3.3.42 \(\int \frac {(37500-15036 x-2484 x^2+4 x^3+(30000-15048 x+24 x^2) \log (625-x)) \log (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)})}{9375 x-1265 x^2-623 x^3+x^4+(7500 x-2512 x^2+4 x^3) \log (625-x)} \, dx\)

Optimal. Leaf size=24 \[ \log ^2\left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right ) \]

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Rubi [F]  time = 21.17, 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 {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((37500 - 15036*x - 2484*x^2 + 4*x^3 + (30000 - 15048*x + 24*x^2)*Log[625 - x])*Log[(-30*x^2 + 10*x^3)/(5
+ x + 4*Log[625 - x])])/(9375*x - 1265*x^2 - 623*x^3 + x^4 + (7500*x - 2512*x^2 + 4*x^3)*Log[625 - x]),x]

[Out]

4*Defer[Int][Log[(10*(-3 + x)*x^2)/(5 + x + 4*Log[625 - x])]/(5 + x + 4*Log[625 - x]), x] - 8*Defer[Int][Log[(
10*(-3 + x)*x^2)/(5 + x + 4*Log[625 - x])]/((-625 + x)*(5 + x + 4*Log[625 - x])), x] + 16*Defer[Int][Log[(10*(
-3 + x)*x^2)/(5 + x + 4*Log[625 - x])]/((-3 + x)*(5 + x + 4*Log[625 - x])), x] + 20*Defer[Int][Log[(10*(-3 + x
)*x^2)/(5 + x + 4*Log[625 - x])]/(x*(5 + x + 4*Log[625 - x])), x] + 8*Defer[Int][(Log[625 - x]*Log[(10*(-3 + x
)*x^2)/(5 + x + 4*Log[625 - x])])/((-3 + x)*(5 + x + 4*Log[625 - x])), x] + 16*Defer[Int][(Log[625 - x]*Log[(1
0*(-3 + x)*x^2)/(5 + x + 4*Log[625 - x])])/(x*(5 + x + 4*Log[625 - x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {x^2 (-30+10 x)}{5+x+4 \log (625-x)}\right )}{x \left (1875-628 x+x^2\right ) (5+x+4 \log (625-x))} \, dx\\ &=\int \left (\frac {2 \left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{194375 (-625+x) (5+x+4 \log (625-x))}-\frac {2 \left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{933 (-3+x) (5+x+4 \log (625-x))}+\frac {4 \left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{1875 x (5+x+4 \log (625-x))}\right ) \, dx\\ &=\frac {2 \int \frac {\left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx}{194375}+\frac {4 \int \frac {\left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{x (5+x+4 \log (625-x))} \, dx}{1875}-\frac {2}{933} \int \frac {\left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx\\ &=\frac {2 \int \left (\frac {9375 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}-\frac {3759 x \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}-\frac {621 x^2 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}+\frac {x^3 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}+\frac {7500 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}-\frac {3762 x \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}+\frac {6 x^2 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}\right ) \, dx}{194375}+\frac {4 \int \frac {\left (9375-3759 x-621 x^2+x^3+6 \left (1250-627 x+x^2\right ) \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{x (5+x+4 \log (625-x))} \, dx}{1875}-\frac {2}{933} \int \left (\frac {9375 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}-\frac {3759 x \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}-\frac {621 x^2 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}+\frac {x^3 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}+\frac {7500 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}-\frac {3762 x \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}+\frac {6 x^2 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.22, size = 24, normalized size = 1.00 \begin {gather*} \log ^2\left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((37500 - 15036*x - 2484*x^2 + 4*x^3 + (30000 - 15048*x + 24*x^2)*Log[625 - x])*Log[(-30*x^2 + 10*x^
3)/(5 + x + 4*Log[625 - x])])/(9375*x - 1265*x^2 - 623*x^3 + x^4 + (7500*x - 2512*x^2 + 4*x^3)*Log[625 - x]),x
]

[Out]

Log[(10*(-3 + x)*x^2)/(5 + x + 4*Log[625 - x])]^2

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fricas [A]  time = 0.58, size = 27, normalized size = 1.12 \begin {gather*} \log \left (\frac {10 \, {\left (x^{3} - 3 \, x^{2}\right )}}{x + 4 \, \log \left (-x + 625\right ) + 5}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^2-15048*x+30000)*log(-x+625)+4*x^3-2484*x^2-15036*x+37500)*log((10*x^3-30*x^2)/(4*log(-x+625)
+5+x))/((4*x^3-2512*x^2+7500*x)*log(-x+625)+x^4-623*x^3-1265*x^2+9375*x),x, algorithm="fricas")

[Out]

log(10*(x^3 - 3*x^2)/(x + 4*log(-x + 625) + 5))^2

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giac [B]  time = 0.53, size = 129, normalized size = 5.38 \begin {gather*} 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \relax (x) - \log \left (-x - 4 \, \log \left (-x + 625\right ) - 5\right )\right )} \log \left (10 \, x^{3} - 30 \, x^{2}\right ) - 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \relax (x)\right )} \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right ) + \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right )^{2} - 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \relax (x)\right )} \log \left (x - 3\right ) + \log \left (x - 3\right )^{2} - 4 \, \log \relax (x)^{2} + 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \relax (x)\right )} \log \left (-x - 4 \, \log \left (-x + 625\right ) - 5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^2-15048*x+30000)*log(-x+625)+4*x^3-2484*x^2-15036*x+37500)*log((10*x^3-30*x^2)/(4*log(-x+625)
+5+x))/((4*x^3-2512*x^2+7500*x)*log(-x+625)+x^4-623*x^3-1265*x^2+9375*x),x, algorithm="giac")

[Out]

2*(log(x - 3) + 2*log(x) - log(-x - 4*log(-x + 625) - 5))*log(10*x^3 - 30*x^2) - 2*(log(x - 3) + 2*log(x))*log
(x + 4*log(-x + 625) + 5) + log(x + 4*log(-x + 625) + 5)^2 - 2*(log(x - 3) + 2*log(x))*log(x - 3) + log(x - 3)
^2 - 4*log(x)^2 + 2*(log(x - 3) + 2*log(x))*log(-x - 4*log(-x + 625) - 5)

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maple [C]  time = 0.84, size = 1445, normalized size = 60.21

method	result	size
risch	\(4 \ln \relax (x )^{2}-i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{3}-i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{3}-2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (i x^{2}\right )^{3}-2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{3}-2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{3}-i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (i x^{2}\right )^{3}+i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (i x^{2}\right )^{3}+i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{3}+i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{3}+2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}+i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}+i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (i \left (x -3\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}+i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (\frac {i}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}+i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}+i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (i \left (x -3\right )\right ) \mathrm {csgn}\left (\frac {i}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )-2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )-2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (i \left (x -3\right )\right ) \mathrm {csgn}\left (\frac {i}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )-i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )-i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (i \left (x -3\right )\right ) \mathrm {csgn}\left (\frac {i}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )+i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )+\ln \left (x -3\right )^{2}+\ln \left (4 \ln \left (-x +625\right )+5+x \right )^{2}-2 i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}-i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (i \left (x -3\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}-i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (\frac {i}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}-i \pi \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}-i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \ln \left (x -3\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+4 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i x^{2} \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}+2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (i \left (x -3\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}+2 i \pi \ln \left (-x \right ) \mathrm {csgn}\left (\frac {i}{4 \ln \left (-x +625\right )+5+x}\right ) \mathrm {csgn}\left (\frac {i \left (x -3\right )}{4 \ln \left (-x +625\right )+5+x}\right )^{2}+2 \ln \relax (2) \ln \left (x -3\right )+4 \ln \relax (2) \ln \left (-x \right )+2 \ln \left (x -3\right ) \ln \relax (5)+4 \ln \left (-x \right ) \ln \relax (5)+4 \ln \relax (x ) \ln \left (x -3\right )+\left (-4 \ln \relax (x )-2 \ln \left (x -3\right )\right ) \ln \left (4 \ln \left (-x +625\right )+5+x \right )-2 \ln \relax (2) \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right )-2 \ln \left (\ln \left (-x +625\right )+\frac {5}{4}+\frac {x}{4}\right ) \ln \relax (5)\)	\(1445\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((24*x^2-15048*x+30000)*ln(-x+625)+4*x^3-2484*x^2-15036*x+37500)*ln((10*x^3-30*x^2)/(4*ln(-x+625)+5+x))/((
4*x^3-2512*x^2+7500*x)*ln(-x+625)+x^4-623*x^3-1265*x^2+9375*x),x,method=_RETURNVERBOSE)

[Out]

4*ln(x)^2-I*Pi*ln(x-3)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))^3-I*Pi*ln(x-3)*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3))^3-
2*I*Pi*ln(-x)*csgn(I*x^2)^3-2*I*Pi*ln(-x)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))^3-2*I*Pi*ln(-x)*csgn(I*x^2/(4*ln(-x
+625)+5+x)*(x-3))^3-I*Pi*ln(x-3)*csgn(I*x^2)^3+I*Pi*ln(ln(-x+625)+5/4+1/4*x)*csgn(I*x^2)^3+I*Pi*ln(ln(-x+625)+
5/4+1/4*x)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))^3+I*Pi*ln(ln(-x+625)+5/4+1/4*x)*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3
))^3-I*Pi*ln(x-3)*csgn(I*(x-3))*csgn(I/(4*ln(-x+625)+5+x))*csgn(I*(x-3)/(4*ln(-x+625)+5+x))+I*Pi*ln(ln(-x+625)
+5/4+1/4*x)*csgn(I*x^2)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3))+I*Pi*ln(ln(-x+62
5)+5/4+1/4*x)*csgn(I*(x-3))*csgn(I/(4*ln(-x+625)+5+x))*csgn(I*(x-3)/(4*ln(-x+625)+5+x))-2*I*Pi*ln(-x)*csgn(I*x
^2)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3))-2*I*Pi*ln(-x)*csgn(I*(x-3))*csgn(I/(
4*ln(-x+625)+5+x))*csgn(I*(x-3)/(4*ln(-x+625)+5+x))-I*Pi*ln(x-3)*csgn(I*x^2)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))*
csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3))-2*I*Pi*ln(ln(-x+625)+5/4+1/4*x)*csgn(I*x)*csgn(I*x^2)^2-I*Pi*ln(ln(-x+625
)+5/4+1/4*x)*csgn(I*x^2)*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3))^2-I*Pi*ln(ln(-x+625)+5/4+1/4*x)*csgn(I*(x-3))*cs
gn(I*(x-3)/(4*ln(-x+625)+5+x))^2-I*Pi*ln(ln(-x+625)+5/4+1/4*x)*csgn(I/(4*ln(-x+625)+5+x))*csgn(I*(x-3)/(4*ln(-
x+625)+5+x))^2-I*Pi*ln(ln(-x+625)+5/4+1/4*x)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x
-3))^2-I*Pi*ln(x-3)*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*ln(x-3)*csgn(I*x)*csgn(I*x^2)^2-2*I*Pi*ln(-x)*csgn(I*x)^2*c
sgn(I*x^2)+4*I*Pi*ln(-x)*csgn(I*x)*csgn(I*x^2)^2+2*I*Pi*ln(-x)*csgn(I*x^2)*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3)
)^2+2*I*Pi*ln(-x)*csgn(I*(x-3))*csgn(I*(x-3)/(4*ln(-x+625)+5+x))^2+2*I*Pi*ln(-x)*csgn(I/(4*ln(-x+625)+5+x))*cs
gn(I*(x-3)/(4*ln(-x+625)+5+x))^2+2*I*Pi*ln(-x)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))*csgn(I*x^2/(4*ln(-x+625)+5+x)*
(x-3))^2+I*Pi*ln(x-3)*csgn(I*x^2)*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3))^2+I*Pi*ln(x-3)*csgn(I*(x-3))*csgn(I*(x-
3)/(4*ln(-x+625)+5+x))^2+I*Pi*ln(x-3)*csgn(I/(4*ln(-x+625)+5+x))*csgn(I*(x-3)/(4*ln(-x+625)+5+x))^2+I*Pi*ln(x-
3)*csgn(I*(x-3)/(4*ln(-x+625)+5+x))*csgn(I*x^2/(4*ln(-x+625)+5+x)*(x-3))^2+I*Pi*ln(ln(-x+625)+5/4+1/4*x)*csgn(
I*x)^2*csgn(I*x^2)+ln(x-3)^2+ln(4*ln(-x+625)+5+x)^2+2*ln(2)*ln(x-3)+4*ln(2)*ln(-x)+2*ln(x-3)*ln(5)+4*ln(-x)*ln
(5)+4*ln(x)*ln(x-3)+(-4*ln(x)-2*ln(x-3))*ln(4*ln(-x+625)+5+x)-2*ln(2)*ln(ln(-x+625)+5/4+1/4*x)-2*ln(ln(-x+625)
+5/4+1/4*x)*ln(5)

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maxima [B]  time = 0.66, size = 125, normalized size = 5.21 \begin {gather*} 2 \, {\left (2 \, \log \relax (2) + \log \left (x - 3\right ) + 2 \, \log \relax (x)\right )} \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right ) - \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right )^{2} - 4 \, {\left (\log \relax (2) + \log \relax (x)\right )} \log \left (x - 3\right ) - \log \left (x - 3\right )^{2} - 8 \, \log \relax (2) \log \relax (x) - 4 \, \log \relax (x)^{2} + 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \relax (x) - \log \left (\frac {1}{4} \, x + \log \left (-x + 625\right ) + \frac {5}{4}\right )\right )} \log \left (\frac {10 \, {\left (x^{3} - 3 \, x^{2}\right )}}{x + 4 \, \log \left (-x + 625\right ) + 5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^2-15048*x+30000)*log(-x+625)+4*x^3-2484*x^2-15036*x+37500)*log((10*x^3-30*x^2)/(4*log(-x+625)
+5+x))/((4*x^3-2512*x^2+7500*x)*log(-x+625)+x^4-623*x^3-1265*x^2+9375*x),x, algorithm="maxima")

[Out]

2*(2*log(2) + log(x - 3) + 2*log(x))*log(x + 4*log(-x + 625) + 5) - log(x + 4*log(-x + 625) + 5)^2 - 4*(log(2)
+ log(x))*log(x - 3) - log(x - 3)^2 - 8*log(2)*log(x) - 4*log(x)^2 + 2*(log(x - 3) + 2*log(x) - log(1/4*x + l
og(-x + 625) + 5/4))*log(10*(x^3 - 3*x^2)/(x + 4*log(-x + 625) + 5))

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mupad [B]  time = 1.70, size = 29, normalized size = 1.21 \begin {gather*} {\ln \left (-\frac {30\,x^2-10\,x^3}{x+4\,\ln \left (625-x\right )+5}\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(-(30*x^2 - 10*x^3)/(x + 4*log(625 - x) + 5))*(log(625 - x)*(24*x^2 - 15048*x + 30000) - 15036*x - 248
4*x^2 + 4*x^3 + 37500))/(9375*x + log(625 - x)*(7500*x - 2512*x^2 + 4*x^3) - 1265*x^2 - 623*x^3 + x^4),x)

[Out]

log(-(30*x^2 - 10*x^3)/(x + 4*log(625 - x) + 5))^2

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sympy [A]  time = 0.64, size = 22, normalized size = 0.92 \begin {gather*} \log {\left (\frac {10 x^{3} - 30 x^{2}}{x + 4 \log {\left (625 - x \right )} + 5} \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x**2-15048*x+30000)*ln(-x+625)+4*x**3-2484*x**2-15036*x+37500)*ln((10*x**3-30*x**2)/(4*ln(-x+62
5)+5+x))/((4*x**3-2512*x**2+7500*x)*ln(-x+625)+x**4-623*x**3-1265*x**2+9375*x),x)

[Out]

log((10*x**3 - 30*x**2)/(x + 4*log(625 - x) + 5))**2

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