\(\int \frac {-128 x^2+160 x^3-32 x^4+e^5 (-640 x+128 x^2)+(-640 x+128 x^2) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} (-960 x-48 x^2+48 x^3)+e^5 (-960 x^2-288 x^3+36 x^4+12 x^5)+(-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} (-240 x+48 x^2)+e^5 (-480 x^2-24 x^3+24 x^4)) \log (2)+(-60 x^3-3 x^4+3 x^5+e^5 (-60 x^2+12 x^3)) \log ^2(2)+(-5 x^3+x^4) \log ^3(2)+(-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} (-240 x+48 x^2)+e^5 (-480 x^2-24 x^3+24 x^4)+(-120 x^3-6 x^4+6 x^5+e^5 (-120 x^2+24 x^3)) \log (2)+(-15 x^3+3 x^4) \log ^2(2)) \log (3)+(-60 x^3-3 x^4+3 x^5+e^5 (-60 x^2+12 x^3)+(-15 x^3+3 x^4) \log (2)) \log ^2(3)+(-5 x^3+x^4) \log ^3(3)+(-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 (-1920 x-96 x^2+96 x^3)+(-480 x^2-24 x^3+24 x^4+e^5 (-480 x+96 x^2)) \log (2)+(-60 x^2+12 x^3) \log ^2(2)+(-480 x^2-24 x^3+24 x^4+e^5 (-480 x+96 x^2)+(-120 x^2+24 x^3) \log (2)) \log (3)+(-60 x^2+12 x^3) \log ^2(3)) \log (-5+x)+(-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+(-240 x+48 x^2) \log (2)+(-240 x+48 x^2) \log (3)) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx\) [2884]

Optimal result

Integrand size = 629, antiderivative size = 26 \[ \int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx=\frac {1}{\left (\frac {1}{4} (x+\log (2)+\log (3))+\frac {e^5+x+\log (-5+x)}{x}\right )^2} \] Output:

1/((x+exp(5)+ln(-5+x))/x+1/4*x+1/4*ln(3)+1/4*ln(2))^2
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 5.04 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx=\frac {16 x^2}{\left (4 e^5+x (4+x+\log (6))+4 \log (-5+x)\right )^2} \] Input:

Integrate[(-128*x^2 + 160*x^3 - 32*x^4 + E^5*(-640*x + 128*x^2) + (-640*x 
+ 128*x^2)*Log[-5 + x])/(-320*x^3 - 176*x^4 - 12*x^5 + 7*x^6 + x^7 + E^15* 
(-320 + 64*x) + E^10*(-960*x - 48*x^2 + 48*x^3) + E^5*(-960*x^2 - 288*x^3 
+ 36*x^4 + 12*x^5) + (-240*x^3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 4 
8*x^2) + E^5*(-480*x^2 - 24*x^3 + 24*x^4))*Log[2] + (-60*x^3 - 3*x^4 + 3*x 
^5 + E^5*(-60*x^2 + 12*x^3))*Log[2]^2 + (-5*x^3 + x^4)*Log[2]^3 + (-240*x^ 
3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x 
^3 + 24*x^4) + (-120*x^3 - 6*x^4 + 6*x^5 + E^5*(-120*x^2 + 24*x^3))*Log[2] 
 + (-15*x^3 + 3*x^4)*Log[2]^2)*Log[3] + (-60*x^3 - 3*x^4 + 3*x^5 + E^5*(-6 
0*x^2 + 12*x^3) + (-15*x^3 + 3*x^4)*Log[2])*Log[3]^2 + (-5*x^3 + x^4)*Log[ 
3]^3 + (-960*x^2 - 288*x^3 + 36*x^4 + 12*x^5 + E^10*(-960 + 192*x) + E^5*( 
-1920*x - 96*x^2 + 96*x^3) + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-480*x + 9 
6*x^2))*Log[2] + (-60*x^2 + 12*x^3)*Log[2]^2 + (-480*x^2 - 24*x^3 + 24*x^4 
 + E^5*(-480*x + 96*x^2) + (-120*x^2 + 24*x^3)*Log[2])*Log[3] + (-60*x^2 + 
 12*x^3)*Log[3]^2)*Log[-5 + x] + (-960*x - 48*x^2 + 48*x^3 + E^5*(-960 + 1 
92*x) + (-240*x + 48*x^2)*Log[2] + (-240*x + 48*x^2)*Log[3])*Log[-5 + x]^2 
 + (-320 + 64*x)*Log[-5 + x]^3),x]
 

Output:

(16*x^2)/(4*E^5 + x*(4 + x + Log[6]) + 4*Log[-5 + x])^2
 

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.

\(\displaystyle \int \frac {-32 x^4+160 x^3-128 x^2+e^5 \left (128 x^2-640 x\right )+\left (128 x^2-640 x\right ) \log (x-5)}{x^7+7 x^6-12 x^5-176 x^4-320 x^3+\left (x^4-5 x^3\right ) \log ^3(3)+\left (x^4-5 x^3\right ) \log ^3(2)+e^{10} \left (48 x^3-48 x^2-960 x\right )+\left (48 x^3-48 x^2+\left (48 x^2-240 x\right ) \log (3)+\left (48 x^2-240 x\right ) \log (2)-960 x+e^5 (192 x-960)\right ) \log ^2(x-5)+e^5 \left (12 x^5+36 x^4-288 x^3-960 x^2\right )+\left (12 x^5+36 x^4-288 x^3-960 x^2+e^5 \left (96 x^3-96 x^2-1920 x\right )+\left (12 x^3-60 x^2\right ) \log ^2(3)+\left (12 x^3-60 x^2\right ) \log ^2(2)+\log (3) \left (24 x^4-24 x^3-480 x^2+e^5 \left (96 x^2-480 x\right )+\left (24 x^3-120 x^2\right ) \log (2)\right )+\left (24 x^4-24 x^3-480 x^2+e^5 \left (96 x^2-480 x\right )\right ) \log (2)+e^{10} (192 x-960)\right ) \log (x-5)+\log ^2(3) \left (3 x^5-3 x^4-60 x^3+\left (3 x^4-15 x^3\right ) \log (2)+e^5 \left (12 x^3-60 x^2\right )\right )+\left (3 x^5-3 x^4-60 x^3+e^5 \left (12 x^3-60 x^2\right )\right ) \log ^2(2)+\log (3) \left (3 x^6+9 x^5-72 x^4-240 x^3+e^{10} \left (48 x^2-240 x\right )+\left (3 x^4-15 x^3\right ) \log ^2(2)+e^5 \left (24 x^4-24 x^3-480 x^2\right )+\left (6 x^5-6 x^4-120 x^3+e^5 \left (24 x^3-120 x^2\right )\right ) \log (2)\right )+\left (3 x^6+9 x^5-72 x^4-240 x^3+e^{10} \left (48 x^2-240 x\right )+e^5 \left (24 x^4-24 x^3-480 x^2\right )\right ) \log (2)+e^{15} (64 x-320)+(64 x-320) \log ^3(x-5)} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {-32 x^4+160 x^3-128 x^2+e^5 \left (128 x^2-640 x\right )+\left (128 x^2-640 x\right ) \log (x-5)}{x^7+7 x^6-12 x^5-176 x^4-320 x^3+\left (x^4-5 x^3\right ) \left (\log ^3(2)+\log ^3(3)\right )+e^{10} \left (48 x^3-48 x^2-960 x\right )+\left (48 x^3-48 x^2+\left (48 x^2-240 x\right ) \log (3)+\left (48 x^2-240 x\right ) \log (2)-960 x+e^5 (192 x-960)\right ) \log ^2(x-5)+e^5 \left (12 x^5+36 x^4-288 x^3-960 x^2\right )+\left (12 x^5+36 x^4-288 x^3-960 x^2+e^5 \left (96 x^3-96 x^2-1920 x\right )+\left (12 x^3-60 x^2\right ) \log ^2(3)+\left (12 x^3-60 x^2\right ) \log ^2(2)+\log (3) \left (24 x^4-24 x^3-480 x^2+e^5 \left (96 x^2-480 x\right )+\left (24 x^3-120 x^2\right ) \log (2)\right )+\left (24 x^4-24 x^3-480 x^2+e^5 \left (96 x^2-480 x\right )\right ) \log (2)+e^{10} (192 x-960)\right ) \log (x-5)+\log ^2(3) \left (3 x^5-3 x^4-60 x^3+\left (3 x^4-15 x^3\right ) \log (2)+e^5 \left (12 x^3-60 x^2\right )\right )+\left (3 x^5-3 x^4-60 x^3+e^5 \left (12 x^3-60 x^2\right )\right ) \log ^2(2)+\log (3) \left (3 x^6+9 x^5-72 x^4-240 x^3+e^{10} \left (48 x^2-240 x\right )+\left (3 x^4-15 x^3\right ) \log ^2(2)+e^5 \left (24 x^4-24 x^3-480 x^2\right )+\left (6 x^5-6 x^4-120 x^3+e^5 \left (24 x^3-120 x^2\right )\right ) \log (2)\right )+\left (3 x^6+9 x^5-72 x^4-240 x^3+e^{10} \left (48 x^2-240 x\right )+e^5 \left (24 x^4-24 x^3-480 x^2\right )\right ) \log (2)+e^{15} (64 x-320)+(64 x-320) \log ^3(x-5)}dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {32 x \left (x \left (x^2-5 x+4\right )-4 e^5 (x-5)-4 (x-5) \log (x-5)\right )}{(5-x) \left (x (x+4+\log (6))+4 \log (x-5)+4 e^5\right )^3}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 32 \int \frac {x \left (4 \log (x-5) (5-x)+4 e^5 (5-x)+x \left (x^2-5 x+4\right )\right )}{(5-x) \left (x (x+\log (6)+4)+4 \log (x-5)+4 e^5\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 32 \int \left (\frac {\left (2 x^2-(6-\log (6)) x-5 \log (6)-16\right ) x^2}{(5-x) \left (x^2+4 \left (1+\frac {\log (6)}{4}\right ) x+4 \log (x-5)+4 e^5\right )^3}+\frac {x}{\left (x^2+4 \left (1+\frac {\log (6)}{4}\right ) x+4 \log (x-5)+4 e^5\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 32 \left (20 \int \frac {1}{\left (-x^2-4 \left (1+\frac {\log (6)}{4}\right ) x-4 \log (x-5)-4 e^5\right )^3}dx+4 \int \frac {x}{\left (-x^2-4 \left (1+\frac {\log (6)}{4}\right ) x-4 \log (x-5)-4 e^5\right )^3}dx+100 \int \frac {1}{(5-x) \left (x^2+4 \left (1+\frac {\log (6)}{4}\right ) x+4 \log (x-5)+4 e^5\right )^3}dx-(4+\log (6)) \int \frac {x^2}{\left (x^2+4 \left (1+\frac {\log (6)}{4}\right ) x+4 \log (x-5)+4 e^5\right )^3}dx+\int \frac {x}{\left (x^2+4 \left (1+\frac {\log (6)}{4}\right ) x+4 \log (x-5)+4 e^5\right )^2}dx+2 \int \frac {x^3}{\left (-x^2-4 \left (1+\frac {\log (6)}{4}\right ) x-4 \log (x-5)-4 e^5\right )^3}dx\right )\)

Input:

Int[(-128*x^2 + 160*x^3 - 32*x^4 + E^5*(-640*x + 128*x^2) + (-640*x + 128* 
x^2)*Log[-5 + x])/(-320*x^3 - 176*x^4 - 12*x^5 + 7*x^6 + x^7 + E^15*(-320 
+ 64*x) + E^10*(-960*x - 48*x^2 + 48*x^3) + E^5*(-960*x^2 - 288*x^3 + 36*x 
^4 + 12*x^5) + (-240*x^3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) 
 + E^5*(-480*x^2 - 24*x^3 + 24*x^4))*Log[2] + (-60*x^3 - 3*x^4 + 3*x^5 + E 
^5*(-60*x^2 + 12*x^3))*Log[2]^2 + (-5*x^3 + x^4)*Log[2]^3 + (-240*x^3 - 72 
*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 + 2 
4*x^4) + (-120*x^3 - 6*x^4 + 6*x^5 + E^5*(-120*x^2 + 24*x^3))*Log[2] + (-1 
5*x^3 + 3*x^4)*Log[2]^2)*Log[3] + (-60*x^3 - 3*x^4 + 3*x^5 + E^5*(-60*x^2 
+ 12*x^3) + (-15*x^3 + 3*x^4)*Log[2])*Log[3]^2 + (-5*x^3 + x^4)*Log[3]^3 + 
 (-960*x^2 - 288*x^3 + 36*x^4 + 12*x^5 + E^10*(-960 + 192*x) + E^5*(-1920* 
x - 96*x^2 + 96*x^3) + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-480*x + 96*x^2) 
)*Log[2] + (-60*x^2 + 12*x^3)*Log[2]^2 + (-480*x^2 - 24*x^3 + 24*x^4 + E^5 
*(-480*x + 96*x^2) + (-120*x^2 + 24*x^3)*Log[2])*Log[3] + (-60*x^2 + 12*x^ 
3)*Log[3]^2)*Log[-5 + x] + (-960*x - 48*x^2 + 48*x^3 + E^5*(-960 + 192*x) 
+ (-240*x + 48*x^2)*Log[2] + (-240*x + 48*x^2)*Log[3])*Log[-5 + x]^2 + (-3 
20 + 64*x)*Log[-5 + x]^3),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 9.65 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.27

method	result	size
risch	\(\frac {16 x^{2}}{\left (x \ln \left (3\right )+x \ln \left (2\right )+x^{2}+4 \ln \left (-5+x \right )+4 \,{\mathrm e}^{5}+4 x \right )^{2}}\)	\(33\)
derivativedivides	\(\frac {-400+160 x +16 \left (-5+x \right )^{2}}{\left (\left (-5+x \right )^{2}+\left (-5+x \right ) \ln \left (3\right )+\left (-5+x \right ) \ln \left (2\right )-25+14 x +4 \,{\mathrm e}^{5}+5 \ln \left (3\right )+5 \ln \left (2\right )+4 \ln \left (-5+x \right )\right )^{2}}\)	\(57\)
default	\(\frac {-400+160 x +16 \left (-5+x \right )^{2}}{\left (\left (-5+x \right )^{2}+\left (-5+x \right ) \ln \left (3\right )+\left (-5+x \right ) \ln \left (2\right )-25+14 x +4 \,{\mathrm e}^{5}+5 \ln \left (3\right )+5 \ln \left (2\right )+4 \ln \left (-5+x \right )\right )^{2}}\)	\(57\)
parallelrisch	\(\frac {16 x^{2}}{x^{2} \ln \left (3\right )^{2}+2 \ln \left (3\right ) \ln \left (2\right ) x^{2}+2 x^{3} \ln \left (3\right )+x^{2} \ln \left (2\right )^{2}+2 x^{3} \ln \left (2\right )+x^{4}+8 x \,{\mathrm e}^{5} \ln \left (3\right )+8 x \,{\mathrm e}^{5} \ln \left (2\right )+8 x^{2} {\mathrm e}^{5}+8 x^{2} \ln \left (3\right )+8 \ln \left (-5+x \right ) x \ln \left (3\right )+8 x^{2} \ln \left (2\right )+8 \ln \left (-5+x \right ) x \ln \left (2\right )+8 x^{3}+8 \ln \left (-5+x \right ) x^{2}+16 \,{\mathrm e}^{10}+32 x \,{\mathrm e}^{5}+32 \ln \left (-5+x \right ) {\mathrm e}^{5}+16 x^{2}+32 \ln \left (-5+x \right ) x +16 \ln \left (-5+x \right )^{2}}\)	\(157\)

Input:

int(((128*x^2-640*x)*ln(-5+x)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^ 
2)/((64*x-320)*ln(-5+x)^3+((48*x^2-240*x)*ln(3)+(48*x^2-240*x)*ln(2)+(192* 
x-960)*exp(5)+48*x^3-48*x^2-960*x)*ln(-5+x)^2+((12*x^3-60*x^2)*ln(3)^2+((2 
4*x^3-120*x^2)*ln(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*ln(3)+(1 
2*x^3-60*x^2)*ln(2)^2+((96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*ln(2)+ 
(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5+36*x^4-288*x^3-9 
60*x^2)*ln(-5+x)+(x^4-5*x^3)*ln(3)^3+((3*x^4-15*x^3)*ln(2)+(12*x^3-60*x^2) 
*exp(5)+3*x^5-3*x^4-60*x^3)*ln(3)^2+((3*x^4-15*x^3)*ln(2)^2+((24*x^3-120*x 
^2)*exp(5)+6*x^5-6*x^4-120*x^3)*ln(2)+(48*x^2-240*x)*exp(5)^2+(24*x^4-24*x 
^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*ln(3)+(x^4-5*x^3)*ln(2)^3+( 
(12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*ln(2)^2+((48*x^2-240*x)*exp(5)^ 
2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*ln(2)+(64*x-3 
20)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2 
)*exp(5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x,method=_RETURNVERBOSE)
 

Output:

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

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 127 vs. \(2 (23) = 46\).

Time = 0.11 (sec) , antiderivative size = 127, normalized size of antiderivative = 4.88 \[ \int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx=\frac {16 \, x^{2}}{x^{4} + x^{2} \log \left (3\right )^{2} + x^{2} \log \left (2\right )^{2} + 8 \, x^{3} + 16 \, x^{2} + 8 \, {\left (x^{2} + 4 \, x\right )} e^{5} + 2 \, {\left (x^{3} + x^{2} \log \left (2\right ) + 4 \, x^{2} + 4 \, x e^{5}\right )} \log \left (3\right ) + 2 \, {\left (x^{3} + 4 \, x^{2} + 4 \, x e^{5}\right )} \log \left (2\right ) + 8 \, {\left (x^{2} + x \log \left (3\right ) + x \log \left (2\right ) + 4 \, x + 4 \, e^{5}\right )} \log \left (x - 5\right ) + 16 \, \log \left (x - 5\right )^{2} + 16 \, e^{10}} \] Input:

integrate(((128*x^2-640*x)*log(-5+x)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3 
-128*x^2)/((64*x-320)*log(-5+x)^3+((48*x^2-240*x)*log(3)+(48*x^2-240*x)*lo 
g(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(-5+x)^2+((12*x^3-60*x^2)* 
log(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480* 
x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+((96*x^2-480*x)*exp(5)+24*x^4-24*x^3- 
480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5+ 
36*x^4-288*x^3-960*x^2)*log(-5+x)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log 
(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*lo 
g(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*x) 
*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3 
)+(x^4-5*x^3)*log(2)^3+((12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^ 
2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x 
^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12* 
x^5+36*x^4-288*x^3-960*x^2)*exp(5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, al 
gorithm="fricas")
 

Output:

16*x^2/(x^4 + x^2*log(3)^2 + x^2*log(2)^2 + 8*x^3 + 16*x^2 + 8*(x^2 + 4*x) 
*e^5 + 2*(x^3 + x^2*log(2) + 4*x^2 + 4*x*e^5)*log(3) + 2*(x^3 + 4*x^2 + 4* 
x*e^5)*log(2) + 8*(x^2 + x*log(3) + x*log(2) + 4*x + 4*e^5)*log(x - 5) + 1 
6*log(x - 5)^2 + 16*e^10)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 162 vs. \(2 (27) = 54\).

Time = 0.33 (sec) , antiderivative size = 162, normalized size of antiderivative = 6.23 \[ \int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx=\frac {16 x^{2}}{x^{4} + 2 x^{3} \log {\left (2 \right )} + 2 x^{3} \log {\left (3 \right )} + 8 x^{3} + x^{2} \log {\left (2 \right )}^{2} + x^{2} \log {\left (3 \right )}^{2} + 2 x^{2} \log {\left (2 \right )} \log {\left (3 \right )} + 8 x^{2} \log {\left (2 \right )} + 8 x^{2} \log {\left (3 \right )} + 16 x^{2} + 8 x^{2} e^{5} + 8 x e^{5} \log {\left (2 \right )} + 8 x e^{5} \log {\left (3 \right )} + 32 x e^{5} + \left (8 x^{2} + 8 x \log {\left (2 \right )} + 8 x \log {\left (3 \right )} + 32 x + 32 e^{5}\right ) \log {\left (x - 5 \right )} + 16 \log {\left (x - 5 \right )}^{2} + 16 e^{10}} \] Input:

integrate(((128*x**2-640*x)*ln(-5+x)+(128*x**2-640*x)*exp(5)-32*x**4+160*x 
**3-128*x**2)/((64*x-320)*ln(-5+x)**3+((48*x**2-240*x)*ln(3)+(48*x**2-240* 
x)*ln(2)+(192*x-960)*exp(5)+48*x**3-48*x**2-960*x)*ln(-5+x)**2+((12*x**3-6 
0*x**2)*ln(3)**2+((24*x**3-120*x**2)*ln(2)+(96*x**2-480*x)*exp(5)+24*x**4- 
24*x**3-480*x**2)*ln(3)+(12*x**3-60*x**2)*ln(2)**2+((96*x**2-480*x)*exp(5) 
+24*x**4-24*x**3-480*x**2)*ln(2)+(192*x-960)*exp(5)**2+(96*x**3-96*x**2-19 
20*x)*exp(5)+12*x**5+36*x**4-288*x**3-960*x**2)*ln(-5+x)+(x**4-5*x**3)*ln( 
3)**3+((3*x**4-15*x**3)*ln(2)+(12*x**3-60*x**2)*exp(5)+3*x**5-3*x**4-60*x* 
*3)*ln(3)**2+((3*x**4-15*x**3)*ln(2)**2+((24*x**3-120*x**2)*exp(5)+6*x**5- 
6*x**4-120*x**3)*ln(2)+(48*x**2-240*x)*exp(5)**2+(24*x**4-24*x**3-480*x**2 
)*exp(5)+3*x**6+9*x**5-72*x**4-240*x**3)*ln(3)+(x**4-5*x**3)*ln(2)**3+((12 
*x**3-60*x**2)*exp(5)+3*x**5-3*x**4-60*x**3)*ln(2)**2+((48*x**2-240*x)*exp 
(5)**2+(24*x**4-24*x**3-480*x**2)*exp(5)+3*x**6+9*x**5-72*x**4-240*x**3)*l 
n(2)+(64*x-320)*exp(5)**3+(48*x**3-48*x**2-960*x)*exp(5)**2+(12*x**5+36*x* 
*4-288*x**3-960*x**2)*exp(5)+x**7+7*x**6-12*x**5-176*x**4-320*x**3),x)
 

Output:

16*x**2/(x**4 + 2*x**3*log(2) + 2*x**3*log(3) + 8*x**3 + x**2*log(2)**2 + 
x**2*log(3)**2 + 2*x**2*log(2)*log(3) + 8*x**2*log(2) + 8*x**2*log(3) + 16 
*x**2 + 8*x**2*exp(5) + 8*x*exp(5)*log(2) + 8*x*exp(5)*log(3) + 32*x*exp(5 
) + (8*x**2 + 8*x*log(2) + 8*x*log(3) + 32*x + 32*exp(5))*log(x - 5) + 16* 
log(x - 5)**2 + 16*exp(10))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 97 vs. \(2 (23) = 46\).

Time = 0.25 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.73 \[ \int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx=\frac {16 \, x^{2}}{x^{4} + 2 \, x^{3} {\left (\log \left (3\right ) + \log \left (2\right ) + 4\right )} + {\left (\log \left (3\right )^{2} + 2 \, {\left (\log \left (3\right ) + 4\right )} \log \left (2\right ) + \log \left (2\right )^{2} + 8 \, e^{5} + 8 \, \log \left (3\right ) + 16\right )} x^{2} + 8 \, x {\left (\log \left (3\right ) + \log \left (2\right ) + 4\right )} e^{5} + 8 \, {\left (x^{2} + x {\left (\log \left (3\right ) + \log \left (2\right ) + 4\right )} + 4 \, e^{5}\right )} \log \left (x - 5\right ) + 16 \, \log \left (x - 5\right )^{2} + 16 \, e^{10}} \] Input:

integrate(((128*x^2-640*x)*log(-5+x)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3 
-128*x^2)/((64*x-320)*log(-5+x)^3+((48*x^2-240*x)*log(3)+(48*x^2-240*x)*lo 
g(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(-5+x)^2+((12*x^3-60*x^2)* 
log(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480* 
x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+((96*x^2-480*x)*exp(5)+24*x^4-24*x^3- 
480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5+ 
36*x^4-288*x^3-960*x^2)*log(-5+x)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log 
(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*lo 
g(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*x) 
*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3 
)+(x^4-5*x^3)*log(2)^3+((12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^ 
2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x 
^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12* 
x^5+36*x^4-288*x^3-960*x^2)*exp(5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, al 
gorithm="maxima")
 

Output:

16*x^2/(x^4 + 2*x^3*(log(3) + log(2) + 4) + (log(3)^2 + 2*(log(3) + 4)*log 
(2) + log(2)^2 + 8*e^5 + 8*log(3) + 16)*x^2 + 8*x*(log(3) + log(2) + 4)*e^ 
5 + 8*(x^2 + x*(log(3) + log(2) + 4) + 4*e^5)*log(x - 5) + 16*log(x - 5)^2 
 + 16*e^10)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 154 vs. \(2 (23) = 46\).

Time = 0.28 (sec) , antiderivative size = 154, normalized size of antiderivative = 5.92 \[ \int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx=\frac {16 \, x^{2}}{x^{4} + 2 \, x^{3} \log \left (3\right ) + x^{2} \log \left (3\right )^{2} + 2 \, x^{3} \log \left (2\right ) + 2 \, x^{2} \log \left (3\right ) \log \left (2\right ) + x^{2} \log \left (2\right )^{2} + 8 \, x^{3} + 8 \, x^{2} e^{5} + 8 \, x^{2} \log \left (3\right ) + 8 \, x e^{5} \log \left (3\right ) + 8 \, x^{2} \log \left (2\right ) + 8 \, x e^{5} \log \left (2\right ) + 8 \, x^{2} \log \left (x - 5\right ) + 8 \, x \log \left (3\right ) \log \left (x - 5\right ) + 8 \, x \log \left (2\right ) \log \left (x - 5\right ) + 16 \, x^{2} + 32 \, x e^{5} + 32 \, x \log \left (x - 5\right ) + 32 \, e^{5} \log \left (x - 5\right ) + 16 \, \log \left (x - 5\right )^{2} + 16 \, e^{10}} \] Input:

integrate(((128*x^2-640*x)*log(-5+x)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3 
-128*x^2)/((64*x-320)*log(-5+x)^3+((48*x^2-240*x)*log(3)+(48*x^2-240*x)*lo 
g(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(-5+x)^2+((12*x^3-60*x^2)* 
log(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480* 
x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+((96*x^2-480*x)*exp(5)+24*x^4-24*x^3- 
480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5+ 
36*x^4-288*x^3-960*x^2)*log(-5+x)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log 
(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*lo 
g(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*x) 
*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3 
)+(x^4-5*x^3)*log(2)^3+((12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^ 
2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x 
^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12* 
x^5+36*x^4-288*x^3-960*x^2)*exp(5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, al 
gorithm="giac")
 

Output:

16*x^2/(x^4 + 2*x^3*log(3) + x^2*log(3)^2 + 2*x^3*log(2) + 2*x^2*log(3)*lo 
g(2) + x^2*log(2)^2 + 8*x^3 + 8*x^2*e^5 + 8*x^2*log(3) + 8*x*e^5*log(3) + 
8*x^2*log(2) + 8*x*e^5*log(2) + 8*x^2*log(x - 5) + 8*x*log(3)*log(x - 5) + 
 8*x*log(2)*log(x - 5) + 16*x^2 + 32*x*e^5 + 32*x*log(x - 5) + 32*e^5*log( 
x - 5) + 16*log(x - 5)^2 + 16*e^10)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx=\text {Hanged} \] Input:

int((log(x - 5)*(640*x - 128*x^2) + exp(5)*(640*x - 128*x^2) + 128*x^2 - 1 
60*x^3 + 32*x^4)/(log(2)*(exp(10)*(240*x - 48*x^2) + exp(5)*(480*x^2 + 24* 
x^3 - 24*x^4) + 240*x^3 + 72*x^4 - 9*x^5 - 3*x^6) + log(x - 5)^2*(960*x + 
log(2)*(240*x - 48*x^2) + log(3)*(240*x - 48*x^2) + 48*x^2 - 48*x^3 - exp( 
5)*(192*x - 960)) - log(x - 5)^3*(64*x - 320) + log(3)^2*(exp(5)*(60*x^2 - 
 12*x^3) + log(2)*(15*x^3 - 3*x^4) + 60*x^3 + 3*x^4 - 3*x^5) + log(3)*(exp 
(10)*(240*x - 48*x^2) + log(2)*(exp(5)*(120*x^2 - 24*x^3) + 120*x^3 + 6*x^ 
4 - 6*x^5) + exp(5)*(480*x^2 + 24*x^3 - 24*x^4) + 240*x^3 + 72*x^4 - 9*x^5 
 - 3*x^6 + log(2)^2*(15*x^3 - 3*x^4)) + exp(10)*(960*x + 48*x^2 - 48*x^3) 
+ log(2)^2*(exp(5)*(60*x^2 - 12*x^3) + 60*x^3 + 3*x^4 - 3*x^5) + log(x - 5 
)*(log(2)*(exp(5)*(480*x - 96*x^2) + 480*x^2 + 24*x^3 - 24*x^4) + exp(5)*( 
1920*x + 96*x^2 - 96*x^3) + log(3)*(exp(5)*(480*x - 96*x^2) + log(2)*(120* 
x^2 - 24*x^3) + 480*x^2 + 24*x^3 - 24*x^4) + 960*x^2 + 288*x^3 - 36*x^4 - 
12*x^5 + log(2)^2*(60*x^2 - 12*x^3) + log(3)^2*(60*x^2 - 12*x^3) - exp(10) 
*(192*x - 960)) + 320*x^3 + 176*x^4 + 12*x^5 - 7*x^6 - x^7 + log(2)^3*(5*x 
^3 - x^4) + log(3)^3*(5*x^3 - x^4) - exp(15)*(64*x - 320) + exp(5)*(960*x^ 
2 + 288*x^3 - 36*x^4 - 12*x^5)),x)
 

Output:

\text{Hanged}
 

Reduce [B] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 1028, normalized size of antiderivative = 39.54 \[ \int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx =\text {Too large to display} \] Input:

int(((128*x^2-640*x)*log(-5+x)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x 
^2)/((64*x-320)*log(-5+x)^3+((48*x^2-240*x)*log(3)+(48*x^2-240*x)*log(2)+( 
192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(-5+x)^2+((12*x^3-60*x^2)*log(3) 
^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*l 
og(3)+(12*x^3-60*x^2)*log(2)^2+((96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^ 
2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5+36*x^4 
-288*x^3-960*x^2)*log(-5+x)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log(2)+(1 
2*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*log(2)^2 
+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*x)*exp(5 
)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3)+(x^4 
-5*x^3)*log(2)^3+((12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^2+((48 
*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240 
*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36 
*x^4-288*x^3-960*x^2)*exp(5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x)
 

Output:

(16*( - 16*log(x - 5)**2 - 8*log(x - 5)*log(3)*x - 8*log(x - 5)*log(2)*x - 
 32*log(x - 5)*e**5 - 8*log(x - 5)*x**2 - 32*log(x - 5)*x - 8*log(3)*e**5* 
x - 2*log(3)*x**3 - 8*log(2)*e**5*x - 2*log(2)*x**3 - 16*e**10 - 32*e**5*x 
 - x**4 - 8*x**3))/(16*log(x - 5)**2*log(3)**2 + 32*log(x - 5)**2*log(3)*l 
og(2) + 128*log(x - 5)**2*log(3) + 16*log(x - 5)**2*log(2)**2 + 128*log(x 
- 5)**2*log(2) + 128*log(x - 5)**2*e**5 + 256*log(x - 5)**2 + 8*log(x - 5) 
*log(3)**3*x + 24*log(x - 5)*log(3)**2*log(2)*x + 32*log(x - 5)*log(3)**2* 
e**5 + 8*log(x - 5)*log(3)**2*x**2 + 96*log(x - 5)*log(3)**2*x + 24*log(x 
- 5)*log(3)*log(2)**2*x + 64*log(x - 5)*log(3)*log(2)*e**5 + 16*log(x - 5) 
*log(3)*log(2)*x**2 + 192*log(x - 5)*log(3)*log(2)*x + 64*log(x - 5)*log(3 
)*e**5*x + 256*log(x - 5)*log(3)*e**5 + 64*log(x - 5)*log(3)*x**2 + 384*lo 
g(x - 5)*log(3)*x + 8*log(x - 5)*log(2)**3*x + 32*log(x - 5)*log(2)**2*e** 
5 + 8*log(x - 5)*log(2)**2*x**2 + 96*log(x - 5)*log(2)**2*x + 64*log(x - 5 
)*log(2)*e**5*x + 256*log(x - 5)*log(2)*e**5 + 64*log(x - 5)*log(2)*x**2 + 
 384*log(x - 5)*log(2)*x + 256*log(x - 5)*e**10 + 64*log(x - 5)*e**5*x**2 
+ 256*log(x - 5)*e**5*x + 512*log(x - 5)*e**5 + 128*log(x - 5)*x**2 + 512* 
log(x - 5)*x + log(3)**4*x**2 + 4*log(3)**3*log(2)*x**2 + 8*log(3)**3*e**5 
*x + 2*log(3)**3*x**3 + 16*log(3)**3*x**2 + 6*log(3)**2*log(2)**2*x**2 + 2 
4*log(3)**2*log(2)*e**5*x + 6*log(3)**2*log(2)*x**3 + 48*log(3)**2*log(2)* 
x**2 + 16*log(3)**2*e**10 + 16*log(3)**2*e**5*x**2 + 96*log(3)**2*e**5*...