∫ (37500−15036x−2484x2+4x3+(30000−15048x+24x2) log(625−x)) log( −30x2+10x3____ 5+x+4 log(625−x)) ____________________________________________________________________________________________________________________9375x−1265x2 −623x3 +x4 +(7500x−2512x2 +4x3 ) log (625−x) dx [242]

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 = 13.36, 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*}

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]

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]

\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 = 0.12, 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*}

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

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(62\) vs. \(2(24)=48\).
time = 1.22, size = 63, normalized size = 2.62


method	result	size

default	\(4 \ln \left (10\right ) \ln \left (-x \right )+2 \ln \left (10\right ) \ln \left (3-x \right )-2 \ln \left (10\right ) \ln \left (4 \ln \left (-x +625\right )+5+x \right )+\ln \left (\frac {x^{2} \left (3-x \right )}{-x -5-4 \ln \left (-x +625\right )}\right )^{2}\)	\(63\)
risch	\(\text {Expression too large to display}\)	\(15602\)

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)

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

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 125 vs. \(2 (24) = 48\).
time = 0.55, size = 125, normalized size = 5.21 \begin {gather*} 2 \, {\left (2 \, \log \left (2\right ) + \log \left (x - 3\right ) + 2 \, \log \left (x\right )\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 \left (2\right ) + \log \left (x\right )\right )} \log \left (x - 3\right ) - \log \left (x - 3\right )^{2} - 8 \, \log \left (2\right ) \log \left (x\right ) - 4 \, \log \left (x\right )^{2} + 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right ) - \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*}

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")

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

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Fricas [A]
time = 0.31, 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*}

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")

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Sympy [A]
time = 0.28, 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*}

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)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (24) = 48\).
time = 0.46, size = 129, normalized size = 5.38 \begin {gather*} 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right ) - \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 \left (x\right )\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 \left (x\right )\right )} \log \left (x - 3\right ) + \log \left (x - 3\right )^{2} - 4 \, \log \left (x\right )^{2} + 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (-x - 4 \, \log \left (-x + 625\right ) - 5\right ) \end {gather*}

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")

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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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*}

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)

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3.3.42 \(\int \frac {(37500-15036 x-2484 x^2+4 x^3+(30000-15048 x+24 x^2) \log (625-x)) \log (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)})}{9375 x-1265 x^2-623 x^3+x^4+(7500 x-2512 x^2+4 x^3) \log (625-x)} \, dx\) [242]