\(\int (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} (-72-132 x-60 x^2)+e^5 (52+144 x+132 x^2+40 x^3)+(-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} (-10+50 x^2)+e^{15} (40+80 x-200 x^2-200 x^3)+e^{10} (-60-240 x+120 x^2+600 x^3+300 x^4)+e^5 (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5)) \log (x)+(75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} (-300 x^2-400 x^3)+e^{10} (450 x^2+1200 x^3+750 x^4)+e^5 (-300 x^2-1200 x^3-1500 x^4-600 x^5)) \log ^2(x)) \, dx\) [420]

Optimal result

Integrand size = 282, antiderivative size = 30 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=\frac {\left (-1+e^5-x\right )^4 \left (-1-x+\left (-1+5 x^2 \log (x)\right )^2\right )}{x} \] Output:

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

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(76\) vs. \(2(30)=60\).

Time = 0.27 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.53 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=x \left (-4+4 e^{15}-6 x-4 x^2-x^3-6 e^{10} (2+x)+4 e^5 \left (3+3 x+x^2\right )-10 \left (1-e^5+x\right )^4 \log (x)+25 x^2 \left (1-e^5+x\right )^4 \log ^2(x)\right ) \] Input:

Integrate[-14 - 10*E^20 - 52*x - 72*x^2 - 44*x^3 - 10*x^4 + E^15*(44 + 40* 
x) + E^10*(-72 - 132*x - 60*x^2) + E^5*(52 + 144*x + 132*x^2 + 40*x^3) + ( 
-10 - 80*x - 130*x^2 + 40*x^3 + 250*x^4 + 200*x^5 + 50*x^6 + E^20*(-10 + 5 
0*x^2) + E^15*(40 + 80*x - 200*x^2 - 200*x^3) + E^10*(-60 - 240*x + 120*x^ 
2 + 600*x^3 + 300*x^4) + E^5*(40 + 240*x + 160*x^2 - 440*x^3 - 600*x^4 - 2 
00*x^5))*Log[x] + (75*x^2 + 75*E^20*x^2 + 400*x^3 + 750*x^4 + 600*x^5 + 17 
5*x^6 + E^15*(-300*x^2 - 400*x^3) + E^10*(450*x^2 + 1200*x^3 + 750*x^4) + 
E^5*(-300*x^2 - 1200*x^3 - 1500*x^4 - 600*x^5))*Log[x]^2,x]
 

Output:

x*(-4 + 4*E^15 - 6*x - 4*x^2 - x^3 - 6*E^10*(2 + x) + 4*E^5*(3 + 3*x + x^2 
) - 10*(1 - E^5 + x)^4*Log[x] + 25*x^2*(1 - E^5 + x)^4*Log[x]^2)
 

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(470\) vs. \(2(30)=60\).

Time = 0.83 (sec) , antiderivative size = 470, normalized size of antiderivative = 15.67, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.004, Rules used = {2009}

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.

\(\displaystyle \int \left (-10 x^4-44 x^3-72 x^2+e^{10} \left (-60 x^2-132 x-72\right )+e^5 \left (40 x^3+132 x^2+144 x+52\right )+\left (175 x^6+600 x^5+750 x^4+400 x^3+75 e^{20} x^2+75 x^2+e^{15} \left (-400 x^3-300 x^2\right )+e^{10} \left (750 x^4+1200 x^3+450 x^2\right )+e^5 \left (-600 x^5-1500 x^4-1200 x^3-300 x^2\right )\right ) \log ^2(x)+\left (50 x^6+200 x^5+250 x^4+40 x^3-130 x^2+e^{20} \left (50 x^2-10\right )+e^{15} \left (-200 x^3-200 x^2+80 x+40\right )+e^{10} \left (300 x^4+600 x^3+120 x^2-240 x-60\right )+e^5 \left (-200 x^5-600 x^4-440 x^3+160 x^2+240 x+40\right )-80 x-10\right ) \log (x)-52 x+e^{15} (40 x+44)-10 e^{20}-14\right ) \, dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 25 x^7 \log ^2(x)+100 \left (1-e^5\right ) x^6 \log ^2(x)-2 \left (5-12 e^5+6 e^{10}\right ) x^5+12 \left (1-e^5\right )^2 x^5-2 x^5+150 \left (1-e^5\right )^2 x^5 \log ^2(x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)-60 \left (1-e^5\right )^2 x^5 \log (x)-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4+\frac {25}{2} \left (1-e^5\right )^3 x^4+10 e^5 x^4-11 x^4+100 \left (1-e^5\right )^3 x^4 \log ^2(x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)-50 \left (1-e^5\right )^3 x^4 \log (x)+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3+\frac {50}{9} \left (1-e^5\right )^4 x^3-20 e^{10} x^3+44 e^5 x^3-24 x^3+25 \left (1-e^5\right )^4 x^3 \log ^2(x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)-\frac {50}{3} \left (1-e^5\right )^4 x^3 \log (x)+20 \left (1-e^5\right )^3 x^2-66 e^{10} x^2+72 e^5 x^2-26 x^2-40 \left (1-e^5\right )^3 x^2 \log (x)-2 \left (7+5 e^{20}\right ) x+10 \left (1-e^5\right )^4 x-72 e^{10} x+52 e^5 x+\frac {1}{5} e^{15} (10 x+11)^2-10 \left (1-e^5\right )^4 x \log (x)\)

Input:

Int[-14 - 10*E^20 - 52*x - 72*x^2 - 44*x^3 - 10*x^4 + E^15*(44 + 40*x) + E 
^10*(-72 - 132*x - 60*x^2) + E^5*(52 + 144*x + 132*x^2 + 40*x^3) + (-10 - 
80*x - 130*x^2 + 40*x^3 + 250*x^4 + 200*x^5 + 50*x^6 + E^20*(-10 + 50*x^2) 
 + E^15*(40 + 80*x - 200*x^2 - 200*x^3) + E^10*(-60 - 240*x + 120*x^2 + 60 
0*x^3 + 300*x^4) + E^5*(40 + 240*x + 160*x^2 - 440*x^3 - 600*x^4 - 200*x^5 
))*Log[x] + (75*x^2 + 75*E^20*x^2 + 400*x^3 + 750*x^4 + 600*x^5 + 175*x^6 
+ E^15*(-300*x^2 - 400*x^3) + E^10*(450*x^2 + 1200*x^3 + 750*x^4) + E^5*(- 
300*x^2 - 1200*x^3 - 1500*x^4 - 600*x^5))*Log[x]^2,x]
 

Output:

52*E^5*x - 72*E^10*x + 10*(1 - E^5)^4*x - 2*(7 + 5*E^20)*x - 26*x^2 + 72*E 
^5*x^2 - 66*E^10*x^2 + 20*(1 - E^5)^3*x^2 - 24*x^3 + 44*E^5*x^3 - 20*E^10* 
x^3 + (50*(1 - E^5)^4*x^3)/9 + (10*(1 - E^5)^2*(13 + 10*E^5 - 5*E^10)*x^3) 
/9 - 11*x^4 + 10*E^5*x^4 + (25*(1 - E^5)^3*x^4)/2 - (5*(1 - 11*E^5 + 15*E^ 
10 - 5*E^15)*x^4)/2 - 2*x^5 + 12*(1 - E^5)^2*x^5 - 2*(5 - 12*E^5 + 6*E^10) 
*x^5 + (E^15*(11 + 10*x)^2)/5 - 10*(1 - E^5)^4*x*Log[x] - 40*(1 - E^5)^3*x 
^2*Log[x] - (50*(1 - E^5)^4*x^3*Log[x])/3 - (10*(1 - E^5)^2*(13 + 10*E^5 - 
 5*E^10)*x^3*Log[x])/3 - 50*(1 - E^5)^3*x^4*Log[x] + 10*(1 - 11*E^5 + 15*E 
^10 - 5*E^15)*x^4*Log[x] - 60*(1 - E^5)^2*x^5*Log[x] + 10*(5 - 12*E^5 + 6* 
E^10)*x^5*Log[x] + 25*(1 - E^5)^4*x^3*Log[x]^2 + 100*(1 - E^5)^3*x^4*Log[x 
]^2 + 150*(1 - E^5)^2*x^5*Log[x]^2 + 100*(1 - E^5)*x^6*Log[x]^2 + 25*x^7*L 
og[x]^2
 

Defintions of rubi rules used

rule 2009

Int[u_, x_Symbol] :> Simp[IntSum[u, x], x] /; SumQ[u]
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(355\) vs. \(2(29)=58\).

Time = 0.02 (sec) , antiderivative size = 356, normalized size of antiderivative = 11.87

\[-4 x +40 \,{\mathrm e}^{15} \ln \left (x \right ) x^{2}-60 \,{\mathrm e}^{10} \ln \left (x \right ) x^{3}-12 \,{\mathrm e}^{10} x +120 x^{2} {\mathrm e}^{5} \ln \left (x \right )+100 x^{6} \ln \left (x \right )^{2}-40 x^{4} \ln \left (x \right )+100 x^{4} \ln \left (x \right )^{2}+150 x^{5} \ln \left (x \right )^{2}+25 x^{7} \ln \left (x \right )^{2}+25 x^{3} \ln \left (x \right )^{2}-60 x^{3} \ln \left (x \right )+4 x^{3} {\mathrm e}^{5}+12 x \,{\mathrm e}^{5}-6 \,{\mathrm e}^{10} x^{2}-10 x^{5} \ln \left (x \right )+12 x^{2} {\mathrm e}^{5}+40 \,{\mathrm e}^{15} \ln \left (x \right ) x -120 \,{\mathrm e}^{10} \ln \left (x \right ) x^{2}-40 x^{2} \ln \left (x \right )-10 x \ln \left (x \right )-6 x^{2}-4 x^{3}-x^{4}+4 x \,{\mathrm e}^{15}-300 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{5}-300 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{4}+40 \,{\mathrm e}^{5} \ln \left (x \right ) x^{4}+120 \,{\mathrm e}^{5} \ln \left (x \right ) x^{3}-100 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{3}+40 \,{\mathrm e}^{5} \ln \left (x \right ) x +300 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{4}+150 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{3}-100 \,{\mathrm e}^{15} \ln \left (x \right )^{2} x^{3}-100 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{6}-60 x \ln \left (x \right ) {\mathrm e}^{10}+150 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{5}-10 \ln \left (x \right ) x \,{\mathrm e}^{20}+25 \,{\mathrm e}^{20} \ln \left (x \right )^{2} x^{3}-100 \,{\mathrm e}^{15} \ln \left (x \right )^{2} x^{4}\]

Input:

int((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+450*x^2 
)*exp(5)^2+(-600*x^5-1500*x^4-1200*x^3-300*x^2)*exp(5)+175*x^6+600*x^5+750 
*x^4+400*x^3+75*x^2)*ln(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*x^2+80*x+ 
40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5-600*x^4 
-440*x^3+160*x^2+240*x+40)*exp(5)+50*x^6+200*x^5+250*x^4+40*x^3-130*x^2-80 
*x-10)*ln(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)*exp(5)^2+(4 
0*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x)
 

Output:

-4*x+4*x*exp(5)^3+120*x^2*exp(5)*ln(x)+100*x^6*ln(x)^2-40*x^4*ln(x)+100*x^ 
4*ln(x)^2+150*x^5*ln(x)^2+25*x^7*ln(x)^2+25*x^3*ln(x)^2-60*x^3*ln(x)+4*x^3 
*exp(5)+12*x*exp(5)-12*x*exp(5)^2-10*x^5*ln(x)+12*x^2*exp(5)-6*x^2*exp(5)^ 
2-40*x^2*ln(x)-10*x*ln(x)-6*x^2-4*x^3-x^4-60*exp(5)^2*ln(x)*x-100*exp(5)^3 
*ln(x)^2*x^3+300*exp(5)^2*ln(x)^2*x^4-300*exp(5)*ln(x)^2*x^5+150*exp(5)^2* 
ln(x)^2*x^3-300*exp(5)*ln(x)^2*x^4+40*exp(5)^3*ln(x)*x^2-60*exp(5)^2*ln(x) 
*x^3+40*exp(5)*ln(x)*x^4+40*exp(5)^3*ln(x)*x-120*exp(5)^2*ln(x)*x^2+120*ex 
p(5)*ln(x)*x^3-100*exp(5)*ln(x)^2*x^3+40*exp(5)*ln(x)*x+150*exp(5)^2*ln(x) 
^2*x^5-100*exp(5)*ln(x)^2*x^6-10*ln(x)*x*exp(5)^4+25*exp(5)^4*ln(x)^2*x^3- 
100*exp(5)^3*ln(x)^2*x^4
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 203 vs. \(2 (29) = 58\).

Time = 0.09 (sec) , antiderivative size = 203, normalized size of antiderivative = 6.77 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=-x^{4} - 4 \, x^{3} + 25 \, {\left (x^{7} + 4 \, x^{6} + 6 \, x^{5} + 4 \, x^{4} + x^{3} e^{20} + x^{3} - 4 \, {\left (x^{4} + x^{3}\right )} e^{15} + 6 \, {\left (x^{5} + 2 \, x^{4} + x^{3}\right )} e^{10} - 4 \, {\left (x^{6} + 3 \, x^{5} + 3 \, x^{4} + x^{3}\right )} e^{5}\right )} \log \left (x\right )^{2} - 6 \, x^{2} + 4 \, x e^{15} - 6 \, {\left (x^{2} + 2 \, x\right )} e^{10} + 4 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x\right )} e^{5} - 10 \, {\left (x^{5} + 4 \, x^{4} + 6 \, x^{3} + 4 \, x^{2} + x e^{20} - 4 \, {\left (x^{2} + x\right )} e^{15} + 6 \, {\left (x^{3} + 2 \, x^{2} + x\right )} e^{10} - 4 \, {\left (x^{4} + 3 \, x^{3} + 3 \, x^{2} + x\right )} e^{5} + x\right )} \log \left (x\right ) - 4 \, x \] Input:

integrate((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+4 
50*x^2)*exp(5)^2+(-600*x^5-1500*x^4-1200*x^3-300*x^2)*exp(5)+175*x^6+600*x 
^5+750*x^4+400*x^3+75*x^2)*log(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*x^ 
2+80*x+40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5- 
600*x^4-440*x^3+160*x^2+240*x+40)*exp(5)+50*x^6+200*x^5+250*x^4+40*x^3-130 
*x^2-80*x-10)*log(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)*exp 
(5)^2+(40*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x, alg 
orithm="fricas")
 

Output:

-x^4 - 4*x^3 + 25*(x^7 + 4*x^6 + 6*x^5 + 4*x^4 + x^3*e^20 + x^3 - 4*(x^4 + 
 x^3)*e^15 + 6*(x^5 + 2*x^4 + x^3)*e^10 - 4*(x^6 + 3*x^5 + 3*x^4 + x^3)*e^ 
5)*log(x)^2 - 6*x^2 + 4*x*e^15 - 6*(x^2 + 2*x)*e^10 + 4*(x^3 + 3*x^2 + 3*x 
)*e^5 - 10*(x^5 + 4*x^4 + 6*x^3 + 4*x^2 + x*e^20 - 4*(x^2 + x)*e^15 + 6*(x 
^3 + 2*x^2 + x)*e^10 - 4*(x^4 + 3*x^3 + 3*x^2 + x)*e^5 + x)*log(x) - 4*x
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 267 vs. \(2 (24) = 48\).

Time = 0.37 (sec) , antiderivative size = 267, normalized size of antiderivative = 8.90 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=- x^{4} + x^{3} \left (-4 + 4 e^{5}\right ) + x^{2} \left (- 6 e^{10} - 6 + 12 e^{5}\right ) + x \left (- 12 e^{10} - 4 + 12 e^{5} + 4 e^{15}\right ) + \left (- 10 x^{5} - 40 x^{4} + 40 x^{4} e^{5} - 60 x^{3} e^{10} - 60 x^{3} + 120 x^{3} e^{5} - 120 x^{2} e^{10} - 40 x^{2} + 120 x^{2} e^{5} + 40 x^{2} e^{15} - 10 x e^{20} - 60 x e^{10} - 10 x + 40 x e^{5} + 40 x e^{15}\right ) \log {\left (x \right )} + \left (25 x^{7} - 100 x^{6} e^{5} + 100 x^{6} - 300 x^{5} e^{5} + 150 x^{5} + 150 x^{5} e^{10} - 100 x^{4} e^{15} - 300 x^{4} e^{5} + 100 x^{4} + 300 x^{4} e^{10} - 100 x^{3} e^{15} - 100 x^{3} e^{5} + 25 x^{3} + 150 x^{3} e^{10} + 25 x^{3} e^{20}\right ) \log {\left (x \right )}^{2} \] Input:

integrate((75*x**2*exp(5)**4+(-400*x**3-300*x**2)*exp(5)**3+(750*x**4+1200 
*x**3+450*x**2)*exp(5)**2+(-600*x**5-1500*x**4-1200*x**3-300*x**2)*exp(5)+ 
175*x**6+600*x**5+750*x**4+400*x**3+75*x**2)*ln(x)**2+((50*x**2-10)*exp(5) 
**4+(-200*x**3-200*x**2+80*x+40)*exp(5)**3+(300*x**4+600*x**3+120*x**2-240 
*x-60)*exp(5)**2+(-200*x**5-600*x**4-440*x**3+160*x**2+240*x+40)*exp(5)+50 
*x**6+200*x**5+250*x**4+40*x**3-130*x**2-80*x-10)*ln(x)-10*exp(5)**4+(40*x 
+44)*exp(5)**3+(-60*x**2-132*x-72)*exp(5)**2+(40*x**3+132*x**2+144*x+52)*e 
xp(5)-10*x**4-44*x**3-72*x**2-52*x-14,x)
 

Output:

-x**4 + x**3*(-4 + 4*exp(5)) + x**2*(-6*exp(10) - 6 + 12*exp(5)) + x*(-12* 
exp(10) - 4 + 12*exp(5) + 4*exp(15)) + (-10*x**5 - 40*x**4 + 40*x**4*exp(5 
) - 60*x**3*exp(10) - 60*x**3 + 120*x**3*exp(5) - 120*x**2*exp(10) - 40*x* 
*2 + 120*x**2*exp(5) + 40*x**2*exp(15) - 10*x*exp(20) - 60*x*exp(10) - 10* 
x + 40*x*exp(5) + 40*x*exp(15))*log(x) + (25*x**7 - 100*x**6*exp(5) + 100* 
x**6 - 300*x**5*exp(5) + 150*x**5 + 150*x**5*exp(10) - 100*x**4*exp(15) - 
300*x**4*exp(5) + 100*x**4 + 300*x**4*exp(10) - 100*x**3*exp(15) - 100*x** 
3*exp(5) + 25*x**3 + 150*x**3*exp(10) + 25*x**3*exp(20))*log(x)**2
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 526 vs. \(2 (29) = 58\).

Time = 0.04 (sec) , antiderivative size = 526, normalized size of antiderivative = 17.53 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx =\text {Too large to display} \] Input:

integrate((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+4 
50*x^2)*exp(5)^2+(-600*x^5-1500*x^4-1200*x^3-300*x^2)*exp(5)+175*x^6+600*x 
^5+750*x^4+400*x^3+75*x^2)*log(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*x^ 
2+80*x+40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5- 
600*x^4-440*x^3+160*x^2+240*x+40)*exp(5)+50*x^6+200*x^5+250*x^4+40*x^3-130 
*x^2-80*x-10)*log(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)*exp 
(5)^2+(40*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x, alg 
orithm="maxima")
 

Output:

25/49*(49*log(x)^2 - 14*log(x) + 2)*x^7 - 50/9*(18*(e^5 - 1)*log(x)^2 - 6* 
(e^5 - 1)*log(x) + e^5 - 1)*x^6 - 50/49*x^7 + 50/9*x^6*(e^5 - 1) + 6*(25*( 
e^10 - 2*e^5 + 1)*log(x)^2 - 10*(e^10 - 2*e^5 + 1)*log(x) + 2*e^10 - 4*e^5 
 + 2)*x^5 - 2*x^5*(6*e^10 - 12*e^5 + 5) - 25/2*(8*(e^15 - 3*e^10 + 3*e^5 - 
 1)*log(x)^2 - 4*(e^15 - 3*e^10 + 3*e^5 - 1)*log(x) + e^15 - 3*e^10 + 3*e^ 
5 - 1)*x^4 - 2*x^5 + 5/2*x^4*(5*e^15 - 15*e^10 + 11*e^5 - 1) + 25/9*(9*(e^ 
20 - 4*e^15 + 6*e^10 - 4*e^5 + 1)*log(x)^2 - 6*(e^20 - 4*e^15 + 6*e^10 - 4 
*e^5 + 1)*log(x) + 2*e^20 - 8*e^15 + 12*e^10 - 8*e^5 + 2)*x^3 - 11*x^4 - 1 
0/9*x^3*(5*e^20 - 20*e^15 + 12*e^10 + 16*e^5 - 13) - 24*x^3 - 20*x^2*(e^15 
 - 3*e^10 + 3*e^5 - 1) - 26*x^2 + 10*x*(e^20 - 4*e^15 + 6*e^10 - 4*e^5 + 1 
) - 10*x*e^20 + 4*(5*x^2 + 11*x)*e^15 - 2*(10*x^3 + 33*x^2 + 36*x)*e^10 + 
2*(5*x^4 + 22*x^3 + 36*x^2 + 26*x)*e^5 + 10/21*(15*x^7 + 70*x^6 + 105*x^5 
+ 21*x^4 - 91*x^3 - 84*x^2 + 7*(5*x^3 - 3*x)*e^20 - 7*(15*x^4 + 20*x^3 - 1 
2*x^2 - 12*x)*e^15 + 21*(6*x^5 + 15*x^4 + 4*x^3 - 12*x^2 - 6*x)*e^10 - 7*( 
10*x^6 + 36*x^5 + 33*x^4 - 16*x^3 - 36*x^2 - 12*x)*e^5 - 21*x)*log(x) - 14 
*x
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 400 vs. \(2 (29) = 58\).

Time = 0.13 (sec) , antiderivative size = 400, normalized size of antiderivative = 13.33 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=25 \, x^{7} \log \left (x\right )^{2} - 100 \, x^{6} e^{5} \log \left (x\right )^{2} + 100 \, x^{6} \log \left (x\right )^{2} + 150 \, x^{5} e^{10} \log \left (x\right )^{2} - 300 \, x^{5} e^{5} \log \left (x\right )^{2} + 150 \, x^{5} \log \left (x\right )^{2} - 100 \, x^{4} e^{15} \log \left (x\right )^{2} + 300 \, x^{4} e^{10} \log \left (x\right )^{2} - 300 \, x^{4} e^{5} \log \left (x\right )^{2} - 10 \, x^{5} \log \left (x\right ) + 40 \, x^{4} e^{5} \log \left (x\right ) + 100 \, x^{4} \log \left (x\right )^{2} + 25 \, x^{3} e^{20} \log \left (x\right )^{2} - 100 \, x^{3} e^{15} \log \left (x\right )^{2} + 150 \, x^{3} e^{10} \log \left (x\right )^{2} - 100 \, x^{3} e^{5} \log \left (x\right )^{2} - 10 \, x^{4} e^{5} - 40 \, x^{4} \log \left (x\right ) - 60 \, x^{3} e^{10} \log \left (x\right ) + 120 \, x^{3} e^{5} \log \left (x\right ) + 25 \, x^{3} \log \left (x\right )^{2} - x^{4} + 20 \, x^{3} e^{10} - 40 \, x^{3} e^{5} - 60 \, x^{3} \log \left (x\right ) + 40 \, x^{2} e^{15} \log \left (x\right ) - 120 \, x^{2} e^{10} \log \left (x\right ) + 120 \, x^{2} e^{5} \log \left (x\right ) - 4 \, x^{3} - 20 \, x^{2} e^{15} + 60 \, x^{2} e^{10} - 60 \, x^{2} e^{5} - 40 \, x^{2} \log \left (x\right ) - 10 \, x e^{20} \log \left (x\right ) + 40 \, x e^{15} \log \left (x\right ) - 60 \, x e^{10} \log \left (x\right ) + 40 \, x e^{5} \log \left (x\right ) - 6 \, x^{2} + 4 \, {\left (5 \, x^{2} + 11 \, x\right )} e^{15} - 40 \, x e^{15} - 2 \, {\left (10 \, x^{3} + 33 \, x^{2} + 36 \, x\right )} e^{10} + 60 \, x e^{10} + 2 \, {\left (5 \, x^{4} + 22 \, x^{3} + 36 \, x^{2} + 26 \, x\right )} e^{5} - 40 \, x e^{5} - 10 \, x \log \left (x\right ) - 4 \, x \] Input:

integrate((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+4 
50*x^2)*exp(5)^2+(-600*x^5-1500*x^4-1200*x^3-300*x^2)*exp(5)+175*x^6+600*x 
^5+750*x^4+400*x^3+75*x^2)*log(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*x^ 
2+80*x+40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5- 
600*x^4-440*x^3+160*x^2+240*x+40)*exp(5)+50*x^6+200*x^5+250*x^4+40*x^3-130 
*x^2-80*x-10)*log(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)*exp 
(5)^2+(40*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x, alg 
orithm="giac")
 

Output:

25*x^7*log(x)^2 - 100*x^6*e^5*log(x)^2 + 100*x^6*log(x)^2 + 150*x^5*e^10*l 
og(x)^2 - 300*x^5*e^5*log(x)^2 + 150*x^5*log(x)^2 - 100*x^4*e^15*log(x)^2 
+ 300*x^4*e^10*log(x)^2 - 300*x^4*e^5*log(x)^2 - 10*x^5*log(x) + 40*x^4*e^ 
5*log(x) + 100*x^4*log(x)^2 + 25*x^3*e^20*log(x)^2 - 100*x^3*e^15*log(x)^2 
 + 150*x^3*e^10*log(x)^2 - 100*x^3*e^5*log(x)^2 - 10*x^4*e^5 - 40*x^4*log( 
x) - 60*x^3*e^10*log(x) + 120*x^3*e^5*log(x) + 25*x^3*log(x)^2 - x^4 + 20* 
x^3*e^10 - 40*x^3*e^5 - 60*x^3*log(x) + 40*x^2*e^15*log(x) - 120*x^2*e^10* 
log(x) + 120*x^2*e^5*log(x) - 4*x^3 - 20*x^2*e^15 + 60*x^2*e^10 - 60*x^2*e 
^5 - 40*x^2*log(x) - 10*x*e^20*log(x) + 40*x*e^15*log(x) - 60*x*e^10*log(x 
) + 40*x*e^5*log(x) - 6*x^2 + 4*(5*x^2 + 11*x)*e^15 - 40*x*e^15 - 2*(10*x^ 
3 + 33*x^2 + 36*x)*e^10 + 60*x*e^10 + 2*(5*x^4 + 22*x^3 + 36*x^2 + 26*x)*e 
^5 - 40*x*e^5 - 10*x*log(x) - 4*x
 

Mupad [B] (verification not implemented)

Time = 2.98 (sec) , antiderivative size = 153, normalized size of antiderivative = 5.10 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=x\,\left (4\,{\left ({\mathrm {e}}^5-1\right )}^3-10\,\ln \left (x\right )\,{\left ({\mathrm {e}}^5-1\right )}^4\right )+25\,x^7\,{\ln \left (x\right )}^2-x^2\,\left (6\,{\left ({\mathrm {e}}^5-1\right )}^2-40\,\ln \left (x\right )\,{\left ({\mathrm {e}}^5-1\right )}^3\right )+x^3\,\left (25\,{\left ({\mathrm {e}}^5-1\right )}^4\,{\ln \left (x\right )}^2-60\,{\left ({\mathrm {e}}^5-1\right )}^2\,\ln \left (x\right )+4\,{\mathrm {e}}^5-4\right )-x^5\,\left (10\,\ln \left (x\right )-150\,{\ln \left (x\right )}^2\,{\left ({\mathrm {e}}^5-1\right )}^2\right )-x^4\,\left (100\,{\left ({\mathrm {e}}^5-1\right )}^3\,{\ln \left (x\right )}^2+\left (40-40\,{\mathrm {e}}^5\right )\,\ln \left (x\right )+1\right )-x^6\,{\ln \left (x\right )}^2\,\left (100\,{\mathrm {e}}^5-100\right ) \] Input:

int(log(x)^2*(75*x^2*exp(20) - exp(15)*(300*x^2 + 400*x^3) + exp(10)*(450* 
x^2 + 1200*x^3 + 750*x^4) + 75*x^2 + 400*x^3 + 750*x^4 + 600*x^5 + 175*x^6 
 - exp(5)*(300*x^2 + 1200*x^3 + 1500*x^4 + 600*x^5)) - 10*exp(20) - 52*x - 
 exp(10)*(132*x + 60*x^2 + 72) + exp(5)*(144*x + 132*x^2 + 40*x^3 + 52) + 
log(x)*(exp(20)*(50*x^2 - 10) - 80*x + exp(15)*(80*x - 200*x^2 - 200*x^3 + 
 40) + exp(10)*(120*x^2 - 240*x + 600*x^3 + 300*x^4 - 60) + exp(5)*(240*x 
+ 160*x^2 - 440*x^3 - 600*x^4 - 200*x^5 + 40) - 130*x^2 + 40*x^3 + 250*x^4 
 + 200*x^5 + 50*x^6 - 10) - 72*x^2 - 44*x^3 - 10*x^4 + exp(15)*(40*x + 44) 
 - 14,x)
 

Output:

x*(4*(exp(5) - 1)^3 - 10*log(x)*(exp(5) - 1)^4) + 25*x^7*log(x)^2 - x^2*(6 
*(exp(5) - 1)^2 - 40*log(x)*(exp(5) - 1)^3) + x^3*(4*exp(5) - 60*log(x)*(e 
xp(5) - 1)^2 + 25*log(x)^2*(exp(5) - 1)^4 - 4) - x^5*(10*log(x) - 150*log( 
x)^2*(exp(5) - 1)^2) - x^4*(100*log(x)^2*(exp(5) - 1)^3 - log(x)*(40*exp(5 
) - 40) + 1) - x^6*log(x)^2*(100*exp(5) - 100)
 

Reduce [B] (verification not implemented)

Time = 0.16 (sec) , antiderivative size = 329, normalized size of antiderivative = 10.97 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=x \left (-4-6 x +150 \mathrm {log}\left (x \right )^{2} x^{4}+100 \mathrm {log}\left (x \right )^{2} x^{3}+100 \mathrm {log}\left (x \right )^{2} x^{5}+12 e^{5}+25 \mathrm {log}\left (x \right )^{2} x^{2}-10 \,\mathrm {log}\left (x \right ) x^{4}-4 x^{2}+25 \mathrm {log}\left (x \right )^{2} x^{6}+40 \,\mathrm {log}\left (x \right ) e^{5}+4 e^{15}-10 \,\mathrm {log}\left (x \right ) e^{20}-120 \,\mathrm {log}\left (x \right ) e^{10} x -6 e^{10} x -x^{3}-12 e^{10}-10 \,\mathrm {log}\left (x \right )-60 \,\mathrm {log}\left (x \right ) x^{2}+25 \mathrm {log}\left (x \right )^{2} e^{20} x^{2}-100 \mathrm {log}\left (x \right )^{2} e^{15} x^{3}-100 \mathrm {log}\left (x \right )^{2} e^{15} x^{2}+150 \mathrm {log}\left (x \right )^{2} e^{10} x^{4}+300 \mathrm {log}\left (x \right )^{2} e^{10} x^{3}+150 \mathrm {log}\left (x \right )^{2} e^{10} x^{2}-100 \mathrm {log}\left (x \right )^{2} e^{5} x^{5}-300 \mathrm {log}\left (x \right )^{2} e^{5} x^{4}-300 \mathrm {log}\left (x \right )^{2} e^{5} x^{3}-100 \mathrm {log}\left (x \right )^{2} e^{5} x^{2}+40 \,\mathrm {log}\left (x \right ) e^{15} x -60 \,\mathrm {log}\left (x \right ) e^{10} x^{2}+40 \,\mathrm {log}\left (x \right ) e^{5} x^{3}+120 \,\mathrm {log}\left (x \right ) e^{5} x^{2}+120 \,\mathrm {log}\left (x \right ) e^{5} x -40 \,\mathrm {log}\left (x \right ) x^{3}+40 \,\mathrm {log}\left (x \right ) e^{15}-60 \,\mathrm {log}\left (x \right ) e^{10}-40 \,\mathrm {log}\left (x \right ) x +4 e^{5} x^{2}+12 e^{5} x \right ) \] Input:

int((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+450*x^2 
)*exp(5)^2+(-600*x^5-1500*x^4-1200*x^3-300*x^2)*exp(5)+175*x^6+600*x^5+750 
*x^4+400*x^3+75*x^2)*log(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*x^2+80*x 
+40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5-600*x^ 
4-440*x^3+160*x^2+240*x+40)*exp(5)+50*x^6+200*x^5+250*x^4+40*x^3-130*x^2-8 
0*x-10)*log(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)*exp(5)^2+ 
(40*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x)
 

Output:

x*(25*log(x)**2*e**20*x**2 - 100*log(x)**2*e**15*x**3 - 100*log(x)**2*e**1 
5*x**2 + 150*log(x)**2*e**10*x**4 + 300*log(x)**2*e**10*x**3 + 150*log(x)* 
*2*e**10*x**2 - 100*log(x)**2*e**5*x**5 - 300*log(x)**2*e**5*x**4 - 300*lo 
g(x)**2*e**5*x**3 - 100*log(x)**2*e**5*x**2 + 25*log(x)**2*x**6 + 100*log( 
x)**2*x**5 + 150*log(x)**2*x**4 + 100*log(x)**2*x**3 + 25*log(x)**2*x**2 - 
 10*log(x)*e**20 + 40*log(x)*e**15*x + 40*log(x)*e**15 - 60*log(x)*e**10*x 
**2 - 120*log(x)*e**10*x - 60*log(x)*e**10 + 40*log(x)*e**5*x**3 + 120*log 
(x)*e**5*x**2 + 120*log(x)*e**5*x + 40*log(x)*e**5 - 10*log(x)*x**4 - 40*l 
og(x)*x**3 - 60*log(x)*x**2 - 40*log(x)*x - 10*log(x) + 4*e**15 - 6*e**10* 
x - 12*e**10 + 4*e**5*x**2 + 12*e**5*x + 12*e**5 - x**3 - 4*x**2 - 6*x - 4 
)