3.32.33 \(\int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5)+(15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x (-20+120 x+40 x^2-120 x^3-20 x^4)) \log (x)+(3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x (10 x-10 x^3)) \log ^2(x)+(200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5) \log ^3(x)+(-200 x+600 x^2-600 x^3+200 x^4) \log ^4(x)}{50 x} \, dx\)

Optimal. Leaf size=28 \[ \left (\frac {1}{10} \left (e^x+x\right )-(1-x)^2 (5+x+\log (x))^2\right )^2 \]

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Rubi [F]  time = 6.67, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(25000 - 185350*x + E^(2*x)*x + 283981*x^2 - 34040*x^3 - 128940*x^4 + 8150*x^5 + 25000*x^6 + 5800*x^7 + 40
0*x^8 + E^x*(-100 + 331*x + 221*x^2 - 320*x^3 - 120*x^4 - 10*x^5) + (15000 - 139120*x + 253000*x^2 - 92000*x^3
- 76680*x^4 + 24600*x^5 + 13800*x^6 + 1400*x^7 + E^x*(-20 + 120*x + 40*x^2 - 120*x^3 - 20*x^4))*Log[x] + (300
0 - 38410*x + 82240*x^2 - 48030*x^3 - 10200*x^4 + 9600*x^5 + 1800*x^6 + E^x*(10*x - 10*x^3))*Log[x]^2 + (200 -
4600*x + 11600*x^2 - 9200*x^3 + 1000*x^4 + 1000*x^5)*Log[x]^3 + (-200*x + 600*x^2 - 600*x^3 + 200*x^4)*Log[x]
^4)/(50*x),x]

[Out]

(-23*E^x)/5 + E^(2*x)/100 - 2005*x + (401*E^x*x)/50 + (190801*x^2)/100 - (6*E^x*x^2)/5 - (406*x^3)/5 - (8*E^x*
x^3)/5 - (2778*x^4)/5 - (E^x*x^4)/5 + (79*x^5)/5 + 76*x^6 + 16*x^7 + x^8 - (6*ExpIntegralEi[x])/5 + (2*x*Hyper
geometricPFQ[{1, 1, 1}, {2, 2, 2}, x])/5 + Log[-x]^2/5 + 500*Log[x] - (4*E^x*Log[x])/5 + (2*EulerGamma*Log[x])
/5 - 1702*x*Log[x] + (16*E^x*x*Log[x])/5 + (9318*x^2*Log[x])/5 - (6*E^x*x^2*Log[x])/5 - (2186*x^3*Log[x])/5 -
(2*E^x*x^3*Log[x])/5 - (1782*x^4*Log[x])/5 + 84*x^5*Log[x] + 44*x^6*Log[x] + 4*x^7*Log[x] - (2*ExpIntegralEi[x
]*Log[x])/5 + (2*(ExpIntegralE[1, -x] + ExpIntegralEi[x])*Log[x])/5 + 150*Log[x]^2 - (2701*x*Log[x]^2)/5 + (33
32*x^2*Log[x]^2)/5 - (1321*x^3*Log[x]^2)/5 - 54*x^4*Log[x]^2 + 36*x^5*Log[x]^2 + 6*x^6*Log[x]^2 + 20*Log[x]^3
- 76*x*Log[x]^3 + 104*x^2*Log[x]^3 - 56*x^3*Log[x]^3 + 4*x^4*Log[x]^3 + 4*x^5*Log[x]^3 + Log[x]^4 - 4*x*Log[x]
^4 + 6*x^2*Log[x]^4 - 4*x^3*Log[x]^4 + x^4*Log[x]^4 + Defer[Int][E^x*Log[x]^2, x]/5 - Defer[Int][E^x*x^2*Log[x
]^2, x]/5

Rubi steps

Aborted

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Mathematica [B]  time = 0.18, size = 177, normalized size = 6.32 \begin {gather*} \frac {1}{50} \left (\frac {e^{2 x}}{2}-100250 x+\frac {190801 x^2}{2}-4060 x^3-27780 x^4+790 x^5+3800 x^6+800 x^7+50 x^8-e^x \left (250-401 x+60 x^2+80 x^3+10 x^4\right )+20 (-1+x)^2 (5+x) \left (250-e^x-401 x+60 x^2+80 x^3+10 x^4\right ) \log (x)+10 (-1+x)^2 \left (750-e^x-1201 x+180 x^2+240 x^3+30 x^4\right ) \log ^2(x)+200 (-1+x)^4 (5+x) \log ^3(x)+50 (-1+x)^4 \log ^4(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(25000 - 185350*x + E^(2*x)*x + 283981*x^2 - 34040*x^3 - 128940*x^4 + 8150*x^5 + 25000*x^6 + 5800*x^
7 + 400*x^8 + E^x*(-100 + 331*x + 221*x^2 - 320*x^3 - 120*x^4 - 10*x^5) + (15000 - 139120*x + 253000*x^2 - 920
00*x^3 - 76680*x^4 + 24600*x^5 + 13800*x^6 + 1400*x^7 + E^x*(-20 + 120*x + 40*x^2 - 120*x^3 - 20*x^4))*Log[x]
+ (3000 - 38410*x + 82240*x^2 - 48030*x^3 - 10200*x^4 + 9600*x^5 + 1800*x^6 + E^x*(10*x - 10*x^3))*Log[x]^2 +
(200 - 4600*x + 11600*x^2 - 9200*x^3 + 1000*x^4 + 1000*x^5)*Log[x]^3 + (-200*x + 600*x^2 - 600*x^3 + 200*x^4)*
Log[x]^4)/(50*x),x]

[Out]

(E^(2*x)/2 - 100250*x + (190801*x^2)/2 - 4060*x^3 - 27780*x^4 + 790*x^5 + 3800*x^6 + 800*x^7 + 50*x^8 - E^x*(2
50 - 401*x + 60*x^2 + 80*x^3 + 10*x^4) + 20*(-1 + x)^2*(5 + x)*(250 - E^x - 401*x + 60*x^2 + 80*x^3 + 10*x^4)*
Log[x] + 10*(-1 + x)^2*(750 - E^x - 1201*x + 180*x^2 + 240*x^3 + 30*x^4)*Log[x]^2 + 200*(-1 + x)^4*(5 + x)*Log
[x]^3 + 50*(-1 + x)^4*Log[x]^4)/50

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fricas [B]  time = 0.53, size = 221, normalized size = 7.89 \begin {gather*} x^{8} + 16 \, x^{7} + 76 \, x^{6} + \frac {79}{5} \, x^{5} + {\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )} \log \relax (x)^{4} - \frac {2778}{5} \, x^{4} + 4 \, {\left (x^{5} + x^{4} - 14 \, x^{3} + 26 \, x^{2} - 19 \, x + 5\right )} \log \relax (x)^{3} - \frac {406}{5} \, x^{3} + \frac {1}{5} \, {\left (30 \, x^{6} + 180 \, x^{5} - 270 \, x^{4} - 1321 \, x^{3} + 3332 \, x^{2} - {\left (x^{2} - 2 \, x + 1\right )} e^{x} - 2701 \, x + 750\right )} \log \relax (x)^{2} + \frac {190801}{100} \, x^{2} - \frac {1}{50} \, {\left (10 \, x^{4} + 80 \, x^{3} + 60 \, x^{2} - 401 \, x + 250\right )} e^{x} + \frac {2}{5} \, {\left (10 \, x^{7} + 110 \, x^{6} + 210 \, x^{5} - 891 \, x^{4} - 1093 \, x^{3} + 4659 \, x^{2} - {\left (x^{3} + 3 \, x^{2} - 9 \, x + 5\right )} e^{x} - 4255 \, x + 1250\right )} \log \relax (x) - 2005 \, x + \frac {1}{100} \, e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/50*((200*x^4-600*x^3+600*x^2-200*x)*log(x)^4+(1000*x^5+1000*x^4-9200*x^3+11600*x^2-4600*x+200)*log
(x)^3+((-10*x^3+10*x)*exp(x)+1800*x^6+9600*x^5-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*log(x)^2+((-20*x^4-
120*x^3+40*x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000*x^3+253000*x^2-139120*x+15000)*lo
g(x)+x*exp(x)^2+(-10*x^5-120*x^4-320*x^3+221*x^2+331*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*
x^4-34040*x^3+283981*x^2-185350*x+25000)/x,x, algorithm="fricas")

[Out]

x^8 + 16*x^7 + 76*x^6 + 79/5*x^5 + (x^4 - 4*x^3 + 6*x^2 - 4*x + 1)*log(x)^4 - 2778/5*x^4 + 4*(x^5 + x^4 - 14*x
^3 + 26*x^2 - 19*x + 5)*log(x)^3 - 406/5*x^3 + 1/5*(30*x^6 + 180*x^5 - 270*x^4 - 1321*x^3 + 3332*x^2 - (x^2 -
2*x + 1)*e^x - 2701*x + 750)*log(x)^2 + 190801/100*x^2 - 1/50*(10*x^4 + 80*x^3 + 60*x^2 - 401*x + 250)*e^x + 2
/5*(10*x^7 + 110*x^6 + 210*x^5 - 891*x^4 - 1093*x^3 + 4659*x^2 - (x^3 + 3*x^2 - 9*x + 5)*e^x - 4255*x + 1250)*
log(x) - 2005*x + 1/100*e^(2*x)

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giac [B]  time = 0.21, size = 327, normalized size = 11.68 \begin {gather*} x^{8} + 4 \, x^{7} \log \relax (x) + 6 \, x^{6} \log \relax (x)^{2} + 4 \, x^{5} \log \relax (x)^{3} + x^{4} \log \relax (x)^{4} + 16 \, x^{7} + 44 \, x^{6} \log \relax (x) + 36 \, x^{5} \log \relax (x)^{2} + 4 \, x^{4} \log \relax (x)^{3} - 4 \, x^{3} \log \relax (x)^{4} + 76 \, x^{6} + 84 \, x^{5} \log \relax (x) - 54 \, x^{4} \log \relax (x)^{2} - 56 \, x^{3} \log \relax (x)^{3} + 6 \, x^{2} \log \relax (x)^{4} + \frac {79}{5} \, x^{5} - \frac {1}{5} \, x^{4} e^{x} - \frac {1782}{5} \, x^{4} \log \relax (x) - \frac {2}{5} \, x^{3} e^{x} \log \relax (x) - \frac {1321}{5} \, x^{3} \log \relax (x)^{2} - \frac {1}{5} \, x^{2} e^{x} \log \relax (x)^{2} + 104 \, x^{2} \log \relax (x)^{3} - 4 \, x \log \relax (x)^{4} - \frac {2778}{5} \, x^{4} - \frac {8}{5} \, x^{3} e^{x} - \frac {2186}{5} \, x^{3} \log \relax (x) - \frac {6}{5} \, x^{2} e^{x} \log \relax (x) + \frac {3332}{5} \, x^{2} \log \relax (x)^{2} + \frac {2}{5} \, x e^{x} \log \relax (x)^{2} - 76 \, x \log \relax (x)^{3} + \log \relax (x)^{4} - \frac {406}{5} \, x^{3} - \frac {6}{5} \, x^{2} e^{x} + \frac {9318}{5} \, x^{2} \log \relax (x) + \frac {18}{5} \, x e^{x} \log \relax (x) - \frac {2701}{5} \, x \log \relax (x)^{2} - \frac {1}{5} \, e^{x} \log \relax (x)^{2} + 20 \, \log \relax (x)^{3} + \frac {190801}{100} \, x^{2} + \frac {401}{50} \, x e^{x} - 1702 \, x \log \relax (x) - 2 \, e^{x} \log \relax (x) + 150 \, \log \relax (x)^{2} - 2005 \, x + \frac {1}{100} \, e^{\left (2 \, x\right )} - 5 \, e^{x} + 500 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/50*((200*x^4-600*x^3+600*x^2-200*x)*log(x)^4+(1000*x^5+1000*x^4-9200*x^3+11600*x^2-4600*x+200)*log
(x)^3+((-10*x^3+10*x)*exp(x)+1800*x^6+9600*x^5-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*log(x)^2+((-20*x^4-
120*x^3+40*x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000*x^3+253000*x^2-139120*x+15000)*lo
g(x)+x*exp(x)^2+(-10*x^5-120*x^4-320*x^3+221*x^2+331*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*
x^4-34040*x^3+283981*x^2-185350*x+25000)/x,x, algorithm="giac")

[Out]

x^8 + 4*x^7*log(x) + 6*x^6*log(x)^2 + 4*x^5*log(x)^3 + x^4*log(x)^4 + 16*x^7 + 44*x^6*log(x) + 36*x^5*log(x)^2
+ 4*x^4*log(x)^3 - 4*x^3*log(x)^4 + 76*x^6 + 84*x^5*log(x) - 54*x^4*log(x)^2 - 56*x^3*log(x)^3 + 6*x^2*log(x)
^4 + 79/5*x^5 - 1/5*x^4*e^x - 1782/5*x^4*log(x) - 2/5*x^3*e^x*log(x) - 1321/5*x^3*log(x)^2 - 1/5*x^2*e^x*log(x
)^2 + 104*x^2*log(x)^3 - 4*x*log(x)^4 - 2778/5*x^4 - 8/5*x^3*e^x - 2186/5*x^3*log(x) - 6/5*x^2*e^x*log(x) + 33
32/5*x^2*log(x)^2 + 2/5*x*e^x*log(x)^2 - 76*x*log(x)^3 + log(x)^4 - 406/5*x^3 - 6/5*x^2*e^x + 9318/5*x^2*log(x
) + 18/5*x*e^x*log(x) - 2701/5*x*log(x)^2 - 1/5*e^x*log(x)^2 + 20*log(x)^3 + 190801/100*x^2 + 401/50*x*e^x - 1
702*x*log(x) - 2*e^x*log(x) + 150*log(x)^2 - 2005*x + 1/100*e^(2*x) - 5*e^x + 500*log(x)

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maple [B]  time = 0.08, size = 248, normalized size = 8.86

method	result	size
risch	\(\frac {\left (50 x^{4}-200 x^{3}+300 x^{2}-200 x +50\right ) \ln \relax (x )^{4}}{50}+\frac {\left (200 x^{5}+200 x^{4}-2800 x^{3}+5200 x^{2}-3800 x +1000\right ) \ln \relax (x )^{3}}{50}+\frac {\left (300 x^{6}+1800 x^{5}-2700 x^{4}-13210 x^{3}-10 \,{\mathrm e}^{x} x^{2}+33320 x^{2}+20 \,{\mathrm e}^{x} x -27010 x -10 \,{\mathrm e}^{x}+7500\right ) \ln \relax (x )^{2}}{50}+\frac {\left (200 x^{7}+2200 x^{6}+4200 x^{5}-17820 x^{4}-20 \,{\mathrm e}^{x} x^{3}-21860 x^{3}-60 \,{\mathrm e}^{x} x^{2}+93180 x^{2}+180 \,{\mathrm e}^{x} x -85100 x -100 \,{\mathrm e}^{x}\right ) \ln \relax (x )}{50}+x^{8}+16 x^{7}+76 x^{6}+\frac {79 x^{5}}{5}-\frac {2778 x^{4}}{5}-\frac {406 x^{3}}{5}+\frac {190801 x^{2}}{100}-2005 x +500 \ln \relax (x )+\frac {{\mathrm e}^{2 x}}{100}-\frac {{\mathrm e}^{x} x^{4}}{5}-\frac {8 \,{\mathrm e}^{x} x^{3}}{5}-\frac {6 \,{\mathrm e}^{x} x^{2}}{5}+\frac {401 \,{\mathrm e}^{x} x}{50}-5 \,{\mathrm e}^{x}\)	\(248\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/50*((200*x^4-600*x^3+600*x^2-200*x)*ln(x)^4+(1000*x^5+1000*x^4-9200*x^3+11600*x^2-4600*x+200)*ln(x)^3+((
-10*x^3+10*x)*exp(x)+1800*x^6+9600*x^5-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*ln(x)^2+((-20*x^4-120*x^3+4
0*x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000*x^3+253000*x^2-139120*x+15000)*ln(x)+x*exp
(x)^2+(-10*x^5-120*x^4-320*x^3+221*x^2+331*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*x^4-34040*
x^3+283981*x^2-185350*x+25000)/x,x,method=_RETURNVERBOSE)

[Out]

1/50*(50*x^4-200*x^3+300*x^2-200*x+50)*ln(x)^4+1/50*(200*x^5+200*x^4-2800*x^3+5200*x^2-3800*x+1000)*ln(x)^3+1/
50*(300*x^6+1800*x^5-2700*x^4-13210*x^3-10*exp(x)*x^2+33320*x^2+20*exp(x)*x-27010*x-10*exp(x)+7500)*ln(x)^2+1/
50*(200*x^7+2200*x^6+4200*x^5-17820*x^4-20*exp(x)*x^3-21860*x^3-60*exp(x)*x^2+93180*x^2+180*exp(x)*x-85100*x-1
00*exp(x))*ln(x)+x^8+16*x^7+76*x^6+79/5*x^5-2778/5*x^4-406/5*x^3+190801/100*x^2-2005*x+500*ln(x)+1/100*exp(2*x
)-1/5*exp(x)*x^4-8/5*exp(x)*x^3-6/5*exp(x)*x^2+401/50*exp(x)*x-5*exp(x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x^{8} + 4 \, x^{7} \log \relax (x) + 16 \, x^{7} + 46 \, x^{6} \log \relax (x) + 76 \, x^{6} + \frac {492}{5} \, x^{5} \log \relax (x) + \frac {79}{5} \, x^{5} - \frac {1917}{5} \, x^{4} \log \relax (x) + {\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )} \log \relax (x)^{4} - \frac {2778}{5} \, x^{4} - \frac {1840}{3} \, x^{3} \log \relax (x) + 4 \, {\left (x^{5} + x^{4} - 14 \, x^{3} + 26 \, x^{2} - 19 \, x + 5\right )} \log \relax (x)^{3} - \frac {406}{5} \, x^{3} + 2530 \, x^{2} \log \relax (x) + \frac {1}{5} \, {\left (30 \, x^{6} + 180 \, x^{5} - 270 \, x^{4} - 1321 \, x^{3} + 3332 \, x^{2} - 2701 \, x\right )} \log \relax (x)^{2} + \frac {190801}{100} \, x^{2} - \frac {1}{5} \, {\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{x} - \frac {12}{5} \, {\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{x} - \frac {1}{5} \, {\left ({\left (x^{2} - 2 \, x + 1\right )} \log \relax (x)^{2} + 2 \, {\left (x^{3} + 3 \, x^{2} - 9 \, x + 11\right )} \log \relax (x)\right )} e^{x} - \frac {32}{5} \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} + \frac {221}{50} \, {\left (x - 1\right )} e^{x} - \frac {1}{15} \, {\left (30 \, x^{6} + 216 \, x^{5} - 405 \, x^{4} - 2642 \, x^{3} + 9996 \, x^{2} - 16206 \, x\right )} \log \relax (x) - \frac {13912}{5} \, x \log \relax (x) + \frac {12}{5} \, e^{x} \log \relax (x) + 150 \, \log \relax (x)^{2} - 2005 \, x - \frac {22}{5} \, {\rm Ei}\relax (x) + \frac {1}{100} \, e^{\left (2 \, x\right )} + \frac {331}{50} \, e^{x} + \frac {1}{50} \, \int \frac {20 \, {\left (x^{3} + 3 \, x^{2} - 9 \, x + 11\right )} e^{x}}{x}\,{d x} + 500 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/50*((200*x^4-600*x^3+600*x^2-200*x)*log(x)^4+(1000*x^5+1000*x^4-9200*x^3+11600*x^2-4600*x+200)*log
(x)^3+((-10*x^3+10*x)*exp(x)+1800*x^6+9600*x^5-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*log(x)^2+((-20*x^4-
120*x^3+40*x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000*x^3+253000*x^2-139120*x+15000)*lo
g(x)+x*exp(x)^2+(-10*x^5-120*x^4-320*x^3+221*x^2+331*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*
x^4-34040*x^3+283981*x^2-185350*x+25000)/x,x, algorithm="maxima")

[Out]

x^8 + 4*x^7*log(x) + 16*x^7 + 46*x^6*log(x) + 76*x^6 + 492/5*x^5*log(x) + 79/5*x^5 - 1917/5*x^4*log(x) + (x^4
- 4*x^3 + 6*x^2 - 4*x + 1)*log(x)^4 - 2778/5*x^4 - 1840/3*x^3*log(x) + 4*(x^5 + x^4 - 14*x^3 + 26*x^2 - 19*x +
5)*log(x)^3 - 406/5*x^3 + 2530*x^2*log(x) + 1/5*(30*x^6 + 180*x^5 - 270*x^4 - 1321*x^3 + 3332*x^2 - 2701*x)*l
og(x)^2 + 190801/100*x^2 - 1/5*(x^4 - 4*x^3 + 12*x^2 - 24*x + 24)*e^x - 12/5*(x^3 - 3*x^2 + 6*x - 6)*e^x - 1/5
*((x^2 - 2*x + 1)*log(x)^2 + 2*(x^3 + 3*x^2 - 9*x + 11)*log(x))*e^x - 32/5*(x^2 - 2*x + 2)*e^x + 221/50*(x - 1
)*e^x - 1/15*(30*x^6 + 216*x^5 - 405*x^4 - 2642*x^3 + 9996*x^2 - 16206*x)*log(x) - 13912/5*x*log(x) + 12/5*e^x
*log(x) + 150*log(x)^2 - 2005*x - 22/5*Ei(x) + 1/100*e^(2*x) + 331/50*e^x + 1/50*integrate(20*(x^3 + 3*x^2 - 9
*x + 11)*e^x/x, x) + 500*log(x)

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mupad [B]  time = 2.43, size = 229, normalized size = 8.18 \begin {gather*} \frac {{\mathrm {e}}^{2\,x}}{100}-2005\,x+500\,\ln \relax (x)-{\mathrm {e}}^x\,\left (\frac {x^4}{5}+\frac {8\,x^3}{5}+\frac {6\,x^2}{5}-\frac {401\,x}{50}+5\right )+{\ln \relax (x)}^4\,\left (x^4-4\,x^3+6\,x^2-4\,x+1\right )-{\ln \relax (x)}^2\,\left (\frac {2701\,x}{5}+{\mathrm {e}}^x\,\left (\frac {x^2}{5}-\frac {2\,x}{5}+\frac {1}{5}\right )-\frac {3332\,x^2}{5}+\frac {1321\,x^3}{5}+54\,x^4-36\,x^5-6\,x^6-150\right )-\ln \relax (x)\,\left (1702\,x-\frac {9318\,x^2}{5}+\frac {2186\,x^3}{5}+\frac {1782\,x^4}{5}-84\,x^5-44\,x^6-4\,x^7+{\mathrm {e}}^x\,\left (\frac {2\,x^3}{5}+\frac {6\,x^2}{5}-\frac {18\,x}{5}+2\right )\right )+{\ln \relax (x)}^3\,\left (4\,x^5+4\,x^4-56\,x^3+104\,x^2-76\,x+20\right )+\frac {190801\,x^2}{100}-\frac {406\,x^3}{5}-\frac {2778\,x^4}{5}+\frac {79\,x^5}{5}+76\,x^6+16\,x^7+x^8 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x*exp(2*x))/50 - 3707*x - (exp(x)*(320*x^3 - 221*x^2 - 331*x + 120*x^4 + 10*x^5 + 100))/50 - (log(x)^4*(
200*x - 600*x^2 + 600*x^3 - 200*x^4))/50 + (log(x)^2*(exp(x)*(10*x - 10*x^3) - 38410*x + 82240*x^2 - 48030*x^3
- 10200*x^4 + 9600*x^5 + 1800*x^6 + 3000))/50 + (log(x)^3*(11600*x^2 - 4600*x - 9200*x^3 + 1000*x^4 + 1000*x^
5 + 200))/50 + (283981*x^2)/50 - (3404*x^3)/5 - (12894*x^4)/5 + 163*x^5 + 500*x^6 + 116*x^7 + 8*x^8 + (log(x)*
(253000*x^2 - exp(x)*(120*x^3 - 40*x^2 - 120*x + 20*x^4 + 20) - 139120*x - 92000*x^3 - 76680*x^4 + 24600*x^5 +
13800*x^6 + 1400*x^7 + 15000))/50 + 500)/x,x)

[Out]

exp(2*x)/100 - 2005*x + 500*log(x) - exp(x)*((6*x^2)/5 - (401*x)/50 + (8*x^3)/5 + x^4/5 + 5) + log(x)^4*(6*x^2
- 4*x - 4*x^3 + x^4 + 1) - log(x)^2*((2701*x)/5 + exp(x)*(x^2/5 - (2*x)/5 + 1/5) - (3332*x^2)/5 + (1321*x^3)/
5 + 54*x^4 - 36*x^5 - 6*x^6 - 150) - log(x)*(1702*x - (9318*x^2)/5 + (2186*x^3)/5 + (1782*x^4)/5 - 84*x^5 - 44
*x^6 - 4*x^7 + exp(x)*((6*x^2)/5 - (18*x)/5 + (2*x^3)/5 + 2)) + log(x)^3*(104*x^2 - 76*x - 56*x^3 + 4*x^4 + 4*
x^5 + 20) + (190801*x^2)/100 - (406*x^3)/5 - (2778*x^4)/5 + (79*x^5)/5 + 76*x^6 + 16*x^7 + x^8

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sympy [B]  time = 0.94, size = 272, normalized size = 9.71 \begin {gather*} x^{8} + 16 x^{7} + 76 x^{6} + \frac {79 x^{5}}{5} - \frac {2778 x^{4}}{5} - \frac {406 x^{3}}{5} + \frac {190801 x^{2}}{100} - 2005 x + \left (x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1\right ) \log {\relax (x )}^{4} + \left (4 x^{5} + 4 x^{4} - 56 x^{3} + 104 x^{2} - 76 x + 20\right ) \log {\relax (x )}^{3} + \left (6 x^{6} + 36 x^{5} - 54 x^{4} - \frac {1321 x^{3}}{5} + \frac {3332 x^{2}}{5} - \frac {2701 x}{5} + 150\right ) \log {\relax (x )}^{2} + \left (4 x^{7} + 44 x^{6} + 84 x^{5} - \frac {1782 x^{4}}{5} - \frac {2186 x^{3}}{5} + \frac {9318 x^{2}}{5} - 1702 x\right ) \log {\relax (x )} + \frac {\left (- 1000 x^{4} - 2000 x^{3} \log {\relax (x )} - 8000 x^{3} - 1000 x^{2} \log {\relax (x )}^{2} - 6000 x^{2} \log {\relax (x )} - 6000 x^{2} + 2000 x \log {\relax (x )}^{2} + 18000 x \log {\relax (x )} + 40100 x - 1000 \log {\relax (x )}^{2} - 10000 \log {\relax (x )} - 25000\right ) e^{x}}{5000} + \frac {e^{2 x}}{100} + 500 \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/50*((200*x**4-600*x**3+600*x**2-200*x)*ln(x)**4+(1000*x**5+1000*x**4-9200*x**3+11600*x**2-4600*x+2
00)*ln(x)**3+((-10*x**3+10*x)*exp(x)+1800*x**6+9600*x**5-10200*x**4-48030*x**3+82240*x**2-38410*x+3000)*ln(x)*
*2+((-20*x**4-120*x**3+40*x**2+120*x-20)*exp(x)+1400*x**7+13800*x**6+24600*x**5-76680*x**4-92000*x**3+253000*x
**2-139120*x+15000)*ln(x)+x*exp(x)**2+(-10*x**5-120*x**4-320*x**3+221*x**2+331*x-100)*exp(x)+400*x**8+5800*x**
7+25000*x**6+8150*x**5-128940*x**4-34040*x**3+283981*x**2-185350*x+25000)/x,x)

[Out]

x**8 + 16*x**7 + 76*x**6 + 79*x**5/5 - 2778*x**4/5 - 406*x**3/5 + 190801*x**2/100 - 2005*x + (x**4 - 4*x**3 +
6*x**2 - 4*x + 1)*log(x)**4 + (4*x**5 + 4*x**4 - 56*x**3 + 104*x**2 - 76*x + 20)*log(x)**3 + (6*x**6 + 36*x**5
- 54*x**4 - 1321*x**3/5 + 3332*x**2/5 - 2701*x/5 + 150)*log(x)**2 + (4*x**7 + 44*x**6 + 84*x**5 - 1782*x**4/5
- 2186*x**3/5 + 9318*x**2/5 - 1702*x)*log(x) + (-1000*x**4 - 2000*x**3*log(x) - 8000*x**3 - 1000*x**2*log(x)*
*2 - 6000*x**2*log(x) - 6000*x**2 + 2000*x*log(x)**2 + 18000*x*log(x) + 40100*x - 1000*log(x)**2 - 10000*log(x
) - 25000)*exp(x)/5000 + exp(2*x)/100 + 500*log(x)

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