3.27.90 \(\int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+(1012500 x^2+2812500 x^3+(607500 x^3+2812500 x^4) \log (2)+(121500 x^4+1012500 x^5) \log ^2(2)+(8100 x^5+157500 x^6) \log ^3(2)+9000 x^7 \log ^4(2)) \log (x)+(-121500 x-1012500 x^2+(-48600 x^2-810000 x^3) \log (2)+(-4860 x^3-202500 x^4) \log ^2(2)-16200 x^5 \log ^3(2)) \log ^2(x)+(4860+121500 x+(972 x+72900 x^2) \log (2)+9720 x^3 \log ^2(2)) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+(-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)) \log (x)+(506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)) \log ^2(x)+(-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)) \log ^3(x)+(1215 x+243 x^2 \log (2)) \log ^4(x)} \, dx\) [2690]

3.27.90.1 Optimal result
3.27.90.2 Mathematica [F]
3.27.90.3 Rubi [F]
3.27.90.4 Maple [B] (verified)
3.27.90.5 Fricas [B] (verification not implemented)
3.27.90.6 Sympy [B] (verification not implemented)
3.27.90.7 Maxima [B] (verification not implemented)
3.27.90.8 Giac [B] (verification not implemented)
3.27.90.9 Mupad [F(-1)]

3.27.90.1 Optimal result

Integrand size = 379, antiderivative size = 24 \[ \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx=\log \left (-\frac {8}{3}+\left (-5+\frac {3 \log (x)}{x (5+x \log (2))}\right )^4\right ) \]

output
ln((3*ln(x)/(5+x*ln(2))/x-5)^4-8/3)
 
3.27.90.2 Mathematica [F]

\[ \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx=\int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx \]

input
Integrate[(-2812500*x^3 - 2250000*x^4*Log[2] - 675000*x^5*Log[2]^2 - 90000 
*x^6*Log[2]^3 - 4500*x^7*Log[2]^4 + (1012500*x^2 + 2812500*x^3 + (607500*x 
^3 + 2812500*x^4)*Log[2] + (121500*x^4 + 1012500*x^5)*Log[2]^2 + (8100*x^5 
 + 157500*x^6)*Log[2]^3 + 9000*x^7*Log[2]^4)*Log[x] + (-121500*x - 1012500 
*x^2 + (-48600*x^2 - 810000*x^3)*Log[2] + (-4860*x^3 - 202500*x^4)*Log[2]^ 
2 - 16200*x^5*Log[2]^3)*Log[x]^2 + (4860 + 121500*x + (972*x + 72900*x^2)* 
Log[2] + 9720*x^3*Log[2]^2)*Log[x]^3 + (-4860 - 1944*x*Log[2])*Log[x]^4)/( 
5834375*x^5 + 5834375*x^6*Log[2] + 2333750*x^7*Log[2]^2 + 466750*x^8*Log[2 
]^3 + 46675*x^9*Log[2]^4 + 1867*x^10*Log[2]^5 + (-2812500*x^4 - 2250000*x^ 
5*Log[2] - 675000*x^6*Log[2]^2 - 90000*x^7*Log[2]^3 - 4500*x^8*Log[2]^4)*L 
og[x] + (506250*x^3 + 303750*x^4*Log[2] + 60750*x^5*Log[2]^2 + 4050*x^6*Lo 
g[2]^3)*Log[x]^2 + (-40500*x^2 - 16200*x^3*Log[2] - 1620*x^4*Log[2]^2)*Log 
[x]^3 + (1215*x + 243*x^2*Log[2])*Log[x]^4),x]
 
output
Integrate[(-2812500*x^3 - 2250000*x^4*Log[2] - 675000*x^5*Log[2]^2 - 90000 
*x^6*Log[2]^3 - 4500*x^7*Log[2]^4 + (1012500*x^2 + 2812500*x^3 + (607500*x 
^3 + 2812500*x^4)*Log[2] + (121500*x^4 + 1012500*x^5)*Log[2]^2 + (8100*x^5 
 + 157500*x^6)*Log[2]^3 + 9000*x^7*Log[2]^4)*Log[x] + (-121500*x - 1012500 
*x^2 + (-48600*x^2 - 810000*x^3)*Log[2] + (-4860*x^3 - 202500*x^4)*Log[2]^ 
2 - 16200*x^5*Log[2]^3)*Log[x]^2 + (4860 + 121500*x + (972*x + 72900*x^2)* 
Log[2] + 9720*x^3*Log[2]^2)*Log[x]^3 + (-4860 - 1944*x*Log[2])*Log[x]^4)/( 
5834375*x^5 + 5834375*x^6*Log[2] + 2333750*x^7*Log[2]^2 + 466750*x^8*Log[2 
]^3 + 46675*x^9*Log[2]^4 + 1867*x^10*Log[2]^5 + (-2812500*x^4 - 2250000*x^ 
5*Log[2] - 675000*x^6*Log[2]^2 - 90000*x^7*Log[2]^3 - 4500*x^8*Log[2]^4)*L 
og[x] + (506250*x^3 + 303750*x^4*Log[2] + 60750*x^5*Log[2]^2 + 4050*x^6*Lo 
g[2]^3)*Log[x]^2 + (-40500*x^2 - 16200*x^3*Log[2] - 1620*x^4*Log[2]^2)*Log 
[x]^3 + (1215*x + 243*x^2*Log[2])*Log[x]^4), x]
 
3.27.90.3 Rubi [F]

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.

\(\displaystyle \int \frac {-4500 x^7 \log ^4(2)-90000 x^6 \log ^3(2)-675000 x^5 \log ^2(2)-2250000 x^4 \log (2)-2812500 x^3+\left (9720 x^3 \log ^2(2)+\left (72900 x^2+972 x\right ) \log (2)+121500 x+4860\right ) \log ^3(x)+\left (-16200 x^5 \log ^3(2)-1012500 x^2+\left (-202500 x^4-4860 x^3\right ) \log ^2(2)+\left (-810000 x^3-48600 x^2\right ) \log (2)-121500 x\right ) \log ^2(x)+\left (9000 x^7 \log ^4(2)+2812500 x^3+1012500 x^2+\left (157500 x^6+8100 x^5\right ) \log ^3(2)+\left (1012500 x^5+121500 x^4\right ) \log ^2(2)+\left (2812500 x^4+607500 x^3\right ) \log (2)\right ) \log (x)+(-1944 x \log (2)-4860) \log ^4(x)}{1867 x^{10} \log ^5(2)+46675 x^9 \log ^4(2)+466750 x^8 \log ^3(2)+2333750 x^7 \log ^2(2)+5834375 x^6 \log (2)+5834375 x^5+\left (243 x^2 \log (2)+1215 x\right ) \log ^4(x)+\left (-1620 x^4 \log ^2(2)-16200 x^3 \log (2)-40500 x^2\right ) \log ^3(x)+\left (4050 x^6 \log ^3(2)+60750 x^5 \log ^2(2)+303750 x^4 \log (2)+506250 x^3\right ) \log ^2(x)+\left (-4500 x^8 \log ^4(2)-90000 x^7 \log ^3(2)-675000 x^6 \log ^2(2)-2250000 x^5 \log (2)-2812500 x^4\right ) \log (x)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {36 (5 x (x \log (2)+5)-3 \log (x))^3 (x (-\log (2))+(x \log (4)+5) \log (x)-5)}{x (x \log (2)+5) \left (1867 x^4 (x \log (2)+5)^4-4500 x^3 \log (x) (x \log (2)+5)^3+4050 x^2 \log ^2(x) (x \log (2)+5)^2+243 \log ^4(x)-1620 x \log ^3(x) (x \log (2)+5)\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 36 \int -\frac {(5 x (\log (2) x+5)-3 \log (x))^3 (\log (2) x-(\log (4) x+5) \log (x)+5)}{x (\log (2) x+5) \left (1867 x^4 (\log (2) x+5)^4-4500 x^3 \log (x) (\log (2) x+5)^3+4050 x^2 \log ^2(x) (\log (2) x+5)^2-1620 x \log ^3(x) (\log (2) x+5)+243 \log ^4(x)\right )}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -36 \int \frac {(5 x (\log (2) x+5)-3 \log (x))^3 (\log (2) x-(\log (4) x+5) \log (x)+5)}{x (\log (2) x+5) \left (1867 x^4 (\log (2) x+5)^4-4500 x^3 \log (x) (\log (2) x+5)^3+4050 x^2 \log ^2(x) (\log (2) x+5)^2-1620 x \log ^3(x) (\log (2) x+5)+243 \log ^4(x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -36 \int \left (\frac {\log (4) x+5}{x (\log (512) x+45)}+\frac {-1867 \log ^3(2) \log (4) x^8-9335 \log ^3(2) \left (1+\frac {\log (64)}{\log (2)}\right ) x^7+3375 \log ^2(2) \log (4) \log (x) x^6-140025 \log ^2(2) \left (1-\frac {15 \log (2)}{1867}+\frac {\log (4)}{\log (2)}\right ) x^6+16875 \log ^2(2) \left (1+\frac {\log (16)}{\log (2)}\right ) \log (x) x^5-700125 \log (2) \left (1-\frac {45 \log (2)}{1867}+\frac {\log (4)}{\log (8)}\right ) x^5-2025 \log (2) \log (4) \log ^2(x) x^4+168750 \left (2-\frac {3 \log (2)}{250}\right ) \log (2) \log (x) x^4-1166875 \left (1-\frac {135 \log (2)}{1867}\right ) x^4-10125 \log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log ^2(x) x^3+421875 \left (1-\frac {6 \log (2)}{125}\right ) \log (x) x^3+140625 x^3+405 \log (4) \log ^3(x) x^2-50625 \left (1-\frac {3 \log (2)}{125}\right ) \log ^2(x) x^2-50625 \log (x) x^2+2025 \log ^3(x) x+6075 \log ^2(x) x-243 \log ^3(x)}{9 x \left (1867 \log ^4(2) x^8+37340 \log ^3(2) x^7-4500 \log ^3(2) \log (x) x^6+280050 \log ^2(2) x^6-67500 \log ^2(2) \log (x) x^5+933500 \log (2) x^5+4050 \log ^2(2) \log ^2(x) x^4-337500 \log (2) \log (x) x^4+1166875 x^4+40500 \log (2) \log ^2(x) x^3-562500 \log (x) x^3-1620 \log (2) \log ^3(x) x^2+101250 \log ^2(x) x^2-8100 \log ^3(x) x+243 \log ^4(x)\right )}\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -36 \int \left (\frac {\log (4) x+5}{x (\log (512) x+45)}+\frac {-1867 \log ^3(2) \log (4) \log (8) x^8-9335 \log ^2(2) \log (8) \log (128) x^7+3375 \log ^2(2) \log (4) \log (8) \log (x) x^6-140025 \log ^2(2) \left (1-\frac {15 \log (2)}{1867}+\frac {\log (4)}{\log (2)}\right ) \log (8) x^6+16875 \log (2) \log (8) \log (32) \log (x) x^5-700125 \log (2) \log (4) \left (1+\frac {\left (1-\frac {45 \log (2)}{1867}\right ) \log (8)}{\log (4)}\right ) x^5-2025 \log (2) \log (4) \log (8) \log ^2(x) x^4+337500 \left (1-\frac {3 \log (2)}{500}\right ) \log (2) \log (8) \log (x) x^4-1166875 \left (1-\frac {135 \log (2)}{1867}\right ) \log (8) x^4-10125 \log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log (8) \log ^2(x) x^3+421875 \left (1-\frac {6 \log (2)}{125}\right ) \log (8) \log (x) x^3+140625 \log (8) x^3+405 \log (4) \log (8) \log ^3(x) x^2-50625 \left (1-\frac {3 \log (2)}{125}\right ) \log (8) \log ^2(x) x^2-50625 \log (8) \log (x) x^2+2025 \log (8) \log ^3(x) x+6075 \log (8) \log ^2(x) x-243 \log (8) \log ^3(x)}{9 x \log (8) \left (1867 \log ^4(2) x^8+37340 \log ^3(2) x^7-4500 \log ^3(2) \log (x) x^6+280050 \log ^2(2) x^6-67500 \log ^2(2) \log (x) x^5+933500 \log (2) x^5+4050 \log ^2(2) \log ^2(x) x^4-337500 \log (2) \log (x) x^4+1166875 x^4+40500 \log (2) \log ^2(x) x^3-562500 \log (x) x^3-1620 \log (2) \log ^3(x) x^2+101250 \log ^2(x) x^2-8100 \log ^3(x) x+243 \log ^4(x)\right )}\right )dx\)

\(\Big \downarrow \) 7299

\(\displaystyle -36 \int \left (\frac {\log (4) x+5}{x (\log (512) x+45)}+\frac {-1867 \log ^3(2) \log (4) \log (8) x^8-9335 \log ^2(2) \log (8) \log (128) x^7+3375 \log ^2(2) \log (4) \log (8) \log (x) x^6-140025 \log ^2(2) \left (1-\frac {15 \log (2)}{1867}+\frac {\log (4)}{\log (2)}\right ) \log (8) x^6+16875 \log (2) \log (8) \log (32) \log (x) x^5-700125 \log (2) \log (4) \left (1+\frac {\left (1-\frac {45 \log (2)}{1867}\right ) \log (8)}{\log (4)}\right ) x^5-2025 \log (2) \log (4) \log (8) \log ^2(x) x^4+337500 \left (1-\frac {3 \log (2)}{500}\right ) \log (2) \log (8) \log (x) x^4-1166875 \left (1-\frac {135 \log (2)}{1867}\right ) \log (8) x^4-10125 \log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log (8) \log ^2(x) x^3+421875 \left (1-\frac {6 \log (2)}{125}\right ) \log (8) \log (x) x^3+140625 \log (8) x^3+405 \log (4) \log (8) \log ^3(x) x^2-50625 \left (1-\frac {3 \log (2)}{125}\right ) \log (8) \log ^2(x) x^2-50625 \log (8) \log (x) x^2+2025 \log (8) \log ^3(x) x+6075 \log (8) \log ^2(x) x-243 \log (8) \log ^3(x)}{9 x \log (8) \left (1867 \log ^4(2) x^8+37340 \log ^3(2) x^7-4500 \log ^3(2) \log (x) x^6+280050 \log ^2(2) x^6-67500 \log ^2(2) \log (x) x^5+933500 \log (2) x^5+4050 \log ^2(2) \log ^2(x) x^4-337500 \log (2) \log (x) x^4+1166875 x^4+40500 \log (2) \log ^2(x) x^3-562500 \log (x) x^3-1620 \log (2) \log ^3(x) x^2+101250 \log ^2(x) x^2-8100 \log ^3(x) x+243 \log ^4(x)\right )}\right )dx\)

input
Int[(-2812500*x^3 - 2250000*x^4*Log[2] - 675000*x^5*Log[2]^2 - 90000*x^6*L 
og[2]^3 - 4500*x^7*Log[2]^4 + (1012500*x^2 + 2812500*x^3 + (607500*x^3 + 2 
812500*x^4)*Log[2] + (121500*x^4 + 1012500*x^5)*Log[2]^2 + (8100*x^5 + 157 
500*x^6)*Log[2]^3 + 9000*x^7*Log[2]^4)*Log[x] + (-121500*x - 1012500*x^2 + 
 (-48600*x^2 - 810000*x^3)*Log[2] + (-4860*x^3 - 202500*x^4)*Log[2]^2 - 16 
200*x^5*Log[2]^3)*Log[x]^2 + (4860 + 121500*x + (972*x + 72900*x^2)*Log[2] 
 + 9720*x^3*Log[2]^2)*Log[x]^3 + (-4860 - 1944*x*Log[2])*Log[x]^4)/(583437 
5*x^5 + 5834375*x^6*Log[2] + 2333750*x^7*Log[2]^2 + 466750*x^8*Log[2]^3 + 
46675*x^9*Log[2]^4 + 1867*x^10*Log[2]^5 + (-2812500*x^4 - 2250000*x^5*Log[ 
2] - 675000*x^6*Log[2]^2 - 90000*x^7*Log[2]^3 - 4500*x^8*Log[2]^4)*Log[x] 
+ (506250*x^3 + 303750*x^4*Log[2] + 60750*x^5*Log[2]^2 + 4050*x^6*Log[2]^3 
)*Log[x]^2 + (-40500*x^2 - 16200*x^3*Log[2] - 1620*x^4*Log[2]^2)*Log[x]^3 
+ (1215*x + 243*x^2*Log[2])*Log[x]^4),x]
 
output
$Aborted
 

3.27.90.3.1 Defintions of rubi rules used

rule 25
Int[-(Fx_), x_Symbol] :> Simp[Identity[-1]   Int[Fx, x], x]
 

rule 27
Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 7239
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl 
erIntegrandQ[v, u, x]]
 

rule 7293
Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v] 
]
 

rule 7299
Int[u_, x_] :> CannotIntegrate[u, x]
 
3.27.90.4 Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(136\) vs. \(2(22)=44\).

Time = 1.60 (sec) , antiderivative size = 137, normalized size of antiderivative = 5.71

method result size
risch \(-4 \ln \left (x^{2} \ln \left (2\right )+5 x \right )+\ln \left (\ln \left (x \right )^{4}+\left (-\frac {20 x^{2} \ln \left (2\right )}{3}-\frac {100 x}{3}\right ) \ln \left (x \right )^{3}+\left (\frac {50 x^{4} \ln \left (2\right )^{2}}{3}+\frac {500 x^{3} \ln \left (2\right )}{3}+\frac {1250 x^{2}}{3}\right ) \ln \left (x \right )^{2}+\left (-\frac {500 x^{6} \ln \left (2\right )^{3}}{27}-\frac {2500 x^{5} \ln \left (2\right )^{2}}{9}-\frac {12500 x^{4} \ln \left (2\right )}{9}-\frac {62500 x^{3}}{27}\right ) \ln \left (x \right )+\frac {1867 x^{8} \ln \left (2\right )^{4}}{243}+\frac {37340 x^{7} \ln \left (2\right )^{3}}{243}+\frac {93350 x^{6} \ln \left (2\right )^{2}}{81}+\frac {933500 x^{5} \ln \left (2\right )}{243}+\frac {1166875 x^{4}}{243}\right )\) \(137\)
default \(-4 \ln \left (x \right )-4 \ln \left (x +\frac {5}{\ln \left (2\right )}\right )+\ln \left (x^{8}+\frac {20 x^{7}}{\ln \left (2\right )}-\frac {150 \left (30 \ln \left (2\right ) \ln \left (x \right )-1867\right ) x^{6}}{1867 \ln \left (2\right )^{2}}-\frac {500 \left (135 \ln \left (2\right ) \ln \left (x \right )-1867\right ) x^{5}}{1867 \ln \left (2\right )^{3}}+\frac {25 \left (162 \ln \left (2\right )^{2} \ln \left (x \right )^{2}-13500 \ln \left (2\right ) \ln \left (x \right )+46675\right ) x^{4}}{1867 \ln \left (2\right )^{4}}+\frac {4500 \ln \left (x \right ) \left (9 \ln \left (2\right ) \ln \left (x \right )-125\right ) x^{3}}{1867 \ln \left (2\right )^{4}}-\frac {810 \ln \left (x \right )^{2} \left (2 \ln \left (2\right ) \ln \left (x \right )-125\right ) x^{2}}{1867 \ln \left (2\right )^{4}}-\frac {8100 \ln \left (x \right )^{3} x}{1867 \ln \left (2\right )^{4}}+\frac {243 \ln \left (x \right )^{4}}{1867 \ln \left (2\right )^{4}}\right )\) \(153\)
parallelrisch \(-4 \ln \left (\frac {5+x \ln \left (2\right )}{\ln \left (2\right )}\right )+\ln \left (\frac {1867 x^{8} \ln \left (2\right )^{4}+37340 x^{7} \ln \left (2\right )^{3}-4500 \ln \left (x \right ) \ln \left (2\right )^{3} x^{6}+280050 x^{6} \ln \left (2\right )^{2}-67500 \ln \left (x \right ) \ln \left (2\right )^{2} x^{5}+4050 x^{4} \ln \left (2\right )^{2} \ln \left (x \right )^{2}+933500 x^{5} \ln \left (2\right )-337500 \ln \left (x \right ) \ln \left (2\right ) x^{4}+40500 \ln \left (x \right )^{2} \ln \left (2\right ) x^{3}-1620 x^{2} \ln \left (x \right )^{3} \ln \left (2\right )+1166875 x^{4}-562500 x^{3} \ln \left (x \right )+101250 x^{2} \ln \left (x \right )^{2}-8100 x \ln \left (x \right )^{3}+243 \ln \left (x \right )^{4}}{1867 \ln \left (2\right )^{4}}\right )-4 \ln \left (x \right )\) \(162\)

input
int(((-1944*x*ln(2)-4860)*ln(x)^4+(9720*x^3*ln(2)^2+(72900*x^2+972*x)*ln(2 
)+121500*x+4860)*ln(x)^3+(-16200*x^5*ln(2)^3+(-202500*x^4-4860*x^3)*ln(2)^ 
2+(-810000*x^3-48600*x^2)*ln(2)-1012500*x^2-121500*x)*ln(x)^2+(9000*x^7*ln 
(2)^4+(157500*x^6+8100*x^5)*ln(2)^3+(1012500*x^5+121500*x^4)*ln(2)^2+(2812 
500*x^4+607500*x^3)*ln(2)+2812500*x^3+1012500*x^2)*ln(x)-4500*x^7*ln(2)^4- 
90000*x^6*ln(2)^3-675000*x^5*ln(2)^2-2250000*x^4*ln(2)-2812500*x^3)/((243* 
x^2*ln(2)+1215*x)*ln(x)^4+(-1620*x^4*ln(2)^2-16200*x^3*ln(2)-40500*x^2)*ln 
(x)^3+(4050*x^6*ln(2)^3+60750*x^5*ln(2)^2+303750*x^4*ln(2)+506250*x^3)*ln( 
x)^2+(-4500*x^8*ln(2)^4-90000*x^7*ln(2)^3-675000*x^6*ln(2)^2-2250000*x^5*l 
n(2)-2812500*x^4)*ln(x)+1867*x^10*ln(2)^5+46675*x^9*ln(2)^4+466750*x^8*ln( 
2)^3+2333750*x^7*ln(2)^2+5834375*x^6*ln(2)+5834375*x^5),x,method=_RETURNVE 
RBOSE)
 
output
-4*ln(x^2*ln(2)+5*x)+ln(ln(x)^4+(-20/3*x^2*ln(2)-100/3*x)*ln(x)^3+(50/3*x^ 
4*ln(2)^2+500/3*x^3*ln(2)+1250/3*x^2)*ln(x)^2+(-500/27*x^6*ln(2)^3-2500/9* 
x^5*ln(2)^2-12500/9*x^4*ln(2)-62500/27*x^3)*ln(x)+1867/243*x^8*ln(2)^4+373 
40/243*x^7*ln(2)^3+93350/81*x^6*ln(2)^2+933500/243*x^5*ln(2)+1166875/243*x 
^4)
 
3.27.90.5 Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 138 vs. \(2 (22) = 44\).

Time = 0.29 (sec) , antiderivative size = 138, normalized size of antiderivative = 5.75 \[ \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx=\log \left (1867 \, x^{8} \log \left (2\right )^{4} + 37340 \, x^{7} \log \left (2\right )^{3} + 280050 \, x^{6} \log \left (2\right )^{2} + 933500 \, x^{5} \log \left (2\right ) + 1166875 \, x^{4} - 1620 \, {\left (x^{2} \log \left (2\right ) + 5 \, x\right )} \log \left (x\right )^{3} + 243 \, \log \left (x\right )^{4} + 4050 \, {\left (x^{4} \log \left (2\right )^{2} + 10 \, x^{3} \log \left (2\right ) + 25 \, x^{2}\right )} \log \left (x\right )^{2} - 4500 \, {\left (x^{6} \log \left (2\right )^{3} + 15 \, x^{5} \log \left (2\right )^{2} + 75 \, x^{4} \log \left (2\right ) + 125 \, x^{3}\right )} \log \left (x\right )\right ) - 4 \, \log \left (x^{2} \log \left (2\right ) + 5 \, x\right ) \]

input
integrate(((-1944*x*log(2)-4860)*log(x)^4+(9720*x^3*log(2)^2+(72900*x^2+97 
2*x)*log(2)+121500*x+4860)*log(x)^3+(-16200*x^5*log(2)^3+(-202500*x^4-4860 
*x^3)*log(2)^2+(-810000*x^3-48600*x^2)*log(2)-1012500*x^2-121500*x)*log(x) 
^2+(9000*x^7*log(2)^4+(157500*x^6+8100*x^5)*log(2)^3+(1012500*x^5+121500*x 
^4)*log(2)^2+(2812500*x^4+607500*x^3)*log(2)+2812500*x^3+1012500*x^2)*log( 
x)-4500*x^7*log(2)^4-90000*x^6*log(2)^3-675000*x^5*log(2)^2-2250000*x^4*lo 
g(2)-2812500*x^3)/((243*x^2*log(2)+1215*x)*log(x)^4+(-1620*x^4*log(2)^2-16 
200*x^3*log(2)-40500*x^2)*log(x)^3+(4050*x^6*log(2)^3+60750*x^5*log(2)^2+3 
03750*x^4*log(2)+506250*x^3)*log(x)^2+(-4500*x^8*log(2)^4-90000*x^7*log(2) 
^3-675000*x^6*log(2)^2-2250000*x^5*log(2)-2812500*x^4)*log(x)+1867*x^10*lo 
g(2)^5+46675*x^9*log(2)^4+466750*x^8*log(2)^3+2333750*x^7*log(2)^2+5834375 
*x^6*log(2)+5834375*x^5),x, algorithm=\
 
output
log(1867*x^8*log(2)^4 + 37340*x^7*log(2)^3 + 280050*x^6*log(2)^2 + 933500* 
x^5*log(2) + 1166875*x^4 - 1620*(x^2*log(2) + 5*x)*log(x)^3 + 243*log(x)^4 
 + 4050*(x^4*log(2)^2 + 10*x^3*log(2) + 25*x^2)*log(x)^2 - 4500*(x^6*log(2 
)^3 + 15*x^5*log(2)^2 + 75*x^4*log(2) + 125*x^3)*log(x)) - 4*log(x^2*log(2 
) + 5*x)
 
3.27.90.6 Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 173 vs. \(2 (20) = 40\).

Time = 0.95 (sec) , antiderivative size = 173, normalized size of antiderivative = 7.21 \[ \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx=- 4 \log {\left (x^{2} \log {\left (2 \right )} + 5 x \right )} + \log {\left (\frac {1867 x^{8} \log {\left (2 \right )}^{4}}{243} + \frac {37340 x^{7} \log {\left (2 \right )}^{3}}{243} + \frac {93350 x^{6} \log {\left (2 \right )}^{2}}{81} + \frac {933500 x^{5} \log {\left (2 \right )}}{243} + \frac {1166875 x^{4}}{243} + \left (- \frac {20 x^{2} \log {\left (2 \right )}}{3} - \frac {100 x}{3}\right ) \log {\left (x \right )}^{3} + \left (\frac {50 x^{4} \log {\left (2 \right )}^{2}}{3} + \frac {500 x^{3} \log {\left (2 \right )}}{3} + \frac {1250 x^{2}}{3}\right ) \log {\left (x \right )}^{2} + \left (- \frac {500 x^{6} \log {\left (2 \right )}^{3}}{27} - \frac {2500 x^{5} \log {\left (2 \right )}^{2}}{9} - \frac {12500 x^{4} \log {\left (2 \right )}}{9} - \frac {62500 x^{3}}{27}\right ) \log {\left (x \right )} + \log {\left (x \right )}^{4} \right )} \]

input
integrate(((-1944*x*ln(2)-4860)*ln(x)**4+(9720*x**3*ln(2)**2+(72900*x**2+9 
72*x)*ln(2)+121500*x+4860)*ln(x)**3+(-16200*x**5*ln(2)**3+(-202500*x**4-48 
60*x**3)*ln(2)**2+(-810000*x**3-48600*x**2)*ln(2)-1012500*x**2-121500*x)*l 
n(x)**2+(9000*x**7*ln(2)**4+(157500*x**6+8100*x**5)*ln(2)**3+(1012500*x**5 
+121500*x**4)*ln(2)**2+(2812500*x**4+607500*x**3)*ln(2)+2812500*x**3+10125 
00*x**2)*ln(x)-4500*x**7*ln(2)**4-90000*x**6*ln(2)**3-675000*x**5*ln(2)**2 
-2250000*x**4*ln(2)-2812500*x**3)/((243*x**2*ln(2)+1215*x)*ln(x)**4+(-1620 
*x**4*ln(2)**2-16200*x**3*ln(2)-40500*x**2)*ln(x)**3+(4050*x**6*ln(2)**3+6 
0750*x**5*ln(2)**2+303750*x**4*ln(2)+506250*x**3)*ln(x)**2+(-4500*x**8*ln( 
2)**4-90000*x**7*ln(2)**3-675000*x**6*ln(2)**2-2250000*x**5*ln(2)-2812500* 
x**4)*ln(x)+1867*x**10*ln(2)**5+46675*x**9*ln(2)**4+466750*x**8*ln(2)**3+2 
333750*x**7*ln(2)**2+5834375*x**6*ln(2)+5834375*x**5),x)
 
output
-4*log(x**2*log(2) + 5*x) + log(1867*x**8*log(2)**4/243 + 37340*x**7*log(2 
)**3/243 + 93350*x**6*log(2)**2/81 + 933500*x**5*log(2)/243 + 1166875*x**4 
/243 + (-20*x**2*log(2)/3 - 100*x/3)*log(x)**3 + (50*x**4*log(2)**2/3 + 50 
0*x**3*log(2)/3 + 1250*x**2/3)*log(x)**2 + (-500*x**6*log(2)**3/27 - 2500* 
x**5*log(2)**2/9 - 12500*x**4*log(2)/9 - 62500*x**3/27)*log(x) + log(x)**4 
)
 
3.27.90.7 Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 136 vs. \(2 (22) = 44\).

Time = 0.34 (sec) , antiderivative size = 136, normalized size of antiderivative = 5.67 \[ \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx=\log \left (\frac {1867}{243} \, x^{8} \log \left (2\right )^{4} + \frac {37340}{243} \, x^{7} \log \left (2\right )^{3} + \frac {93350}{81} \, x^{6} \log \left (2\right )^{2} + \frac {933500}{243} \, x^{5} \log \left (2\right ) + \frac {1166875}{243} \, x^{4} - \frac {20}{3} \, {\left (x^{2} \log \left (2\right ) + 5 \, x\right )} \log \left (x\right )^{3} + \log \left (x\right )^{4} + \frac {50}{3} \, {\left (x^{4} \log \left (2\right )^{2} + 10 \, x^{3} \log \left (2\right ) + 25 \, x^{2}\right )} \log \left (x\right )^{2} - \frac {500}{27} \, {\left (x^{6} \log \left (2\right )^{3} + 15 \, x^{5} \log \left (2\right )^{2} + 75 \, x^{4} \log \left (2\right ) + 125 \, x^{3}\right )} \log \left (x\right )\right ) - 4 \, \log \left (x \log \left (2\right ) + 5\right ) - 4 \, \log \left (x\right ) \]

input
integrate(((-1944*x*log(2)-4860)*log(x)^4+(9720*x^3*log(2)^2+(72900*x^2+97 
2*x)*log(2)+121500*x+4860)*log(x)^3+(-16200*x^5*log(2)^3+(-202500*x^4-4860 
*x^3)*log(2)^2+(-810000*x^3-48600*x^2)*log(2)-1012500*x^2-121500*x)*log(x) 
^2+(9000*x^7*log(2)^4+(157500*x^6+8100*x^5)*log(2)^3+(1012500*x^5+121500*x 
^4)*log(2)^2+(2812500*x^4+607500*x^3)*log(2)+2812500*x^3+1012500*x^2)*log( 
x)-4500*x^7*log(2)^4-90000*x^6*log(2)^3-675000*x^5*log(2)^2-2250000*x^4*lo 
g(2)-2812500*x^3)/((243*x^2*log(2)+1215*x)*log(x)^4+(-1620*x^4*log(2)^2-16 
200*x^3*log(2)-40500*x^2)*log(x)^3+(4050*x^6*log(2)^3+60750*x^5*log(2)^2+3 
03750*x^4*log(2)+506250*x^3)*log(x)^2+(-4500*x^8*log(2)^4-90000*x^7*log(2) 
^3-675000*x^6*log(2)^2-2250000*x^5*log(2)-2812500*x^4)*log(x)+1867*x^10*lo 
g(2)^5+46675*x^9*log(2)^4+466750*x^8*log(2)^3+2333750*x^7*log(2)^2+5834375 
*x^6*log(2)+5834375*x^5),x, algorithm=\
 
output
log(1867/243*x^8*log(2)^4 + 37340/243*x^7*log(2)^3 + 93350/81*x^6*log(2)^2 
 + 933500/243*x^5*log(2) + 1166875/243*x^4 - 20/3*(x^2*log(2) + 5*x)*log(x 
)^3 + log(x)^4 + 50/3*(x^4*log(2)^2 + 10*x^3*log(2) + 25*x^2)*log(x)^2 - 5 
00/27*(x^6*log(2)^3 + 15*x^5*log(2)^2 + 75*x^4*log(2) + 125*x^3)*log(x)) - 
 4*log(x*log(2) + 5) - 4*log(x)
 
3.27.90.8 Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 150 vs. \(2 (22) = 44\).

Time = 1.13 (sec) , antiderivative size = 150, normalized size of antiderivative = 6.25 \[ \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx=\log \left (1867 \, x^{8} \log \left (2\right )^{4} + 37340 \, x^{7} \log \left (2\right )^{3} - 4500 \, x^{6} \log \left (2\right )^{3} \log \left (x\right ) + 280050 \, x^{6} \log \left (2\right )^{2} - 67500 \, x^{5} \log \left (2\right )^{2} \log \left (x\right ) + 4050 \, x^{4} \log \left (2\right )^{2} \log \left (x\right )^{2} + 933500 \, x^{5} \log \left (2\right ) - 337500 \, x^{4} \log \left (2\right ) \log \left (x\right ) + 40500 \, x^{3} \log \left (2\right ) \log \left (x\right )^{2} - 1620 \, x^{2} \log \left (2\right ) \log \left (x\right )^{3} + 1166875 \, x^{4} - 562500 \, x^{3} \log \left (x\right ) + 101250 \, x^{2} \log \left (x\right )^{2} - 8100 \, x \log \left (x\right )^{3} + 243 \, \log \left (x\right )^{4}\right ) - 4 \, \log \left (x \log \left (2\right ) + 5\right ) - 4 \, \log \left (x\right ) \]

input
integrate(((-1944*x*log(2)-4860)*log(x)^4+(9720*x^3*log(2)^2+(72900*x^2+97 
2*x)*log(2)+121500*x+4860)*log(x)^3+(-16200*x^5*log(2)^3+(-202500*x^4-4860 
*x^3)*log(2)^2+(-810000*x^3-48600*x^2)*log(2)-1012500*x^2-121500*x)*log(x) 
^2+(9000*x^7*log(2)^4+(157500*x^6+8100*x^5)*log(2)^3+(1012500*x^5+121500*x 
^4)*log(2)^2+(2812500*x^4+607500*x^3)*log(2)+2812500*x^3+1012500*x^2)*log( 
x)-4500*x^7*log(2)^4-90000*x^6*log(2)^3-675000*x^5*log(2)^2-2250000*x^4*lo 
g(2)-2812500*x^3)/((243*x^2*log(2)+1215*x)*log(x)^4+(-1620*x^4*log(2)^2-16 
200*x^3*log(2)-40500*x^2)*log(x)^3+(4050*x^6*log(2)^3+60750*x^5*log(2)^2+3 
03750*x^4*log(2)+506250*x^3)*log(x)^2+(-4500*x^8*log(2)^4-90000*x^7*log(2) 
^3-675000*x^6*log(2)^2-2250000*x^5*log(2)-2812500*x^4)*log(x)+1867*x^10*lo 
g(2)^5+46675*x^9*log(2)^4+466750*x^8*log(2)^3+2333750*x^7*log(2)^2+5834375 
*x^6*log(2)+5834375*x^5),x, algorithm=\
 
output
log(1867*x^8*log(2)^4 + 37340*x^7*log(2)^3 - 4500*x^6*log(2)^3*log(x) + 28 
0050*x^6*log(2)^2 - 67500*x^5*log(2)^2*log(x) + 4050*x^4*log(2)^2*log(x)^2 
 + 933500*x^5*log(2) - 337500*x^4*log(2)*log(x) + 40500*x^3*log(2)*log(x)^ 
2 - 1620*x^2*log(2)*log(x)^3 + 1166875*x^4 - 562500*x^3*log(x) + 101250*x^ 
2*log(x)^2 - 8100*x*log(x)^3 + 243*log(x)^4) - 4*log(x*log(2) + 5) - 4*log 
(x)
 
3.27.90.9 Mupad [F(-1)]

Timed out. \[ \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx=\int -\frac {675000\,x^5\,{\ln \left (2\right )}^2+90000\,x^6\,{\ln \left (2\right )}^3+4500\,x^7\,{\ln \left (2\right )}^4-{\ln \left (x\right )}^3\,\left (121500\,x+9720\,x^3\,{\ln \left (2\right )}^2+\ln \left (2\right )\,\left (72900\,x^2+972\,x\right )+4860\right )+{\ln \left (x\right )}^4\,\left (1944\,x\,\ln \left (2\right )+4860\right )-\ln \left (x\right )\,\left (9000\,x^7\,{\ln \left (2\right )}^4+\ln \left (2\right )\,\left (2812500\,x^4+607500\,x^3\right )+1012500\,x^2+2812500\,x^3+{\ln \left (2\right )}^3\,\left (157500\,x^6+8100\,x^5\right )+{\ln \left (2\right )}^2\,\left (1012500\,x^5+121500\,x^4\right )\right )+2250000\,x^4\,\ln \left (2\right )+{\ln \left (x\right )}^2\,\left (121500\,x+16200\,x^5\,{\ln \left (2\right )}^3+\ln \left (2\right )\,\left (810000\,x^3+48600\,x^2\right )+1012500\,x^2+{\ln \left (2\right )}^2\,\left (202500\,x^4+4860\,x^3\right )\right )+2812500\,x^3}{2333750\,x^7\,{\ln \left (2\right )}^2+466750\,x^8\,{\ln \left (2\right )}^3+46675\,x^9\,{\ln \left (2\right )}^4+1867\,x^{10}\,{\ln \left (2\right )}^5+{\ln \left (x\right )}^4\,\left (243\,\ln \left (2\right )\,x^2+1215\,x\right )-\ln \left (x\right )\,\left (4500\,{\ln \left (2\right )}^4\,x^8+90000\,{\ln \left (2\right )}^3\,x^7+675000\,{\ln \left (2\right )}^2\,x^6+2250000\,\ln \left (2\right )\,x^5+2812500\,x^4\right )+5834375\,x^6\,\ln \left (2\right )+5834375\,x^5-{\ln \left (x\right )}^3\,\left (1620\,{\ln \left (2\right )}^2\,x^4+16200\,\ln \left (2\right )\,x^3+40500\,x^2\right )+{\ln \left (x\right )}^2\,\left (4050\,{\ln \left (2\right )}^3\,x^6+60750\,{\ln \left (2\right )}^2\,x^5+303750\,\ln \left (2\right )\,x^4+506250\,x^3\right )} \,d x \]

input
int(-(675000*x^5*log(2)^2 + 90000*x^6*log(2)^3 + 4500*x^7*log(2)^4 - log(x 
)^3*(121500*x + 9720*x^3*log(2)^2 + log(2)*(972*x + 72900*x^2) + 4860) + l 
og(x)^4*(1944*x*log(2) + 4860) - log(x)*(9000*x^7*log(2)^4 + log(2)*(60750 
0*x^3 + 2812500*x^4) + 1012500*x^2 + 2812500*x^3 + log(2)^3*(8100*x^5 + 15 
7500*x^6) + log(2)^2*(121500*x^4 + 1012500*x^5)) + 2250000*x^4*log(2) + lo 
g(x)^2*(121500*x + 16200*x^5*log(2)^3 + log(2)*(48600*x^2 + 810000*x^3) + 
1012500*x^2 + log(2)^2*(4860*x^3 + 202500*x^4)) + 2812500*x^3)/(2333750*x^ 
7*log(2)^2 + 466750*x^8*log(2)^3 + 46675*x^9*log(2)^4 + 1867*x^10*log(2)^5 
 + log(x)^4*(1215*x + 243*x^2*log(2)) - log(x)*(675000*x^6*log(2)^2 + 9000 
0*x^7*log(2)^3 + 4500*x^8*log(2)^4 + 2250000*x^5*log(2) + 2812500*x^4) + 5 
834375*x^6*log(2) + 5834375*x^5 - log(x)^3*(1620*x^4*log(2)^2 + 16200*x^3* 
log(2) + 40500*x^2) + log(x)^2*(60750*x^5*log(2)^2 + 4050*x^6*log(2)^3 + 3 
03750*x^4*log(2) + 506250*x^3)),x)
 
output
int(-(675000*x^5*log(2)^2 + 90000*x^6*log(2)^3 + 4500*x^7*log(2)^4 - log(x 
)^3*(121500*x + 9720*x^3*log(2)^2 + log(2)*(972*x + 72900*x^2) + 4860) + l 
og(x)^4*(1944*x*log(2) + 4860) - log(x)*(9000*x^7*log(2)^4 + log(2)*(60750 
0*x^3 + 2812500*x^4) + 1012500*x^2 + 2812500*x^3 + log(2)^3*(8100*x^5 + 15 
7500*x^6) + log(2)^2*(121500*x^4 + 1012500*x^5)) + 2250000*x^4*log(2) + lo 
g(x)^2*(121500*x + 16200*x^5*log(2)^3 + log(2)*(48600*x^2 + 810000*x^3) + 
1012500*x^2 + log(2)^2*(4860*x^3 + 202500*x^4)) + 2812500*x^3)/(2333750*x^ 
7*log(2)^2 + 466750*x^8*log(2)^3 + 46675*x^9*log(2)^4 + 1867*x^10*log(2)^5 
 + log(x)^4*(1215*x + 243*x^2*log(2)) - log(x)*(675000*x^6*log(2)^2 + 9000 
0*x^7*log(2)^3 + 4500*x^8*log(2)^4 + 2250000*x^5*log(2) + 2812500*x^4) + 5 
834375*x^6*log(2) + 5834375*x^5 - log(x)^3*(1620*x^4*log(2)^2 + 16200*x^3* 
log(2) + 40500*x^2) + log(x)^2*(60750*x^5*log(2)^2 + 4050*x^6*log(2)^3 + 3 
03750*x^4*log(2) + 506250*x^3)), x)