3.62.96 \(\int ((3200 x+1600 x^2+200 x^3+e^x (-1280 x^2-1920 x^3-720 x^4-80 x^5)+e^{2 x} (128 x^3+320 x^4+264 x^5+80 x^6+8 x^7)) \log (x)+(3200 x+2400 x^2+400 x^3+e^x (-1920 x^2-4480 x^3-2760 x^4-600 x^5-40 x^6)+e^{2 x} (256 x^3+928 x^4+1112 x^5+544 x^6+112 x^7+8 x^8)) \log ^2(x)) \, dx\)

Optimal. Leaf size=26 \[ 4 x^2 (4+x)^2 \left (-5+e^x x (1+x)\right )^2 \log ^2(x) \]

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Rubi [F]  time = 3.01, 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 \left (\left (3200 x+1600 x^2+200 x^3+e^x \left (-1280 x^2-1920 x^3-720 x^4-80 x^5\right )+e^{2 x} \left (128 x^3+320 x^4+264 x^5+80 x^6+8 x^7\right )\right ) \log (x)+\left (3200 x+2400 x^2+400 x^3+e^x \left (-1920 x^2-4480 x^3-2760 x^4-600 x^5-40 x^6\right )+e^{2 x} \left (256 x^3+928 x^4+1112 x^5+544 x^6+112 x^7+8 x^8\right )\right ) \log ^2(x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3200*x + 1600*x^2 + 200*x^3 + E^x*(-1280*x^2 - 1920*x^3 - 720*x^4 - 80*x^5) + E^(2*x)*(128*x^3 + 320*x^4
+ 264*x^5 + 80*x^6 + 8*x^7))*Log[x] + (3200*x + 2400*x^2 + 400*x^3 + E^x*(-1920*x^2 - 4480*x^3 - 2760*x^4 - 60
0*x^5 - 40*x^6) + E^(2*x)*(256*x^3 + 928*x^4 + 1112*x^5 + 544*x^6 + 112*x^7 + 8*x^8))*Log[x]^2,x]

[Out]

3200*E^x - (193*E^(2*x))/8 - 1920*E^x*x + (109*E^(2*x)*x)/4 + 640*E^x*x^2 - (67*E^(2*x)*x^2)/4 + (13*E^(2*x)*x
^3)/2 + 80*E^x*x^4 - (19*E^(2*x)*x^4)/2 - 7*E^(2*x)*x^5 - 2*E^(2*x)*x^6 - 1280*ExpIntegralEi[x] + (21*ExpInteg
ralEi[2*x])/2 + 1280*E^x*Log[x] - (21*E^(2*x)*Log[x])/2 - 1280*E^x*x*Log[x] + 21*E^(2*x)*x*Log[x] + 640*E^x*x^
2*Log[x] - 21*E^(2*x)*x^2*Log[x] - 640*E^x*x^3*Log[x] + 14*E^(2*x)*x^3*Log[x] - 320*E^x*x^4*Log[x] + 25*E^(2*x
)*x^4*Log[x] - 80*E^x*x^5*Log[x] + 54*E^(2*x)*x^5*Log[x] + 26*E^(2*x)*x^6*Log[x] + 4*E^(2*x)*x^7*Log[x] + 1600
*x^2*Log[x]^2 + 800*x^3*Log[x]^2 + 100*x^4*Log[x]^2 - 1920*Defer[Int][E^x*x^2*Log[x]^2, x] - 4480*Defer[Int][E
^x*x^3*Log[x]^2, x] + 256*Defer[Int][E^(2*x)*x^3*Log[x]^2, x] - 2760*Defer[Int][E^x*x^4*Log[x]^2, x] + 928*Def
er[Int][E^(2*x)*x^4*Log[x]^2, x] - 600*Defer[Int][E^x*x^5*Log[x]^2, x] + 1112*Defer[Int][E^(2*x)*x^5*Log[x]^2,
x] - 40*Defer[Int][E^x*x^6*Log[x]^2, x] + 544*Defer[Int][E^(2*x)*x^6*Log[x]^2, x] + 112*Defer[Int][E^(2*x)*x^
7*Log[x]^2, x] + 8*Defer[Int][E^(2*x)*x^8*Log[x]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (3200 x+1600 x^2+200 x^3+e^x \left (-1280 x^2-1920 x^3-720 x^4-80 x^5\right )+e^{2 x} \left (128 x^3+320 x^4+264 x^5+80 x^6+8 x^7\right )\right ) \log (x) \, dx+\int \left (3200 x+2400 x^2+400 x^3+e^x \left (-1920 x^2-4480 x^3-2760 x^4-600 x^5-40 x^6\right )+e^{2 x} \left (256 x^3+928 x^4+1112 x^5+544 x^6+112 x^7+8 x^8\right )\right ) \log ^2(x) \, dx\\ &=1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+1600 x^2 \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)+\frac {1600}{3} x^3 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)+50 x^4 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)-\int \frac {100 x^2 \left (96+32 x+3 x^2\right )-480 e^x \left (-16+16 x-8 x^2+8 x^3+4 x^4+x^5\right )+3 e^{2 x} \left (-21+42 x-42 x^2+28 x^3+50 x^4+108 x^5+52 x^6+8 x^7\right )}{6 x} \, dx+\int \left (400 x \left (8+6 x+x^2\right ) \log ^2(x)+8 e^{2 x} x^3 (1+x) (4+x) \left (8+19 x+9 x^2+x^3\right ) \log ^2(x)-40 e^x x^2 (4+x) \left (12+25 x+11 x^2+x^3\right ) \log ^2(x)\right ) \, dx\\ &=1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+1600 x^2 \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)+\frac {1600}{3} x^3 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)+50 x^4 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)-\frac {1}{6} \int \frac {100 x^2 \left (96+32 x+3 x^2\right )-480 e^x \left (-16+16 x-8 x^2+8 x^3+4 x^4+x^5\right )+3 e^{2 x} \left (-21+42 x-42 x^2+28 x^3+50 x^4+108 x^5+52 x^6+8 x^7\right )}{x} \, dx+8 \int e^{2 x} x^3 (1+x) (4+x) \left (8+19 x+9 x^2+x^3\right ) \log ^2(x) \, dx-40 \int e^x x^2 (4+x) \left (12+25 x+11 x^2+x^3\right ) \log ^2(x) \, dx+400 \int x \left (8+6 x+x^2\right ) \log ^2(x) \, dx\\ &=1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+1600 x^2 \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)+\frac {1600}{3} x^3 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)+50 x^4 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)-\frac {1}{6} \int \left (100 x \left (96+32 x+3 x^2\right )-\frac {480 e^x \left (-16+16 x-8 x^2+8 x^3+4 x^4+x^5\right )}{x}+\frac {3 e^{2 x} \left (-21+42 x-42 x^2+28 x^3+50 x^4+108 x^5+52 x^6+8 x^7\right )}{x}\right ) \, dx+8 \int \left (32 e^{2 x} x^3 \log ^2(x)+116 e^{2 x} x^4 \log ^2(x)+139 e^{2 x} x^5 \log ^2(x)+68 e^{2 x} x^6 \log ^2(x)+14 e^{2 x} x^7 \log ^2(x)+e^{2 x} x^8 \log ^2(x)\right ) \, dx-40 \int \left (48 e^x x^2 \log ^2(x)+112 e^x x^3 \log ^2(x)+69 e^x x^4 \log ^2(x)+15 e^x x^5 \log ^2(x)+e^x x^6 \log ^2(x)\right ) \, dx+400 \int \left (8 x \log ^2(x)+6 x^2 \log ^2(x)+x^3 \log ^2(x)\right ) \, dx\\ &=1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+1600 x^2 \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)+\frac {1600}{3} x^3 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)+50 x^4 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)-\frac {1}{2} \int \frac {e^{2 x} \left (-21+42 x-42 x^2+28 x^3+50 x^4+108 x^5+52 x^6+8 x^7\right )}{x} \, dx+8 \int e^{2 x} x^8 \log ^2(x) \, dx-\frac {50}{3} \int x \left (96+32 x+3 x^2\right ) \, dx-40 \int e^x x^6 \log ^2(x) \, dx+80 \int \frac {e^x \left (-16+16 x-8 x^2+8 x^3+4 x^4+x^5\right )}{x} \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+400 \int x^3 \log ^2(x) \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx-1920 \int e^x x^2 \log ^2(x) \, dx+2400 \int x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx+3200 \int x \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+1600 x^2 \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)+\frac {1600}{3} x^3 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)+50 x^4 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)-\frac {1}{2} \int \left (42 e^{2 x}-\frac {21 e^{2 x}}{x}-42 e^{2 x} x+28 e^{2 x} x^2+50 e^{2 x} x^3+108 e^{2 x} x^4+52 e^{2 x} x^5+8 e^{2 x} x^6\right ) \, dx+8 \int e^{2 x} x^8 \log ^2(x) \, dx-\frac {50}{3} \int \left (96 x+32 x^2+3 x^3\right ) \, dx-40 \int e^x x^6 \log ^2(x) \, dx+80 \int \left (16 e^x-\frac {16 e^x}{x}-8 e^x x+8 e^x x^2+4 e^x x^3+e^x x^4\right ) \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx-200 \int x^3 \log (x) \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx-1600 \int x^2 \log (x) \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-3200 \int x \log (x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)-4 \int e^{2 x} x^6 \, dx+8 \int e^{2 x} x^8 \log ^2(x) \, dx+\frac {21}{2} \int \frac {e^{2 x}}{x} \, dx-14 \int e^{2 x} x^2 \, dx-21 \int e^{2 x} \, dx+21 \int e^{2 x} x \, dx-25 \int e^{2 x} x^3 \, dx-26 \int e^{2 x} x^5 \, dx-40 \int e^x x^6 \log ^2(x) \, dx-54 \int e^{2 x} x^4 \, dx+80 \int e^x x^4 \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+320 \int e^x x^3 \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx-640 \int e^x x \, dx+640 \int e^x x^2 \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx+1280 \int e^x \, dx-1280 \int \frac {e^x}{x} \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=1280 e^x-\frac {21 e^{2 x}}{2}-640 e^x x+\frac {21}{2} e^{2 x} x+640 e^x x^2-7 e^{2 x} x^2+320 e^x x^3-\frac {25}{2} e^{2 x} x^3+80 e^x x^4-27 e^{2 x} x^4-13 e^{2 x} x^5-2 e^{2 x} x^6-1280 \text {Ei}(x)+\frac {21 \text {Ei}(2 x)}{2}+1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)+8 \int e^{2 x} x^8 \log ^2(x) \, dx-\frac {21}{2} \int e^{2 x} \, dx+12 \int e^{2 x} x^5 \, dx+14 \int e^{2 x} x \, dx+\frac {75}{2} \int e^{2 x} x^2 \, dx-40 \int e^x x^6 \log ^2(x) \, dx+65 \int e^{2 x} x^4 \, dx+108 \int e^{2 x} x^3 \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx-320 \int e^x x^3 \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+640 \int e^x \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx-960 \int e^x x^2 \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx-1280 \int e^x x \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=1920 e^x-\frac {63 e^{2 x}}{4}-1920 e^x x+\frac {35}{2} e^{2 x} x-320 e^x x^2+\frac {47}{4} e^{2 x} x^2+\frac {83}{2} e^{2 x} x^3+80 e^x x^4+\frac {11}{2} e^{2 x} x^4-7 e^{2 x} x^5-2 e^{2 x} x^6-1280 \text {Ei}(x)+\frac {21 \text {Ei}(2 x)}{2}+1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)-7 \int e^{2 x} \, dx+8 \int e^{2 x} x^8 \log ^2(x) \, dx-30 \int e^{2 x} x^4 \, dx-\frac {75}{2} \int e^{2 x} x \, dx-40 \int e^x x^6 \log ^2(x) \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx-130 \int e^{2 x} x^3 \, dx-162 \int e^{2 x} x^2 \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+960 \int e^x x^2 \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx+1280 \int e^x \, dx+1920 \int e^x x \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=3200 e^x-\frac {77 e^{2 x}}{4}-\frac {5}{4} e^{2 x} x+640 e^x x^2-\frac {277}{4} e^{2 x} x^2-\frac {47}{2} e^{2 x} x^3+80 e^x x^4-\frac {19}{2} e^{2 x} x^4-7 e^{2 x} x^5-2 e^{2 x} x^6-1280 \text {Ei}(x)+\frac {21 \text {Ei}(2 x)}{2}+1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)+8 \int e^{2 x} x^8 \log ^2(x) \, dx+\frac {75}{4} \int e^{2 x} \, dx-40 \int e^x x^6 \log ^2(x) \, dx+60 \int e^{2 x} x^3 \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx+162 \int e^{2 x} x \, dx+195 \int e^{2 x} x^2 \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx-1920 \int e^x \, dx-1920 \int e^x x \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=1280 e^x-\frac {79 e^{2 x}}{8}-1920 e^x x+\frac {319}{4} e^{2 x} x+640 e^x x^2+\frac {113}{4} e^{2 x} x^2+\frac {13}{2} e^{2 x} x^3+80 e^x x^4-\frac {19}{2} e^{2 x} x^4-7 e^{2 x} x^5-2 e^{2 x} x^6-1280 \text {Ei}(x)+\frac {21 \text {Ei}(2 x)}{2}+1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)+8 \int e^{2 x} x^8 \log ^2(x) \, dx-40 \int e^x x^6 \log ^2(x) \, dx-81 \int e^{2 x} \, dx-90 \int e^{2 x} x^2 \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx-195 \int e^{2 x} x \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx+1920 \int e^x \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=3200 e^x-\frac {403 e^{2 x}}{8}-1920 e^x x-\frac {71}{4} e^{2 x} x+640 e^x x^2-\frac {67}{4} e^{2 x} x^2+\frac {13}{2} e^{2 x} x^3+80 e^x x^4-\frac {19}{2} e^{2 x} x^4-7 e^{2 x} x^5-2 e^{2 x} x^6-1280 \text {Ei}(x)+\frac {21 \text {Ei}(2 x)}{2}+1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)+8 \int e^{2 x} x^8 \log ^2(x) \, dx-40 \int e^x x^6 \log ^2(x) \, dx+90 \int e^{2 x} x \, dx+\frac {195}{2} \int e^{2 x} \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=3200 e^x-\frac {13 e^{2 x}}{8}-1920 e^x x+\frac {109}{4} e^{2 x} x+640 e^x x^2-\frac {67}{4} e^{2 x} x^2+\frac {13}{2} e^{2 x} x^3+80 e^x x^4-\frac {19}{2} e^{2 x} x^4-7 e^{2 x} x^5-2 e^{2 x} x^6-1280 \text {Ei}(x)+\frac {21 \text {Ei}(2 x)}{2}+1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)+8 \int e^{2 x} x^8 \log ^2(x) \, dx-40 \int e^x x^6 \log ^2(x) \, dx-45 \int e^{2 x} \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ &=3200 e^x-\frac {193 e^{2 x}}{8}-1920 e^x x+\frac {109}{4} e^{2 x} x+640 e^x x^2-\frac {67}{4} e^{2 x} x^2+\frac {13}{2} e^{2 x} x^3+80 e^x x^4-\frac {19}{2} e^{2 x} x^4-7 e^{2 x} x^5-2 e^{2 x} x^6-1280 \text {Ei}(x)+\frac {21 \text {Ei}(2 x)}{2}+1280 e^x \log (x)-\frac {21}{2} e^{2 x} \log (x)-1280 e^x x \log (x)+21 e^{2 x} x \log (x)+640 e^x x^2 \log (x)-21 e^{2 x} x^2 \log (x)-640 e^x x^3 \log (x)+14 e^{2 x} x^3 \log (x)-320 e^x x^4 \log (x)+25 e^{2 x} x^4 \log (x)-80 e^x x^5 \log (x)+54 e^{2 x} x^5 \log (x)+26 e^{2 x} x^6 \log (x)+4 e^{2 x} x^7 \log (x)+1600 x^2 \log ^2(x)+800 x^3 \log ^2(x)+100 x^4 \log ^2(x)+8 \int e^{2 x} x^8 \log ^2(x) \, dx-40 \int e^x x^6 \log ^2(x) \, dx+112 \int e^{2 x} x^7 \log ^2(x) \, dx+256 \int e^{2 x} x^3 \log ^2(x) \, dx+544 \int e^{2 x} x^6 \log ^2(x) \, dx-600 \int e^x x^5 \log ^2(x) \, dx+928 \int e^{2 x} x^4 \log ^2(x) \, dx+1112 \int e^{2 x} x^5 \log ^2(x) \, dx-1920 \int e^x x^2 \log ^2(x) \, dx-2760 \int e^x x^4 \log ^2(x) \, dx-4480 \int e^x x^3 \log ^2(x) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [C]  time = 3.07, size = 769, normalized size = 29.58 \begin {gather*} 8 \left (-\frac {25491}{64}+\frac {1899 x^2}{8}-\frac {907 x^4}{16}-\frac {7 x^6}{3}+\frac {89 x^8}{24}+\frac {17 x^{10}}{30}+\frac {x^{12}}{45}+\frac {21}{32} e^{2 x} (-1+2 x) \Gamma (2,2 x)+80 e^x \Gamma (3,x)-80 e^x x \Gamma (3,x)+40 e^x x^2 \Gamma (3,x)-\frac {7}{32} e^{2 x} \Gamma (3,2 x)+\frac {7}{16} e^{2 x} x \Gamma (3,2 x)-\frac {7}{16} e^{2 x} x^2 \Gamma (3,2 x)-40 e^x \Gamma (4,x)+40 e^x x \Gamma (4,x)-20 e^x x^2 \Gamma (4,x)+\frac {20}{3} e^x x^3 \Gamma (4,x)+\frac {25}{128} e^{2 x} \Gamma (4,2 x)-\frac {25}{64} e^{2 x} x \Gamma (4,2 x)+\frac {25}{64} e^{2 x} x^2 \Gamma (4,2 x)-\frac {25}{96} e^{2 x} x^3 \Gamma (4,2 x)+10 e^x \Gamma (5,x)-10 e^x x \Gamma (5,x)+5 e^x x^2 \Gamma (5,x)-\frac {5}{3} e^x x^3 \Gamma (5,x)+\frac {5}{12} e^x x^4 \Gamma (5,x)-\frac {27}{128} e^{2 x} \Gamma (5,2 x)+\frac {27}{64} e^{2 x} x \Gamma (5,2 x)-\frac {27}{64} e^{2 x} x^2 \Gamma (5,2 x)+\frac {9}{32} e^{2 x} x^3 \Gamma (5,2 x)-\frac {9}{64} e^{2 x} x^4 \Gamma (5,2 x)+\frac {13}{256} e^{2 x} \Gamma (6,2 x)-\frac {13}{128} e^{2 x} x \Gamma (6,2 x)+\frac {13}{128} e^{2 x} x^2 \Gamma (6,2 x)-\frac {13}{192} e^{2 x} x^3 \Gamma (6,2 x)+\frac {13}{384} e^{2 x} x^4 \Gamma (6,2 x)-\frac {13}{960} e^{2 x} x^5 \Gamma (6,2 x)-\frac {1}{256} e^{2 x} \Gamma (7,2 x)+\frac {1}{128} e^{2 x} x \Gamma (7,2 x)-\frac {1}{128} e^{2 x} x^2 \Gamma (7,2 x)+\frac {1}{192} e^{2 x} x^3 \Gamma (7,2 x)-\frac {1}{384} e^{2 x} x^4 \Gamma (7,2 x)+\frac {1}{960} e^{2 x} x^5 \Gamma (7,2 x)-\frac {e^{2 x} x^6 \Gamma (7,2 x)}{2880}-480 \log (x)+480 x^2 \log (x)+200 x^2 \log ^2(x)+100 x^3 \log ^2(x)-80 e^x x^3 \log ^2(x)+\frac {25}{2} x^4 \log ^2(x)-120 e^x x^4 \log ^2(x)+8 e^{2 x} x^4 \log ^2(x)-45 e^x x^5 \log ^2(x)+20 e^{2 x} x^5 \log ^2(x)-5 e^x x^6 \log ^2(x)+\frac {33}{2} e^{2 x} x^6 \log ^2(x)+5 e^{2 x} x^7 \log ^2(x)+\frac {1}{2} e^{2 x} x^8 \log ^2(x)-240 e^x (-1+x) \Gamma (2,x) (1+2 \log (x))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3200*x + 1600*x^2 + 200*x^3 + E^x*(-1280*x^2 - 1920*x^3 - 720*x^4 - 80*x^5) + E^(2*x)*(128*x^3 + 32
0*x^4 + 264*x^5 + 80*x^6 + 8*x^7))*Log[x] + (3200*x + 2400*x^2 + 400*x^3 + E^x*(-1920*x^2 - 4480*x^3 - 2760*x^
4 - 600*x^5 - 40*x^6) + E^(2*x)*(256*x^3 + 928*x^4 + 1112*x^5 + 544*x^6 + 112*x^7 + 8*x^8))*Log[x]^2,x]

[Out]

8*(-25491/64 + (1899*x^2)/8 - (907*x^4)/16 - (7*x^6)/3 + (89*x^8)/24 + (17*x^10)/30 + x^12/45 + (21*E^(2*x)*(-
1 + 2*x)*Gamma[2, 2*x])/32 + 80*E^x*Gamma[3, x] - 80*E^x*x*Gamma[3, x] + 40*E^x*x^2*Gamma[3, x] - (7*E^(2*x)*G
amma[3, 2*x])/32 + (7*E^(2*x)*x*Gamma[3, 2*x])/16 - (7*E^(2*x)*x^2*Gamma[3, 2*x])/16 - 40*E^x*Gamma[4, x] + 40
*E^x*x*Gamma[4, x] - 20*E^x*x^2*Gamma[4, x] + (20*E^x*x^3*Gamma[4, x])/3 + (25*E^(2*x)*Gamma[4, 2*x])/128 - (2
5*E^(2*x)*x*Gamma[4, 2*x])/64 + (25*E^(2*x)*x^2*Gamma[4, 2*x])/64 - (25*E^(2*x)*x^3*Gamma[4, 2*x])/96 + 10*E^x
*Gamma[5, x] - 10*E^x*x*Gamma[5, x] + 5*E^x*x^2*Gamma[5, x] - (5*E^x*x^3*Gamma[5, x])/3 + (5*E^x*x^4*Gamma[5,
x])/12 - (27*E^(2*x)*Gamma[5, 2*x])/128 + (27*E^(2*x)*x*Gamma[5, 2*x])/64 - (27*E^(2*x)*x^2*Gamma[5, 2*x])/64
+ (9*E^(2*x)*x^3*Gamma[5, 2*x])/32 - (9*E^(2*x)*x^4*Gamma[5, 2*x])/64 + (13*E^(2*x)*Gamma[6, 2*x])/256 - (13*E
^(2*x)*x*Gamma[6, 2*x])/128 + (13*E^(2*x)*x^2*Gamma[6, 2*x])/128 - (13*E^(2*x)*x^3*Gamma[6, 2*x])/192 + (13*E^
(2*x)*x^4*Gamma[6, 2*x])/384 - (13*E^(2*x)*x^5*Gamma[6, 2*x])/960 - (E^(2*x)*Gamma[7, 2*x])/256 + (E^(2*x)*x*G
amma[7, 2*x])/128 - (E^(2*x)*x^2*Gamma[7, 2*x])/128 + (E^(2*x)*x^3*Gamma[7, 2*x])/192 - (E^(2*x)*x^4*Gamma[7,
2*x])/384 + (E^(2*x)*x^5*Gamma[7, 2*x])/960 - (E^(2*x)*x^6*Gamma[7, 2*x])/2880 - 480*Log[x] + 480*x^2*Log[x] +
200*x^2*Log[x]^2 + 100*x^3*Log[x]^2 - 80*E^x*x^3*Log[x]^2 + (25*x^4*Log[x]^2)/2 - 120*E^x*x^4*Log[x]^2 + 8*E^
(2*x)*x^4*Log[x]^2 - 45*E^x*x^5*Log[x]^2 + 20*E^(2*x)*x^5*Log[x]^2 - 5*E^x*x^6*Log[x]^2 + (33*E^(2*x)*x^6*Log[
x]^2)/2 + 5*E^(2*x)*x^7*Log[x]^2 + (E^(2*x)*x^8*Log[x]^2)/2 - 240*E^x*(-1 + x)*Gamma[2, x]*(1 + 2*Log[x]))

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fricas [B]  time = 0.67, size = 74, normalized size = 2.85 \begin {gather*} 4 \, {\left (25 \, x^{4} + 200 \, x^{3} + 400 \, x^{2} + {\left (x^{8} + 10 \, x^{7} + 33 \, x^{6} + 40 \, x^{5} + 16 \, x^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left (x^{6} + 9 \, x^{5} + 24 \, x^{4} + 16 \, x^{3}\right )} e^{x}\right )} \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^8+112*x^7+544*x^6+1112*x^5+928*x^4+256*x^3)*exp(x)^2+(-40*x^6-600*x^5-2760*x^4-4480*x^3-1920*x
^2)*exp(x)+400*x^3+2400*x^2+3200*x)*log(x)^2+((8*x^7+80*x^6+264*x^5+320*x^4+128*x^3)*exp(x)^2+(-80*x^5-720*x^4
-1920*x^3-1280*x^2)*exp(x)+200*x^3+1600*x^2+3200*x)*log(x),x, algorithm="fricas")

[Out]

4*(25*x^4 + 200*x^3 + 400*x^2 + (x^8 + 10*x^7 + 33*x^6 + 40*x^5 + 16*x^4)*e^(2*x) - 10*(x^6 + 9*x^5 + 24*x^4 +
16*x^3)*e^x)*log(x)^2

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giac [B]  time = 0.17, size = 137, normalized size = 5.27 \begin {gather*} 4 \, x^{8} e^{\left (2 \, x\right )} \log \relax (x)^{2} + 40 \, x^{7} e^{\left (2 \, x\right )} \log \relax (x)^{2} + 132 \, x^{6} e^{\left (2 \, x\right )} \log \relax (x)^{2} - 40 \, x^{6} e^{x} \log \relax (x)^{2} + 160 \, x^{5} e^{\left (2 \, x\right )} \log \relax (x)^{2} - 360 \, x^{5} e^{x} \log \relax (x)^{2} + 64 \, x^{4} e^{\left (2 \, x\right )} \log \relax (x)^{2} - 960 \, x^{4} e^{x} \log \relax (x)^{2} + 100 \, x^{4} \log \relax (x)^{2} - 640 \, x^{3} e^{x} \log \relax (x)^{2} + 800 \, x^{3} \log \relax (x)^{2} + 1600 \, x^{2} \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^8+112*x^7+544*x^6+1112*x^5+928*x^4+256*x^3)*exp(x)^2+(-40*x^6-600*x^5-2760*x^4-4480*x^3-1920*x
^2)*exp(x)+400*x^3+2400*x^2+3200*x)*log(x)^2+((8*x^7+80*x^6+264*x^5+320*x^4+128*x^3)*exp(x)^2+(-80*x^5-720*x^4
-1920*x^3-1280*x^2)*exp(x)+200*x^3+1600*x^2+3200*x)*log(x),x, algorithm="giac")

[Out]

4*x^8*e^(2*x)*log(x)^2 + 40*x^7*e^(2*x)*log(x)^2 + 132*x^6*e^(2*x)*log(x)^2 - 40*x^6*e^x*log(x)^2 + 160*x^5*e^
(2*x)*log(x)^2 - 360*x^5*e^x*log(x)^2 + 64*x^4*e^(2*x)*log(x)^2 - 960*x^4*e^x*log(x)^2 + 100*x^4*log(x)^2 - 64
0*x^3*e^x*log(x)^2 + 800*x^3*log(x)^2 + 1600*x^2*log(x)^2

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maple [B]  time = 0.13, size = 138, normalized size = 5.31

method	result	size
risch	\(4 \ln \relax (x )^{2} {\mathrm e}^{2 x} x^{8}+40 \ln \relax (x )^{2} {\mathrm e}^{2 x} x^{7}+132 \ln \relax (x )^{2} {\mathrm e}^{2 x} x^{6}+160 \ln \relax (x )^{2} {\mathrm e}^{2 x} x^{5}-40 \ln \relax (x )^{2} {\mathrm e}^{x} x^{6}+64 \ln \relax (x )^{2} {\mathrm e}^{2 x} x^{4}-360 \ln \relax (x )^{2} {\mathrm e}^{x} x^{5}-960 x^{4} {\mathrm e}^{x} \ln \relax (x )^{2}-640 \ln \relax (x )^{2} {\mathrm e}^{x} x^{3}+100 x^{4} \ln \relax (x )^{2}+800 x^{3} \ln \relax (x )^{2}+1600 x^{2} \ln \relax (x )^{2}\)	\(138\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((8*x^8+112*x^7+544*x^6+1112*x^5+928*x^4+256*x^3)*exp(x)^2+(-40*x^6-600*x^5-2760*x^4-4480*x^3-1920*x^2)*ex
p(x)+400*x^3+2400*x^2+3200*x)*ln(x)^2+((8*x^7+80*x^6+264*x^5+320*x^4+128*x^3)*exp(x)^2+(-80*x^5-720*x^4-1920*x
^3-1280*x^2)*exp(x)+200*x^3+1600*x^2+3200*x)*ln(x),x,method=_RETURNVERBOSE)

[Out]

4*ln(x)^2*exp(2*x)*x^8+40*ln(x)^2*exp(2*x)*x^7+132*ln(x)^2*exp(2*x)*x^6+160*ln(x)^2*exp(2*x)*x^5-40*ln(x)^2*ex
p(x)*x^6+64*ln(x)^2*exp(2*x)*x^4-360*ln(x)^2*exp(x)*x^5-960*x^4*exp(x)*ln(x)^2-640*ln(x)^2*exp(x)*x^3+100*x^4*
ln(x)^2+800*x^3*ln(x)^2+1600*x^2*ln(x)^2

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maxima [B]  time = 0.39, size = 82, normalized size = 3.15 \begin {gather*} 4 \, {\left (x^{8} + 10 \, x^{7} + 33 \, x^{6} + 40 \, x^{5} + 16 \, x^{4}\right )} e^{\left (2 \, x\right )} \log \relax (x)^{2} - 40 \, {\left (x^{6} + 9 \, x^{5} + 24 \, x^{4} + 16 \, x^{3}\right )} e^{x} \log \relax (x)^{2} + 100 \, {\left (x^{4} + 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^8+112*x^7+544*x^6+1112*x^5+928*x^4+256*x^3)*exp(x)^2+(-40*x^6-600*x^5-2760*x^4-4480*x^3-1920*x
^2)*exp(x)+400*x^3+2400*x^2+3200*x)*log(x)^2+((8*x^7+80*x^6+264*x^5+320*x^4+128*x^3)*exp(x)^2+(-80*x^5-720*x^4
-1920*x^3-1280*x^2)*exp(x)+200*x^3+1600*x^2+3200*x)*log(x),x, algorithm="maxima")

[Out]

4*(x^8 + 10*x^7 + 33*x^6 + 40*x^5 + 16*x^4)*e^(2*x)*log(x)^2 - 40*(x^6 + 9*x^5 + 24*x^4 + 16*x^3)*e^x*log(x)^2
+ 100*(x^4 + 8*x^3 + 16*x^2)*log(x)^2

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mupad [B]  time = 4.18, size = 77, normalized size = 2.96 \begin {gather*} {\ln \relax (x)}^2\,\left ({\mathrm {e}}^{2\,x}\,\left (4\,x^8+40\,x^7+132\,x^6+160\,x^5+64\,x^4\right )-{\mathrm {e}}^x\,\left (40\,x^6+360\,x^5+960\,x^4+640\,x^3\right )+1600\,x^2+800\,x^3+100\,x^4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x)^2*(3200*x + exp(2*x)*(256*x^3 + 928*x^4 + 1112*x^5 + 544*x^6 + 112*x^7 + 8*x^8) - exp(x)*(1920*x^2
+ 4480*x^3 + 2760*x^4 + 600*x^5 + 40*x^6) + 2400*x^2 + 400*x^3) + log(x)*(3200*x + exp(2*x)*(128*x^3 + 320*x^4
+ 264*x^5 + 80*x^6 + 8*x^7) - exp(x)*(1280*x^2 + 1920*x^3 + 720*x^4 + 80*x^5) + 1600*x^2 + 200*x^3),x)

[Out]

log(x)^2*(exp(2*x)*(64*x^4 + 160*x^5 + 132*x^6 + 40*x^7 + 4*x^8) - exp(x)*(640*x^3 + 960*x^4 + 360*x^5 + 40*x^
6) + 1600*x^2 + 800*x^3 + 100*x^4)

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sympy [B]  time = 0.62, size = 121, normalized size = 4.65 \begin {gather*} \left (100 x^{4} + 800 x^{3} + 1600 x^{2}\right ) \log {\relax (x )}^{2} + \left (- 40 x^{6} \log {\relax (x )}^{2} - 360 x^{5} \log {\relax (x )}^{2} - 960 x^{4} \log {\relax (x )}^{2} - 640 x^{3} \log {\relax (x )}^{2}\right ) e^{x} + \left (4 x^{8} \log {\relax (x )}^{2} + 40 x^{7} \log {\relax (x )}^{2} + 132 x^{6} \log {\relax (x )}^{2} + 160 x^{5} \log {\relax (x )}^{2} + 64 x^{4} \log {\relax (x )}^{2}\right ) e^{2 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x**8+112*x**7+544*x**6+1112*x**5+928*x**4+256*x**3)*exp(x)**2+(-40*x**6-600*x**5-2760*x**4-4480*
x**3-1920*x**2)*exp(x)+400*x**3+2400*x**2+3200*x)*ln(x)**2+((8*x**7+80*x**6+264*x**5+320*x**4+128*x**3)*exp(x)
**2+(-80*x**5-720*x**4-1920*x**3-1280*x**2)*exp(x)+200*x**3+1600*x**2+3200*x)*ln(x),x)

[Out]

(100*x**4 + 800*x**3 + 1600*x**2)*log(x)**2 + (-40*x**6*log(x)**2 - 360*x**5*log(x)**2 - 960*x**4*log(x)**2 -
640*x**3*log(x)**2)*exp(x) + (4*x**8*log(x)**2 + 40*x**7*log(x)**2 + 132*x**6*log(x)**2 + 160*x**5*log(x)**2 +
64*x**4*log(x)**2)*exp(2*x)

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