2*ln(-3+x)^2-8/625*ln(2)^2*ln(-3+x)*x^2+4/625*x^2*ln(2)^2+ 4/625*ln(2)*ln(-3+x)*ln(9*x^2)*x-4/625*ln(2)*ln(9*x^2)*x+12/25*ln(2)*ln(-3 +x)*x-36/625*ln(2)^2-12/25*x*ln(2)+1/625*ln(9*x^2)^2-72/25*ln(2)+6/25*ln(9 *x^2)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (26) = 52\).
Time = 0.24 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.04 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {4}{625} \, x^{2} \log \left (2\right )^{2} \log \left (x - 3\right )^{2} + \frac {4}{625} \, x^{2} \log \left (2\right )^{2} - \frac {12}{25} \, x \log \left (2\right ) + \frac {2}{625} \, {\left (2 \, x \log \left (2\right ) \log \left (x - 3\right ) - 2 \, x \log \left (2\right ) + 75\right )} \log \left (9 \, x^{2}\right ) + \frac {1}{625} \, \log \left (9 \, x^{2}\right )^{2} - \frac {4}{625} \, {\left (2 \, x^{2} \log \left (2\right )^{2} - 75 \, x \log \left (2\right )\right )} \log \left (x - 3\right ) \]
integrate(((2*(2*x^2-6*x)*log(2)*log(-3+x)+12*x*log(2)+4*x-12)*log(9*x^2)+ 4*(2*x^3-6*x^2)*log(2)^2*log(-3+x)^2+(4*(-2*x^3+12*x^2)*log(2)^2+2*(154*x^ 2-462*x)*log(2))*log(-3+x)-24*x^2*log(2)^2+2*(-4*x^2+462*x)*log(2)+300*x-9 00)/(625*x^2-1875*x),x, algorithm=\
4/625*x^2*log(2)^2*log(x - 3)^2 + 4/625*x^2*log(2)^2 - 12/25*x*log(2) + 2/ 625*(2*x*log(2)*log(x - 3) - 2*x*log(2) + 75)*log(9*x^2) + 1/625*log(9*x^2 )^2 - 4/625*(2*x^2*log(2)^2 - 75*x*log(2))*log(x - 3)
Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (29) = 58\).
Time = 0.37 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.89 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {4 x^{2} \log {\left (2 \right )}^{2} \log {\left (x - 3 \right )}^{2}}{625} + \frac {4 x^{2} \log {\left (2 \right )}^{2}}{625} - \frac {12 x \log {\left (2 \right )}}{25} + \left (- \frac {8 x^{2} \log {\left (2 \right )}^{2}}{625} + \frac {12 x \log {\left (2 \right )}}{25}\right ) \log {\left (x - 3 \right )} + \left (\frac {4 x \log {\left (2 \right )} \log {\left (x - 3 \right )}}{625} - \frac {4 x \log {\left (2 \right )}}{625}\right ) \log {\left (9 x^{2} \right )} + \frac {12 \log {\left (x \right )}}{25} + \frac {\log {\left (9 x^{2} \right )}^{2}}{625} \]
integrate(((2*(2*x**2-6*x)*ln(2)*ln(-3+x)+12*x*ln(2)+4*x-12)*ln(9*x**2)+4* (2*x**3-6*x**2)*ln(2)**2*ln(-3+x)**2+(4*(-2*x**3+12*x**2)*ln(2)**2+2*(154* x**2-462*x)*ln(2))*ln(-3+x)-24*x**2*ln(2)**2+2*(-4*x**2+462*x)*ln(2)+300*x -900)/(625*x**2-1875*x),x)
4*x**2*log(2)**2*log(x - 3)**2/625 + 4*x**2*log(2)**2/625 - 12*x*log(2)/25 + (-8*x**2*log(2)**2/625 + 12*x*log(2)/25)*log(x - 3) + (4*x*log(2)*log(x - 3)/625 - 4*x*log(2)/625)*log(9*x**2) + 12*log(x)/25 + log(9*x**2)**2/62 5
Leaf count of result is larger than twice the leaf count of optimal. 319 vs. \(2 (26) = 52\).
Time = 0.32 (sec) , antiderivative size = 319, normalized size of antiderivative = 11.39 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=-\frac {4}{625} \, {\left (x^{2} + 6 \, x + 18 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} \log \left (x - 3\right ) + \frac {48}{625} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} \log \left (x - 3\right ) - \frac {8}{625} \, x {\left (\log \left (3\right ) - 2\right )} \log \left (2\right ) + \frac {2}{625} \, {\left ({\left (2 \, \log \left (x - 3\right )^{2} - 2 \, \log \left (x - 3\right ) + 1\right )} {\left (x - 3\right )}^{2} + 12 \, \log \left (x - 3\right )^{3} + 24 \, {\left (\log \left (x - 3\right )^{2} - 2 \, \log \left (x - 3\right ) + 2\right )} {\left (x - 3\right )}\right )} \log \left (2\right )^{2} - \frac {24}{625} \, {\left (\log \left (x - 3\right )^{3} + {\left (\log \left (x - 3\right )^{2} - 2 \, \log \left (x - 3\right ) + 2\right )} {\left (x - 3\right )}\right )} \log \left (2\right )^{2} + \frac {2}{625} \, {\left (x^{2} + 18 \, \log \left (x - 3\right )^{2} + 18 \, x + 54 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} - \frac {24}{625} \, {\left (3 \, \log \left (x - 3\right )^{2} + 2 \, x + 6 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} - \frac {24}{625} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} + \frac {308}{625} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (2\right ) \log \left (x - 3\right ) - \frac {462}{625} \, \log \left (2\right ) \log \left (x - 3\right )^{2} - \frac {154}{625} \, {\left (3 \, \log \left (x - 3\right )^{2} + 2 \, x + 6 \, \log \left (x - 3\right )\right )} \log \left (2\right ) - \frac {8}{625} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (2\right ) + \frac {8}{625} \, {\left (x {\left (\log \left (3\right ) - 1\right )} \log \left (2\right ) + x \log \left (2\right ) \log \left (x\right ) + 3 \, \log \left (2\right )\right )} \log \left (x - 3\right ) + \frac {924}{625} \, \log \left (2\right ) \log \left (x - 3\right ) - \frac {8}{625} \, {\left (x \log \left (2\right ) - \log \left (3\right )\right )} \log \left (x\right ) + \frac {4}{625} \, \log \left (x\right )^{2} + \frac {12}{25} \, \log \left (x\right ) \]
integrate(((2*(2*x^2-6*x)*log(2)*log(-3+x)+12*x*log(2)+4*x-12)*log(9*x^2)+ 4*(2*x^3-6*x^2)*log(2)^2*log(-3+x)^2+(4*(-2*x^3+12*x^2)*log(2)^2+2*(154*x^ 2-462*x)*log(2))*log(-3+x)-24*x^2*log(2)^2+2*(-4*x^2+462*x)*log(2)+300*x-9 00)/(625*x^2-1875*x),x, algorithm=\
-4/625*(x^2 + 6*x + 18*log(x - 3))*log(2)^2*log(x - 3) + 48/625*(x + 3*log (x - 3))*log(2)^2*log(x - 3) - 8/625*x*(log(3) - 2)*log(2) + 2/625*((2*log (x - 3)^2 - 2*log(x - 3) + 1)*(x - 3)^2 + 12*log(x - 3)^3 + 24*(log(x - 3) ^2 - 2*log(x - 3) + 2)*(x - 3))*log(2)^2 - 24/625*(log(x - 3)^3 + (log(x - 3)^2 - 2*log(x - 3) + 2)*(x - 3))*log(2)^2 + 2/625*(x^2 + 18*log(x - 3)^2 + 18*x + 54*log(x - 3))*log(2)^2 - 24/625*(3*log(x - 3)^2 + 2*x + 6*log(x - 3))*log(2)^2 - 24/625*(x + 3*log(x - 3))*log(2)^2 + 308/625*(x + 3*log( x - 3))*log(2)*log(x - 3) - 462/625*log(2)*log(x - 3)^2 - 154/625*(3*log(x - 3)^2 + 2*x + 6*log(x - 3))*log(2) - 8/625*(x + 3*log(x - 3))*log(2) + 8 /625*(x*(log(3) - 1)*log(2) + x*log(2)*log(x) + 3*log(2))*log(x - 3) + 924 /625*log(2)*log(x - 3) - 8/625*(x*log(2) - log(3))*log(x) + 4/625*log(x)^2 + 12/25*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (26) = 52\).
Time = 0.29 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.04 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {4}{625} \, x^{2} \log \left (2\right )^{2} \log \left (x - 3\right )^{2} + \frac {4}{625} \, x^{2} \log \left (2\right )^{2} - \frac {12}{25} \, x \log \left (2\right ) + \frac {4}{625} \, {\left (x \log \left (2\right ) \log \left (x - 3\right ) - x \log \left (2\right ) + \log \left (x\right )\right )} \log \left (9 \, x^{2}\right ) - \frac {4}{625} \, {\left (2 \, x^{2} \log \left (2\right )^{2} - 75 \, x \log \left (2\right )\right )} \log \left (x - 3\right ) - \frac {4}{625} \, \log \left (x\right )^{2} + \frac {12}{25} \, \log \left (x\right ) \]
integrate(((2*(2*x^2-6*x)*log(2)*log(-3+x)+12*x*log(2)+4*x-12)*log(9*x^2)+ 4*(2*x^3-6*x^2)*log(2)^2*log(-3+x)^2+(4*(-2*x^3+12*x^2)*log(2)^2+2*(154*x^ 2-462*x)*log(2))*log(-3+x)-24*x^2*log(2)^2+2*(-4*x^2+462*x)*log(2)+300*x-9 00)/(625*x^2-1875*x),x, algorithm=\
4/625*x^2*log(2)^2*log(x - 3)^2 + 4/625*x^2*log(2)^2 - 12/25*x*log(2) + 4/ 625*(x*log(2)*log(x - 3) - x*log(2) + log(x))*log(9*x^2) - 4/625*(2*x^2*lo g(2)^2 - 75*x*log(2))*log(x - 3) - 4/625*log(x)^2 + 12/25*log(x)
Time = 11.87 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.14 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {12\,\ln \left (x\right )}{25}+\frac {4\,x^2\,{\ln \left (2\right )}^2}{625}+\frac {{\ln \left (9\,x^2\right )}^2}{625}-\ln \left (9\,x^2\right )\,\left (\frac {4\,x\,\ln \left (2\right )}{625}-\frac {4\,x\,\ln \left (x-3\right )\,\ln \left (2\right )}{625}\right )-\frac {12\,x\,\ln \left (2\right )}{25}-\ln \left (x-3\right )\,\left (\frac {8\,x^2\,{\ln \left (2\right )}^2}{625}-\frac {12\,x\,\ln \left (2\right )}{25}\right )+\frac {4\,x^2\,{\ln \left (x-3\right )}^2\,{\ln \left (2\right )}^2}{625} \]
int((24*x^2*log(2)^2 - 300*x + log(x - 3)*(2*log(2)*(462*x - 154*x^2) - 4* log(2)^2*(12*x^2 - 2*x^3)) - 2*log(2)*(462*x - 4*x^2) - log(9*x^2)*(4*x + 12*x*log(2) - 2*log(x - 3)*log(2)*(6*x - 2*x^2) - 12) + 4*log(x - 3)^2*log (2)^2*(6*x^2 - 2*x^3) + 900)/(1875*x - 625*x^2),x)