\(\int \frac {-27000 x+5400 x^2+(216000-54000 x-27000 x^2) \log (4+x)+(9000 x-1800 x^2+(-72000+39600 x+14400 x^2) \log (4+x)) \log (\frac {x^2}{\log (4+x)})+(-7200 x-1800 x^2) \log (4+x) \log ^2(\frac {x^2}{\log (4+x)})}{(-500 x+175 x^2+15 x^3-11 x^4+x^5) \log (4+x)} \, dx\) [1616]

Optimal result

Integrand size = 118, antiderivative size = 24 \[ \int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx=\frac {900 \left (3-\log \left (\frac {x^2}{\log (4+x)}\right )\right )^2}{(-5+x)^2} \]

[Out]

900*(3-ln(x^2/ln(4+x)))^2/(-5+x)^2

Rubi [F]

\[ \int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx=\int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx \]

[In]

Int[(-27000*x + 5400*x^2 + (216000 - 54000*x - 27000*x^2)*Log[4 + x] + (9000*x - 1800*x^2 + (-72000 + 39600*x
+ 14400*x^2)*Log[4 + x])*Log[x^2/Log[4 + x]] + (-7200*x - 1800*x^2)*Log[4 + x]*Log[x^2/Log[4 + x]]^2)/((-500*x
+ 175*x^2 + 15*x^3 - 11*x^4 + x^5)*Log[4 + x]),x]

[Out]

8100/(5 - x)^2 + 288*Log[5 - x] - 112*Log[x] - (3200*Log[x^2/Log[4 + x]])/(5 - x)^2 - (160*Log[x^2/Log[4 + x]]
)/(5 - x) - (88*x^2*Log[x^2/Log[4 + x]])/(5 - x)^2 - 8*Log[Log[4 + x]] - 80*Defer[Int][1/((-5 + x)*Log[4 + x])
, x] - 144*Defer[Int][Log[x^2/Log[4 + x]]/(-5 + x), x] + 144*Defer[Int][Log[x^2/Log[4 + x]]/x, x] - 200*Defer[
Int][Log[x^2/Log[4 + x]]/((-5 + x)^2*Log[4 + x]), x] + (200*Defer[Int][Log[x^2/Log[4 + x]]/((-5 + x)*Log[4 + x
]), x])/9 - (200*Defer[Int][Log[x^2/Log[4 + x]]/((4 + x)*Log[4 + x]), x])/9 - 1800*Defer[Int][Log[x^2/Log[4 +
x]]^2/(-5 + x)^3, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {1800 \left (3-\log \left (\frac {x^2}{\log (4+x)}\right )\right ) \left (-((-5+x) x)-(4+x) \log (4+x) \left (10-5 x+x \log \left (\frac {x^2}{\log (4+x)}\right )\right )\right )}{(5-x)^3 x (4+x) \log (4+x)} \, dx \\ & = 1800 \int \frac {\left (3-\log \left (\frac {x^2}{\log (4+x)}\right )\right ) \left (-((-5+x) x)-(4+x) \log (4+x) \left (10-5 x+x \log \left (\frac {x^2}{\log (4+x)}\right )\right )\right )}{(5-x)^3 x (4+x) \log (4+x)} \, dx \\ & = 1800 \int \left (-\frac {15}{(-5+x)^3}+\frac {30}{(-5+x)^3 x}+\frac {3}{(-5+x)^2 (4+x) \log (4+x)}+\frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3 x (4+x) \log (4+x)}-\frac {\log ^2\left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3}\right ) \, dx \\ & = \frac {13500}{(5-x)^2}+1800 \int \frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3 x (4+x) \log (4+x)} \, dx-1800 \int \frac {\log ^2\left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3} \, dx+5400 \int \frac {1}{(-5+x)^2 (4+x) \log (4+x)} \, dx+54000 \int \frac {1}{(-5+x)^3 x} \, dx \\ & = \frac {13500}{(5-x)^2}-1800 \int \frac {\log ^2\left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3} \, dx+1800 \int \left (\frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{45 (-5+x)^3 \log (4+x)}-\frac {14 \left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{2025 (-5+x)^2 \log (4+x)}+\frac {151 \left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{91125 (-5+x) \log (4+x)}-\frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{500 x \log (4+x)}+\frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{2916 (4+x) \log (4+x)}\right ) \, dx+5400 \int \left (\frac {1}{9 (-5+x)^2 \log (4+x)}-\frac {1}{81 (-5+x) \log (4+x)}+\frac {1}{81 (4+x) \log (4+x)}\right ) \, dx+54000 \int \left (\frac {1}{5 (-5+x)^3}-\frac {1}{25 (-5+x)^2}+\frac {1}{125 (-5+x)}-\frac {1}{125 x}\right ) \, dx \\ & = \frac {8100}{(5-x)^2}-\frac {2160}{5-x}+432 \log (5-x)-432 \log (x)+\frac {50}{81} \int \frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{(4+x) \log (4+x)} \, dx+\frac {1208}{405} \int \frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x) \log (4+x)} \, dx-\frac {18}{5} \int \frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{x \log (4+x)} \, dx-\frac {112}{9} \int \frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2 \log (4+x)} \, dx+40 \int \frac {\left (5 x-x^2-40 \log (4+x)+22 x \log (4+x)+8 x^2 \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3 \log (4+x)} \, dx-\frac {200}{3} \int \frac {1}{(-5+x) \log (4+x)} \, dx+\frac {200}{3} \int \frac {1}{(4+x) \log (4+x)} \, dx+600 \int \frac {1}{(-5+x)^2 \log (4+x)} \, dx-1800 \int \frac {\log ^2\left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3} \, dx \\ & = \frac {8100}{(5-x)^2}-\frac {2160}{5-x}+432 \log (5-x)-432 \log (x)+\frac {50}{81} \int \frac {\left (-((-5+x) x)+\left (-40+22 x+8 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{(4+x) \log (4+x)} \, dx+\frac {1208}{405} \int \left (-\frac {40 \log \left (\frac {x^2}{\log (4+x)}\right )}{-5+x}+\frac {22 x \log \left (\frac {x^2}{\log (4+x)}\right )}{-5+x}+\frac {8 x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{-5+x}+\frac {5 x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x) \log (4+x)}-\frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x) \log (4+x)}\right ) \, dx-\frac {18}{5} \int \frac {\left (-((-5+x) x)+\left (-40+22 x+8 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )}{x \log (4+x)} \, dx-\frac {112}{9} \int \left (-\frac {40 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2}+\frac {22 x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2}+\frac {8 x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2}+\frac {5 x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2 \log (4+x)}-\frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2 \log (4+x)}\right ) \, dx+40 \int \left (-\frac {40 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3}+\frac {22 x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3}+\frac {8 x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3}+\frac {5 x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3 \log (4+x)}-\frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3 \log (4+x)}\right ) \, dx-\frac {200}{3} \int \frac {1}{(-5+x) \log (4+x)} \, dx+\frac {200}{3} \text {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,4+x\right )+600 \int \frac {1}{(-5+x)^2 \log (4+x)} \, dx-1800 \int \frac {\log ^2\left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3} \, dx \\ & = \frac {8100}{(5-x)^2}-\frac {2160}{5-x}+432 \log (5-x)-432 \log (x)+\frac {50}{81} \int \left (-\frac {40 \log \left (\frac {x^2}{\log (4+x)}\right )}{4+x}+\frac {22 x \log \left (\frac {x^2}{\log (4+x)}\right )}{4+x}+\frac {8 x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{4+x}+\frac {5 x \log \left (\frac {x^2}{\log (4+x)}\right )}{(4+x) \log (4+x)}-\frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(4+x) \log (4+x)}\right ) \, dx-\frac {1208}{405} \int \frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x) \log (4+x)} \, dx-\frac {18}{5} \int \left (22 \log \left (\frac {x^2}{\log (4+x)}\right )-\frac {40 \log \left (\frac {x^2}{\log (4+x)}\right )}{x}+8 x \log \left (\frac {x^2}{\log (4+x)}\right )+\frac {5 \log \left (\frac {x^2}{\log (4+x)}\right )}{\log (4+x)}-\frac {x \log \left (\frac {x^2}{\log (4+x)}\right )}{\log (4+x)}\right ) \, dx+\frac {112}{9} \int \frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2 \log (4+x)} \, dx+\frac {1208}{81} \int \frac {x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x) \log (4+x)} \, dx+\frac {9664}{405} \int \frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{-5+x} \, dx-40 \int \frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3 \log (4+x)} \, dx-\frac {560}{9} \int \frac {x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2 \log (4+x)} \, dx+\frac {26576}{405} \int \frac {x \log \left (\frac {x^2}{\log (4+x)}\right )}{-5+x} \, dx-\frac {200}{3} \int \frac {1}{(-5+x) \log (4+x)} \, dx+\frac {200}{3} \text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (4+x)\right )-\frac {896}{9} \int \frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2} \, dx-\frac {9664}{81} \int \frac {\log \left (\frac {x^2}{\log (4+x)}\right )}{-5+x} \, dx+200 \int \frac {x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3 \log (4+x)} \, dx-\frac {2464}{9} \int \frac {x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2} \, dx+320 \int \frac {x^2 \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3} \, dx+\frac {4480}{9} \int \frac {\log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^2} \, dx+600 \int \frac {1}{(-5+x)^2 \log (4+x)} \, dx+880 \int \frac {x \log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3} \, dx-1600 \int \frac {\log \left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3} \, dx-1800 \int \frac {\log ^2\left (\frac {x^2}{\log (4+x)}\right )}{(-5+x)^3} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx=\frac {900 \left (-3+\log \left (\frac {x^2}{\log (4+x)}\right )\right )^2}{(-5+x)^2} \]

[In]

Integrate[(-27000*x + 5400*x^2 + (216000 - 54000*x - 27000*x^2)*Log[4 + x] + (9000*x - 1800*x^2 + (-72000 + 39
600*x + 14400*x^2)*Log[4 + x])*Log[x^2/Log[4 + x]] + (-7200*x - 1800*x^2)*Log[4 + x]*Log[x^2/Log[4 + x]]^2)/((
-500*x + 175*x^2 + 15*x^3 - 11*x^4 + x^5)*Log[4 + x]),x]

[Out]

(900*(-3 + Log[x^2/Log[4 + x]])^2)/(-5 + x)^2

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(50\) vs. \(2(24)=48\).

Time = 4.89 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12

method	result	size
parallelrisch	\(\frac {1036800+16200 x^{2}+70200 \ln \left (\frac {x^{2}}{\ln \left (4+x \right )}\right )^{2}-162000 x -421200 \ln \left (\frac {x^{2}}{\ln \left (4+x \right )}\right )}{78 x^{2}-780 x +1950}\)	\(51\)
risch	\(\text {Expression too large to display}\)	\(1389\)

[In]

int(((-1800*x^2-7200*x)*ln(4+x)*ln(x^2/ln(4+x))^2+((14400*x^2+39600*x-72000)*ln(4+x)-1800*x^2+9000*x)*ln(x^2/l
n(4+x))+(-27000*x^2-54000*x+216000)*ln(4+x)+5400*x^2-27000*x)/(x^5-11*x^4+15*x^3+175*x^2-500*x)/ln(4+x),x,meth
od=_RETURNVERBOSE)

[Out]

1/78*(1036800+16200*x^2+70200*ln(x^2/ln(4+x))^2-162000*x-421200*ln(x^2/ln(4+x)))/(x^2-10*x+25)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.67 \[ \int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx=\frac {900 \, {\left (\log \left (\frac {x^{2}}{\log \left (x + 4\right )}\right )^{2} - 6 \, \log \left (\frac {x^{2}}{\log \left (x + 4\right )}\right ) + 9\right )}}{x^{2} - 10 \, x + 25} \]

[In]

integrate(((-1800*x^2-7200*x)*log(4+x)*log(x^2/log(4+x))^2+((14400*x^2+39600*x-72000)*log(4+x)-1800*x^2+9000*x
)*log(x^2/log(4+x))+(-27000*x^2-54000*x+216000)*log(4+x)+5400*x^2-27000*x)/(x^5-11*x^4+15*x^3+175*x^2-500*x)/l
og(4+x),x, algorithm="fricas")

[Out]

900*(log(x^2/log(x + 4))^2 - 6*log(x^2/log(x + 4)) + 9)/(x^2 - 10*x + 25)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (19) = 38\).

Time = 0.24 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.21 \[ \int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx=\frac {16200}{2 x^{2} - 20 x + 50} + \frac {900 \log {\left (\frac {x^{2}}{\log {\left (x + 4 \right )}} \right )}^{2}}{x^{2} - 10 x + 25} - \frac {5400 \log {\left (\frac {x^{2}}{\log {\left (x + 4 \right )}} \right )}}{x^{2} - 10 x + 25} \]

[In]

integrate(((-1800*x**2-7200*x)*ln(4+x)*ln(x**2/ln(4+x))**2+((14400*x**2+39600*x-72000)*ln(4+x)-1800*x**2+9000*
x)*ln(x**2/ln(4+x))+(-27000*x**2-54000*x+216000)*ln(4+x)+5400*x**2-27000*x)/(x**5-11*x**4+15*x**3+175*x**2-500
*x)/ln(4+x),x)

[Out]

16200/(2*x**2 - 20*x + 50) + 900*log(x**2/log(x + 4))**2/(x**2 - 10*x + 25) - 5400*log(x**2/log(x + 4))/(x**2
- 10*x + 25)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.83 \[ \int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx=\frac {900 \, {\left (4 \, \log \left (x\right )^{2} - 2 \, {\left (2 \, \log \left (x\right ) - 3\right )} \log \left (\log \left (x + 4\right )\right ) + \log \left (\log \left (x + 4\right )\right )^{2} - 12 \, \log \left (x\right ) + 9\right )}}{x^{2} - 10 \, x + 25} \]

[In]

integrate(((-1800*x^2-7200*x)*log(4+x)*log(x^2/log(4+x))^2+((14400*x^2+39600*x-72000)*log(4+x)-1800*x^2+9000*x
)*log(x^2/log(4+x))+(-27000*x^2-54000*x+216000)*log(4+x)+5400*x^2-27000*x)/(x^5-11*x^4+15*x^3+175*x^2-500*x)/l
og(4+x),x, algorithm="maxima")

[Out]

900*(4*log(x)^2 - 2*(2*log(x) - 3)*log(log(x + 4)) + log(log(x + 4))^2 - 12*log(x) + 9)/(x^2 - 10*x + 25)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 101 vs. \(2 (22) = 44\).

Time = 0.51 (sec) , antiderivative size = 101, normalized size of antiderivative = 4.21 \[ \int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx=-1800 \, {\left (\frac {\log \left (x^{2}\right )}{x^{2} - 10 \, x + 25} - \frac {3}{x^{2} - 10 \, x + 25}\right )} \log \left (\log \left (x + 4\right )\right ) + \frac {900 \, \log \left (x^{2}\right )^{2}}{x^{2} - 10 \, x + 25} + \frac {900 \, \log \left (\log \left (x + 4\right )\right )^{2}}{x^{2} - 10 \, x + 25} - \frac {5400 \, \log \left (x^{2}\right )}{x^{2} - 10 \, x + 25} + \frac {8100}{x^{2} - 10 \, x + 25} \]

[In]

integrate(((-1800*x^2-7200*x)*log(4+x)*log(x^2/log(4+x))^2+((14400*x^2+39600*x-72000)*log(4+x)-1800*x^2+9000*x
)*log(x^2/log(4+x))+(-27000*x^2-54000*x+216000)*log(4+x)+5400*x^2-27000*x)/(x^5-11*x^4+15*x^3+175*x^2-500*x)/l
og(4+x),x, algorithm="giac")

[Out]

-1800*(log(x^2)/(x^2 - 10*x + 25) - 3/(x^2 - 10*x + 25))*log(log(x + 4)) + 900*log(x^2)^2/(x^2 - 10*x + 25) +
900*log(log(x + 4))^2/(x^2 - 10*x + 25) - 5400*log(x^2)/(x^2 - 10*x + 25) + 8100/(x^2 - 10*x + 25)

Mupad [B] (verification not implemented)

Time = 9.20 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {-27000 x+5400 x^2+\left (216000-54000 x-27000 x^2\right ) \log (4+x)+\left (9000 x-1800 x^2+\left (-72000+39600 x+14400 x^2\right ) \log (4+x)\right ) \log \left (\frac {x^2}{\log (4+x)}\right )+\left (-7200 x-1800 x^2\right ) \log (4+x) \log ^2\left (\frac {x^2}{\log (4+x)}\right )}{\left (-500 x+175 x^2+15 x^3-11 x^4+x^5\right ) \log (4+x)} \, dx=\frac {900\,{\left (\ln \left (\frac {x^2}{\ln \left (x+4\right )}\right )-3\right )}^2}{{\left (x-5\right )}^2} \]

[In]

int(-(27000*x + log(x + 4)*(54000*x + 27000*x^2 - 216000) - log(x^2/log(x + 4))*(9000*x + log(x + 4)*(39600*x
+ 14400*x^2 - 72000) - 1800*x^2) - 5400*x^2 + log(x + 4)*log(x^2/log(x + 4))^2*(7200*x + 1800*x^2))/(log(x + 4
)*(175*x^2 - 500*x + 15*x^3 - 11*x^4 + x^5)),x)

[Out]

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