3.17.16 $\int \frac{-27000x+5400x^2+(216000-54000x-27000x^2)\log (4+x)+(9000x-1800x^2+(-72000+39600x+14400x^2)\log (4+x))\log (\frac{x^2}{\log (4+x)})+(-7200x-1800x^2)\log (4+x){\log }^2(\frac{x^2}{\log (4+x)})}{(-500x+175x^2+15x^3-11x^4+x^5)\log (4+x)}dx$

Optimal. Leaf size=24 $$\frac{900{(3-\log \left(\frac{x^2}{\log (4+x)}\right))}^2}{(-5+x{)}^2}$$

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Rubi [F]  time = 14.75, 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 = {} $$\begin{array}{c}\int \frac{-27000x+5400x^2+(216000-54000x-27000x^2)\log (4+x)+(9000x-1800x^2+(-72000+39600x+14400x^2)\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)+(-7200x-1800x^2)\log (4+x){\log }^2\left(\frac{x^2}{\log (4+x)}\right)}{(-500x+175x^2+15x^3-11x^4+x^5)\log (4+x)}dx\end{array}$$

Verification is not applicable to the result.

[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{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{1800(3-\log \left(\frac{x^2}{\log (4+x)}\right))(-((-5+x)x)-(4+x)\log (4+x)(10-5x+x\log \left(\frac{x^2}{\log (4+x)}\right)))}{(5-x{)}^{3}x(4+x)\log (4+x)}dx\\ & =1800\int \frac{(3-\log \left(\frac{x^2}{\log (4+x)}\right))(-((-5+x)x)-(4+x)\log (4+x)(10-5x+x\log \left(\frac{x^2}{\log (4+x)}\right)))}{(5-x{)}^{3}x(4+x)\log (4+x)}dx\\ & =1800\int (-\frac{15}{(-5+x{)}^3}+\frac{30}{(-5+x{)}^{3}x}+\frac{3}{(-5+x{)}^2(4+x)\log (4+x)}+\frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\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})dx\\ & =\frac{13500}{(5-x{)}^2}+1800\int \frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\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 (\frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{45(-5+x{)}^3\log (4+x)}-\frac{14(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{2025(-5+x{)}^2\log (4+x)}+\frac{151(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{91125(-5+x)\log (4+x)}-\frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{500x\log (4+x)}+\frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{2916(4+x)\log (4+x)})dx+5400\int (\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)})dx+54000\int (\frac{1}{5(-5+x{)}^3}-\frac{1}{25(-5+x{)}^2}+\frac{1}{125(-5+x)}-\frac{1}{125x})dx\\ & =\frac{8100}{(5-x{)}^2}-\frac{2160}{5-x}+432\log (5-x)-432\log (x)+\frac{50}{81}\int \frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{(4+x)\log (4+x)}dx+\frac{1208}{405}\int \frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{(-5+x)\log (4+x)}dx-\frac{18}{5}\int \frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{x\log (4+x)}dx-\frac{112}{9}\int \frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{(-5+x{)}^2\log (4+x)}dx+40\int \frac{(5x-x^2-40\log (4+x)+22x\log (4+x)+8x^2\log (4+x))\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{(-((-5+x)x)+(-40+22x+8x^2)\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{(4+x)\log (4+x)}dx+\frac{1208}{405}\int (-\frac{40\log \left(\frac{x^2}{\log (4+x)}\right)}{-5+x}+\frac{22x\log \left(\frac{x^2}{\log (4+x)}\right)}{-5+x}+\frac{8x^2\log \left(\frac{x^2}{\log (4+x)}\right)}{-5+x}+\frac{5x\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)})dx-\frac{18}{5}\int \frac{(-((-5+x)x)+(-40+22x+8x^2)\log (4+x))\log \left(\frac{x^2}{\log (4+x)}\right)}{x\log (4+x)}dx-\frac{112}{9}\int (-\frac{40\log \left(\frac{x^2}{\log (4+x)}\right)}{(-5+x{)}^2}+\frac{22x\log \left(\frac{x^2}{\log (4+x)}\right)}{(-5+x{)}^2}+\frac{8x^2\log \left(\frac{x^2}{\log (4+x)}\right)}{(-5+x{)}^2}+\frac{5x\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)})dx+40\int (-\frac{40\log \left(\frac{x^2}{\log (4+x)}\right)}{(-5+x{)}^3}+\frac{22x\log \left(\frac{x^2}{\log (4+x)}\right)}{(-5+x{)}^3}+\frac{8x^2\log \left(\frac{x^2}{\log (4+x)}\right)}{(-5+x{)}^3}+\frac{5x\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)})dx-\frac{200}{3}\int \frac{1}{(-5+x)\log (4+x)}dx+\frac{200}{3}\mathrm{Subst}(\int \frac{1}{x\log (x)}dx,x,4+x)+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\\ & =\text{Rest of rules removed due to large latex content}\end{array}\end{array}$$

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Mathematica [A]  time = 0.34, size = 22, normalized size = 0.92 $$\begin{array}{c}\frac{900{(-3+\log \left(\frac{x^2}{\log (4+x)}\right))}^2}{(-5+x{)}^2}\end{array}$$

Antiderivative was successfully verified.

[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

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fricas [A]  time = 0.70, size = 40, normalized size = 1.67 $$\begin{array}{c}\frac{900(\log {\left(\frac{x^2}{\log (x+4)}\right)}^2-6\log \left(\frac{x^2}{\log (x+4)}\right)+9)}{x^2-10x+25}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[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)

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giac [B]  time = 0.76, size = 101, normalized size = 4.21 $$\begin{array}{c}-1800(\frac{\log \left(x^2\right)}{x^2-10x+25}-\frac{3}{x^2-10x+25})\log (\log (x+4))+\frac{900\log {\left(x^2\right)}^2}{x^2-10x+25}+\frac{900\log {(\log (x+4))}^2}{x^2-10x+25}-\frac{5400\log \left(x^2\right)}{x^2-10x+25}+\frac{8100}{x^2-10x+25}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maple [C]  time = 0.33, size = 1389, normalized size = 57.88

method	result	size
risch	$\frac{900\ln {(\ln (4+x))}^2}{x^2-10x+25}-\frac{900(-i\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(ix\right)}^2+2i\pi \mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}\left(ix\right)-i\pi \mathrm{csgn}{\left(i{x}^2\right)}^3-i\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}\left(\frac{i{x}^2}{\ln (4+x)}\right)+i\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2+i\pi \mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2-i\pi \mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^3+4\ln (x)-6)\ln (\ln (4+x))}{x^2-10x+25}+\frac{8100-10800\ln (x)+3600\ln (x{)}^2-225{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^6-225{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}{\left(\frac{i}{\ln (4+x)}\right)}^2\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2+450{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^3+450{\pi }^2\mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(\frac{i}{\ln (4+x)}\right)}^2\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^3-900{\pi }^2\mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^4-1800i\ln (x)\pi \mathrm{csgn}{\left(i{x}^2\right)}^3-1800i\ln (x)\pi \mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^3-2700i\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2-2700i\pi \mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2+450{\pi }^2\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2-450{\pi }^2\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^3-900{\pi }^2\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^3\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2+900{\pi }^2\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^3-450{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^4\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}\left(\frac{i{x}^2}{\ln (4+x)}\right)+450{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^3\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2-5400i\pi \mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}\left(ix\right)+2700i\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(ix\right)}^2+2700i\pi \mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^3-225{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^4+450{\pi }^2\mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^5-225{\pi }^2\mathrm{csgn}{\left(\frac{i}{\ln (4+x)}\right)}^2\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^4+450{\pi }^2\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^5+450{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^4\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2-450{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^3\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^3-225{\pi }^2\mathrm{csgn}{\left(ix\right)}^4\mathrm{csgn}{\left(i{x}^2\right)}^2+900{\pi }^2\mathrm{csgn}{\left(ix\right)}^3\mathrm{csgn}{\left(i{x}^2\right)}^3-1350{\pi }^2\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}{\left(i{x}^2\right)}^4+900{\pi }^2\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^5-225{\pi }^2\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^6+2700i\pi \mathrm{csgn}{\left(i{x}^2\right)}^3+3600i\ln (x)\pi \mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2+1800i\ln (x)\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2+1800i\ln (x)\pi \mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2+2700i\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}\left(\frac{i{x}^2}{\ln (4+x)}\right)-450{\pi }^2\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}\left(\frac{i{x}^2}{\ln (4+x)}\right)+450{\pi }^2\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2+900{\pi }^2\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^3\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}\left(\frac{i{x}^2}{\ln (4+x)}\right)-900{\pi }^2\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}{\left(\frac{i{x}^2}{\ln (4+x)}\right)}^2-1800i\ln (x)\pi \mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)-1800i\ln (x)\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}\left(\frac{i}{\ln (4+x)}\right)\mathrm{csgn}\left(\frac{i{x}^2}{\ln (4+x)}\right)}{x^2-10x+25}$	$1389$

Verification of antiderivative is not currently implemented for this CAS.

[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]

900/(x^2-10*x+25)*ln(ln(4+x))^2-900*(-I*Pi*csgn(I*x^2)*csgn(I*x)^2+2*I*Pi*csgn(I*x^2)^2*csgn(I*x)-I*Pi*csgn(I*
x^2)^3-I*Pi*csgn(I*x^2)*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))+I*Pi*csgn(I*x^2)*csgn(I*x^2/ln(4+x))^2+I*Pi*csgn(I
/ln(4+x))*csgn(I*x^2/ln(4+x))^2-I*Pi*csgn(I*x^2/ln(4+x))^3+4*ln(x)-6)/(x^2-10*x+25)*ln(ln(4+x))+225*(36-48*ln(
x)+16*ln(x)^2-Pi^2*csgn(I*x^2)^6+2*Pi^2*csgn(I*x)^2*csgn(I*x^2)^2*csgn(I*x^2/ln(4+x))^2-2*Pi^2*csgn(I*x)^2*csg
n(I*x^2)*csgn(I*x^2/ln(4+x))^3-4*Pi^2*csgn(I*x)*csgn(I*x^2)^3*csgn(I*x^2/ln(4+x))^2+4*Pi^2*csgn(I*x)*csgn(I*x^
2)^2*csgn(I*x^2/ln(4+x))^3-2*Pi^2*csgn(I*x^2)^4*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))+2*Pi^2*csgn(I*x^2)^3*csgn(
I/ln(4+x))*csgn(I*x^2/ln(4+x))^2-Pi^2*csgn(I*x^2)^2*csgn(I/ln(4+x))^2*csgn(I*x^2/ln(4+x))^2+2*Pi^2*csgn(I*x^2)
^2*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))^3+2*Pi^2*csgn(I*x^2)*csgn(I/ln(4+x))^2*csgn(I*x^2/ln(4+x))^3-4*Pi^2*csg
n(I*x^2)*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))^4-8*I*ln(x)*Pi*csgn(I*x^2)^3-8*I*ln(x)*Pi*csgn(I*x^2/ln(4+x))^3+1
2*I*Pi*csgn(I*x)^2*csgn(I*x^2)-24*I*Pi*csgn(I*x)*csgn(I*x^2)^2-12*I*Pi*csgn(I*x^2)*csgn(I*x^2/ln(4+x))^2-12*I*
Pi*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))^2-Pi^2*csgn(I*x)^4*csgn(I*x^2)^2+4*Pi^2*csgn(I*x)^3*csgn(I*x^2)^3-6*Pi^
2*csgn(I*x)^2*csgn(I*x^2)^4+4*Pi^2*csgn(I*x)*csgn(I*x^2)^5-Pi^2*csgn(I*x^2/ln(4+x))^6-2*Pi^2*csgn(I*x)^2*csgn(
I*x^2)^2*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))+2*Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x)
)^2+4*Pi^2*csgn(I*x)*csgn(I*x^2)^3*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))-4*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I/l
n(4+x))*csgn(I*x^2/ln(4+x))^2+12*I*Pi*csgn(I*x^2)*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))-8*I*ln(x)*Pi*csgn(I*x)^2
*csgn(I*x^2)+16*I*ln(x)*Pi*csgn(I*x)*csgn(I*x^2)^2+8*I*ln(x)*Pi*csgn(I*x^2)*csgn(I*x^2/ln(4+x))^2+8*I*ln(x)*Pi
*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))^2+12*I*Pi*csgn(I*x^2/ln(4+x))^3+12*I*Pi*csgn(I*x^2)^3-Pi^2*csgn(I*x^2)^2*
csgn(I*x^2/ln(4+x))^4+2*Pi^2*csgn(I*x^2)*csgn(I*x^2/ln(4+x))^5-Pi^2*csgn(I/ln(4+x))^2*csgn(I*x^2/ln(4+x))^4+2*
Pi^2*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x))^5+2*Pi^2*csgn(I*x^2)^4*csgn(I*x^2/ln(4+x))^2-2*Pi^2*csgn(I*x^2)^3*csg
n(I*x^2/ln(4+x))^3-8*I*ln(x)*Pi*csgn(I*x^2)*csgn(I/ln(4+x))*csgn(I*x^2/ln(4+x)))/(x^2-10*x+25)

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maxima [A]  time = 0.69, size = 44, normalized size = 1.83 $$\begin{array}{c}\frac{900(4\log (x{)}^2-2(2\log (x)-3)\log (\log (x+4))+\log {(\log (x+4))}^2-12\log (x)+9)}{x^2-10x+25}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[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)

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mupad [B]  time = 1.42, size = 22, normalized size = 0.92 $$\begin{array}{c}\frac{900{(\ln \left(\frac{x^2}{\ln (x+4)}\right)-3)}^2}{{(x-5)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[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

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sympy [B]  time = 0.58, size = 53, normalized size = 2.21 $$\begin{array}{c}\frac{16200}{2x^2-20x+50}+\frac{900\log {\left(\frac{x^2}{\log (x+4)}\right)}^2}{x^2-10x+25}-\frac{5400\log \left(\frac{x^2}{\log (x+4)}\right)}{x^2-10x+25}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[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)

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