3.33.80 \(\int \frac {e^{5 x} (-396+4 e^3+80 x-4 x^2)+e^{4 x} (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 (16 x-16 x^2))+e^{3 x} (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 (24 x^2-48 x^3+24 x^4))+e^{2 x} (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 (16 x^3-48 x^4+48 x^5-16 x^6))+e^x (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8))}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 (x^4-4 x^5+6 x^6-4 x^7+x^8)+e^3 (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10})+e^{4 x} (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 (-162+36 x-2 x^2))+e^{3 x} (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 (4 x-4 x^2)+e^3 (-648 x+792 x^2-152 x^3+8 x^4))+e^{2 x} (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 (6 x^2-12 x^3+6 x^4)+e^3 (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6))+e^x (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 (4 x^3-12 x^4+12 x^5-4 x^6)+e^3 (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8))} \, dx\)
Optimal. Leaf size=34 \[ \frac {4 e^x}{e^3-(9-x)^2-\frac {4}{\left (e^x+x-x^2\right )^2}} \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(E^(5*x)*(-396 + 4*E^3 + 80*x - 4*x^2) + E^(4*x)*(-1584*x + 1904*x^2 - 336*x^3 + 16*x^4 + E^3*(16*x - 16*x
^2)) + E^(3*x)*(-48 - 2376*x^2 + 5232*x^3 - 3360*x^4 + 528*x^5 - 24*x^6 + E^3*(24*x^2 - 48*x^3 + 24*x^4)) + E^
(2*x)*(-32 + 64*x^2 - 1584*x^3 + 5072*x^4 - 5728*x^5 + 2592*x^6 - 368*x^7 + 16*x^8 + E^3*(16*x^3 - 48*x^4 + 48
*x^5 - 16*x^6)) + E^x*(-32*x + 80*x^2 - 32*x^3 - 412*x^4 + 1664*x^5 - 2700*x^6 + 2080*x^7 - 740*x^8 + 96*x^9 -
4*x^10 + E^3*(4*x^4 - 16*x^5 + 24*x^6 - 16*x^7 + 4*x^8)))/(16 + 648*x^2 - 1440*x^3 + 7505*x^4 - 29320*x^5 + 5
1524*x^6 - 45720*x^7 + 21286*x^8 - 5080*x^9 + 636*x^10 - 40*x^11 + x^12 + E^6*(x^4 - 4*x^5 + 6*x^6 - 4*x^7 + x
^8) + E^3*(-8*x^2 + 16*x^3 - 170*x^4 + 684*x^5 - 1118*x^6 + 872*x^7 - 318*x^8 + 44*x^9 - 2*x^10) + E^(4*x)*(65
61 + E^6 - 2916*x + 486*x^2 - 36*x^3 + x^4 + E^3*(-162 + 36*x - 2*x^2)) + E^(3*x)*(26244*x - 37908*x^2 + 13608
*x^3 - 2088*x^4 + 148*x^5 - 4*x^6 + E^6*(4*x - 4*x^2) + E^3*(-648*x + 792*x^2 - 152*x^3 + 8*x^4)) + E^(2*x)*(6
48 - 144*x + 39374*x^2 - 96228*x^3 + 77274*x^4 - 23544*x^5 + 3354*x^6 - 228*x^7 + 6*x^8 + E^6*(6*x^2 - 12*x^3
+ 6*x^4) + E^3*(-8 - 972*x^2 + 2160*x^3 - 1416*x^4 + 240*x^5 - 12*x^6)) + E^x*(1296*x - 1584*x^2 + 26548*x^3 -
90412*x^4 + 115668*x^5 - 67212*x^6 + 17932*x^7 - 2388*x^8 + 156*x^9 - 4*x^10 + E^6*(4*x^3 - 12*x^4 + 12*x^5 -
4*x^6) + E^3*(-16*x + 16*x^2 - 648*x^3 + 2088*x^4 - 2384*x^5 + 1104*x^6 - 168*x^7 + 8*x^8))),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [B] time = 0.40, size = 102, normalized size = 3.00 \begin {gather*} -\frac {4 e^x \left (e^x+x-x^2\right )^2}{4-e^{3+2 x}+e^{2 x} (-9+x)^2+2 e^{3+x} (-1+x) x-2 e^x (-9+x)^2 (-1+x) x+81 x^2-e^3 (-1+x)^2 x^2-180 x^3+118 x^4-20 x^5+x^6} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^(5*x)*(-396 + 4*E^3 + 80*x - 4*x^2) + E^(4*x)*(-1584*x + 1904*x^2 - 336*x^3 + 16*x^4 + E^3*(16*x
- 16*x^2)) + E^(3*x)*(-48 - 2376*x^2 + 5232*x^3 - 3360*x^4 + 528*x^5 - 24*x^6 + E^3*(24*x^2 - 48*x^3 + 24*x^4)
) + E^(2*x)*(-32 + 64*x^2 - 1584*x^3 + 5072*x^4 - 5728*x^5 + 2592*x^6 - 368*x^7 + 16*x^8 + E^3*(16*x^3 - 48*x^
4 + 48*x^5 - 16*x^6)) + E^x*(-32*x + 80*x^2 - 32*x^3 - 412*x^4 + 1664*x^5 - 2700*x^6 + 2080*x^7 - 740*x^8 + 96
*x^9 - 4*x^10 + E^3*(4*x^4 - 16*x^5 + 24*x^6 - 16*x^7 + 4*x^8)))/(16 + 648*x^2 - 1440*x^3 + 7505*x^4 - 29320*x
^5 + 51524*x^6 - 45720*x^7 + 21286*x^8 - 5080*x^9 + 636*x^10 - 40*x^11 + x^12 + E^6*(x^4 - 4*x^5 + 6*x^6 - 4*x
^7 + x^8) + E^3*(-8*x^2 + 16*x^3 - 170*x^4 + 684*x^5 - 1118*x^6 + 872*x^7 - 318*x^8 + 44*x^9 - 2*x^10) + E^(4*
x)*(6561 + E^6 - 2916*x + 486*x^2 - 36*x^3 + x^4 + E^3*(-162 + 36*x - 2*x^2)) + E^(3*x)*(26244*x - 37908*x^2 +
13608*x^3 - 2088*x^4 + 148*x^5 - 4*x^6 + E^6*(4*x - 4*x^2) + E^3*(-648*x + 792*x^2 - 152*x^3 + 8*x^4)) + E^(2
*x)*(648 - 144*x + 39374*x^2 - 96228*x^3 + 77274*x^4 - 23544*x^5 + 3354*x^6 - 228*x^7 + 6*x^8 + E^6*(6*x^2 - 1
2*x^3 + 6*x^4) + E^3*(-8 - 972*x^2 + 2160*x^3 - 1416*x^4 + 240*x^5 - 12*x^6)) + E^x*(1296*x - 1584*x^2 + 26548
*x^3 - 90412*x^4 + 115668*x^5 - 67212*x^6 + 17932*x^7 - 2388*x^8 + 156*x^9 - 4*x^10 + E^6*(4*x^3 - 12*x^4 + 12
*x^5 - 4*x^6) + E^3*(-16*x + 16*x^2 - 648*x^3 + 2088*x^4 - 2384*x^5 + 1104*x^6 - 168*x^7 + 8*x^8))),x]
[Out]
(-4*E^x*(E^x + x - x^2)^2)/(4 - E^(3 + 2*x) + E^(2*x)*(-9 + x)^2 + 2*E^(3 + x)*(-1 + x)*x - 2*E^x*(-9 + x)^2*(
-1 + x)*x + 81*x^2 - E^3*(-1 + x)^2*x^2 - 180*x^3 + 118*x^4 - 20*x^5 + x^6)
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fricas [B] time = 0.66, size = 130, normalized size = 3.82 \begin {gather*} \frac {4 \, {\left (2 \, {\left (x^{2} - x\right )} e^{\left (2 \, x\right )} - {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{x} - e^{\left (3 \, x\right )}\right )}}{x^{6} - 20 \, x^{5} + 118 \, x^{4} - 180 \, x^{3} + 81 \, x^{2} - {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{3} + {\left (x^{2} - 18 \, x - e^{3} + 81\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{4} - 19 \, x^{3} + 99 \, x^{2} - {\left (x^{2} - x\right )} e^{3} - 81 \, x\right )} e^{x} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+
((24*x^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+
16*x^3)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16
*x^5+4*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(
3)^2+(-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+7
92*x^2-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)
^2+(-12*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+3
9374*x^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-
648*x^3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^
2+1296*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4
+16*x^3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3
+648*x^2+16),x, algorithm="fricas")
[Out]
4*(2*(x^2 - x)*e^(2*x) - (x^4 - 2*x^3 + x^2)*e^x - e^(3*x))/(x^6 - 20*x^5 + 118*x^4 - 180*x^3 + 81*x^2 - (x^4
- 2*x^3 + x^2)*e^3 + (x^2 - 18*x - e^3 + 81)*e^(2*x) - 2*(x^4 - 19*x^3 + 99*x^2 - (x^2 - x)*e^3 - 81*x)*e^x +
4)
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+
((24*x^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+
16*x^3)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16
*x^5+4*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(
3)^2+(-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+7
92*x^2-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)
^2+(-12*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+3
9374*x^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-
648*x^3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^
2+1296*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4
+16*x^3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3
+648*x^2+16),x, algorithm="giac")
[Out]
Timed out
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maple [F] time = 0.31, size = 0, normalized size = 0.00 \[\int \frac {\left (4 \,{\mathrm e}^{3}-4 x^{2}+80 x -396\right ) {\mathrm e}^{5 x}+\left (\left (-16 x^{2}+16 x \right ) {\mathrm e}^{3}+16 x^{4}-336 x^{3}+1904 x^{2}-1584 x \right ) {\mathrm e}^{4 x}+\left (\left (24 x^{4}-48 x^{3}+24 x^{2}\right ) {\mathrm e}^{3}-24 x^{6}+528 x^{5}-3360 x^{4}+5232 x^{3}-2376 x^{2}-48\right ) {\mathrm e}^{3 x}+\left (\left (-16 x^{6}+48 x^{5}-48 x^{4}+16 x^{3}\right ) {\mathrm e}^{3}+16 x^{8}-368 x^{7}+2592 x^{6}-5728 x^{5}+5072 x^{4}-1584 x^{3}+64 x^{2}-32\right ) {\mathrm e}^{2 x}+\left (\left (4 x^{8}-16 x^{7}+24 x^{6}-16 x^{5}+4 x^{4}\right ) {\mathrm e}^{3}-4 x^{10}+96 x^{9}-740 x^{8}+2080 x^{7}-2700 x^{6}+1664 x^{5}-412 x^{4}-32 x^{3}+80 x^{2}-32 x \right ) {\mathrm e}^{x}}{\left ({\mathrm e}^{6}+\left (-2 x^{2}+36 x -162\right ) {\mathrm e}^{3}+x^{4}-36 x^{3}+486 x^{2}-2916 x +6561\right ) {\mathrm e}^{4 x}+\left (\left (-4 x^{2}+4 x \right ) {\mathrm e}^{6}+\left (8 x^{4}-152 x^{3}+792 x^{2}-648 x \right ) {\mathrm e}^{3}-4 x^{6}+148 x^{5}-2088 x^{4}+13608 x^{3}-37908 x^{2}+26244 x \right ) {\mathrm e}^{3 x}+\left (\left (6 x^{4}-12 x^{3}+6 x^{2}\right ) {\mathrm e}^{6}+\left (-12 x^{6}+240 x^{5}-1416 x^{4}+2160 x^{3}-972 x^{2}-8\right ) {\mathrm e}^{3}+6 x^{8}-228 x^{7}+3354 x^{6}-23544 x^{5}+77274 x^{4}-96228 x^{3}+39374 x^{2}-144 x +648\right ) {\mathrm e}^{2 x}+\left (\left (-4 x^{6}+12 x^{5}-12 x^{4}+4 x^{3}\right ) {\mathrm e}^{6}+\left (8 x^{8}-168 x^{7}+1104 x^{6}-2384 x^{5}+2088 x^{4}-648 x^{3}+16 x^{2}-16 x \right ) {\mathrm e}^{3}-4 x^{10}+156 x^{9}-2388 x^{8}+17932 x^{7}-67212 x^{6}+115668 x^{5}-90412 x^{4}+26548 x^{3}-1584 x^{2}+1296 x \right ) {\mathrm e}^{x}+\left (x^{8}-4 x^{7}+6 x^{6}-4 x^{5}+x^{4}\right ) {\mathrm e}^{6}+\left (-2 x^{10}+44 x^{9}-318 x^{8}+872 x^{7}-1118 x^{6}+684 x^{5}-170 x^{4}+16 x^{3}-8 x^{2}\right ) {\mathrm e}^{3}+x^{12}-40 x^{11}+636 x^{10}-5080 x^{9}+21286 x^{8}-45720 x^{7}+51524 x^{6}-29320 x^{5}+7505 x^{4}-1440 x^{3}+648 x^{2}+16}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+((24*x
^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+16*x^3
)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16*x^5+4
*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(3)^2+(
-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+792*x^2
-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)^2+(-1
2*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+39374*x
^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-648*x^
3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^2+1296
*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4+16*x^
3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3+648*x
^2+16),x)
[Out]
int(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+((24*x
^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+16*x^3
)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16*x^5+4
*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(3)^2+(
-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+792*x^2
-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)^2+(-1
2*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+39374*x
^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-648*x^
3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^2+1296
*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4+16*x^
3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3+648*x
^2+16),x)
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maxima [B] time = 1.05, size = 122, normalized size = 3.59 \begin {gather*} \frac {4 \, {\left (2 \, {\left (x^{2} - x\right )} e^{\left (2 \, x\right )} - {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{x} - e^{\left (3 \, x\right )}\right )}}{x^{6} - 20 \, x^{5} - x^{4} {\left (e^{3} - 118\right )} + 2 \, x^{3} {\left (e^{3} - 90\right )} - x^{2} {\left (e^{3} - 81\right )} + {\left (x^{2} - 18 \, x - e^{3} + 81\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{4} - 19 \, x^{3} - x^{2} {\left (e^{3} - 99\right )} + x {\left (e^{3} - 81\right )}\right )} e^{x} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+
((24*x^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+
16*x^3)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16
*x^5+4*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(
3)^2+(-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+7
92*x^2-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)
^2+(-12*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+3
9374*x^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-
648*x^3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^
2+1296*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4
+16*x^3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3
+648*x^2+16),x, algorithm="maxima")
[Out]
4*(2*(x^2 - x)*e^(2*x) - (x^4 - 2*x^3 + x^2)*e^x - e^(3*x))/(x^6 - 20*x^5 - x^4*(e^3 - 118) + 2*x^3*(e^3 - 90)
- x^2*(e^3 - 81) + (x^2 - 18*x - e^3 + 81)*e^(2*x) - 2*(x^4 - 19*x^3 - x^2*(e^3 - 99) + x*(e^3 - 81))*e^x + 4
)
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{2\,x}\,\left (64\,x^2-1584\,x^3+5072\,x^4-5728\,x^5+2592\,x^6-368\,x^7+16\,x^8+{\mathrm {e}}^3\,\left (-16\,x^6+48\,x^5-48\,x^4+16\,x^3\right )-32\right )-{\mathrm {e}}^x\,\left (32\,x-{\mathrm {e}}^3\,\left (4\,x^8-16\,x^7+24\,x^6-16\,x^5+4\,x^4\right )-80\,x^2+32\,x^3+412\,x^4-1664\,x^5+2700\,x^6-2080\,x^7+740\,x^8-96\,x^9+4\,x^{10}\right )+{\mathrm {e}}^{4\,x}\,\left ({\mathrm {e}}^3\,\left (16\,x-16\,x^2\right )-1584\,x+1904\,x^2-336\,x^3+16\,x^4\right )+{\mathrm {e}}^{5\,x}\,\left (-4\,x^2+80\,x+4\,{\mathrm {e}}^3-396\right )-{\mathrm {e}}^{3\,x}\,\left (2376\,x^2-{\mathrm {e}}^3\,\left (24\,x^4-48\,x^3+24\,x^2\right )-5232\,x^3+3360\,x^4-528\,x^5+24\,x^6+48\right )}{{\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^6\,\left (6\,x^4-12\,x^3+6\,x^2\right )-{\mathrm {e}}^3\,\left (12\,x^6-240\,x^5+1416\,x^4-2160\,x^3+972\,x^2+8\right )-144\,x+39374\,x^2-96228\,x^3+77274\,x^4-23544\,x^5+3354\,x^6-228\,x^7+6\,x^8+648\right )-{\mathrm {e}}^3\,\left (2\,x^{10}-44\,x^9+318\,x^8-872\,x^7+1118\,x^6-684\,x^5+170\,x^4-16\,x^3+8\,x^2\right )+{\mathrm {e}}^6\,\left (x^8-4\,x^7+6\,x^6-4\,x^5+x^4\right )+{\mathrm {e}}^{4\,x}\,\left ({\mathrm {e}}^6-2916\,x-{\mathrm {e}}^3\,\left (2\,x^2-36\,x+162\right )+486\,x^2-36\,x^3+x^4+6561\right )+{\mathrm {e}}^{3\,x}\,\left (26244\,x+{\mathrm {e}}^6\,\left (4\,x-4\,x^2\right )-{\mathrm {e}}^3\,\left (-8\,x^4+152\,x^3-792\,x^2+648\,x\right )-37908\,x^2+13608\,x^3-2088\,x^4+148\,x^5-4\,x^6\right )+648\,x^2-1440\,x^3+7505\,x^4-29320\,x^5+51524\,x^6-45720\,x^7+21286\,x^8-5080\,x^9+636\,x^{10}-40\,x^{11}+x^{12}+{\mathrm {e}}^x\,\left (1296\,x-{\mathrm {e}}^3\,\left (-8\,x^8+168\,x^7-1104\,x^6+2384\,x^5-2088\,x^4+648\,x^3-16\,x^2+16\,x\right )-1584\,x^2+26548\,x^3-90412\,x^4+115668\,x^5-67212\,x^6+17932\,x^7-2388\,x^8+156\,x^9-4\,x^{10}+{\mathrm {e}}^6\,\left (-4\,x^6+12\,x^5-12\,x^4+4\,x^3\right )\right )+16} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp(2*x)*(64*x^2 - 1584*x^3 + 5072*x^4 - 5728*x^5 + 2592*x^6 - 368*x^7 + 16*x^8 + exp(3)*(16*x^3 - 48*x^4
+ 48*x^5 - 16*x^6) - 32) - exp(x)*(32*x - exp(3)*(4*x^4 - 16*x^5 + 24*x^6 - 16*x^7 + 4*x^8) - 80*x^2 + 32*x^3
+ 412*x^4 - 1664*x^5 + 2700*x^6 - 2080*x^7 + 740*x^8 - 96*x^9 + 4*x^10) + exp(4*x)*(exp(3)*(16*x - 16*x^2) -
1584*x + 1904*x^2 - 336*x^3 + 16*x^4) + exp(5*x)*(80*x + 4*exp(3) - 4*x^2 - 396) - exp(3*x)*(2376*x^2 - exp(3)
*(24*x^2 - 48*x^3 + 24*x^4) - 5232*x^3 + 3360*x^4 - 528*x^5 + 24*x^6 + 48))/(exp(2*x)*(exp(6)*(6*x^2 - 12*x^3
+ 6*x^4) - exp(3)*(972*x^2 - 2160*x^3 + 1416*x^4 - 240*x^5 + 12*x^6 + 8) - 144*x + 39374*x^2 - 96228*x^3 + 772
74*x^4 - 23544*x^5 + 3354*x^6 - 228*x^7 + 6*x^8 + 648) - exp(3)*(8*x^2 - 16*x^3 + 170*x^4 - 684*x^5 + 1118*x^6
- 872*x^7 + 318*x^8 - 44*x^9 + 2*x^10) + exp(6)*(x^4 - 4*x^5 + 6*x^6 - 4*x^7 + x^8) + exp(4*x)*(exp(6) - 2916
*x - exp(3)*(2*x^2 - 36*x + 162) + 486*x^2 - 36*x^3 + x^4 + 6561) + exp(3*x)*(26244*x + exp(6)*(4*x - 4*x^2) -
exp(3)*(648*x - 792*x^2 + 152*x^3 - 8*x^4) - 37908*x^2 + 13608*x^3 - 2088*x^4 + 148*x^5 - 4*x^6) + 648*x^2 -
1440*x^3 + 7505*x^4 - 29320*x^5 + 51524*x^6 - 45720*x^7 + 21286*x^8 - 5080*x^9 + 636*x^10 - 40*x^11 + x^12 + e
xp(x)*(1296*x - exp(3)*(16*x - 16*x^2 + 648*x^3 - 2088*x^4 + 2384*x^5 - 1104*x^6 + 168*x^7 - 8*x^8) - 1584*x^2
+ 26548*x^3 - 90412*x^4 + 115668*x^5 - 67212*x^6 + 17932*x^7 - 2388*x^8 + 156*x^9 - 4*x^10 + exp(6)*(4*x^3 -
12*x^4 + 12*x^5 - 4*x^6)) + 16),x)
[Out]
int((exp(2*x)*(64*x^2 - 1584*x^3 + 5072*x^4 - 5728*x^5 + 2592*x^6 - 368*x^7 + 16*x^8 + exp(3)*(16*x^3 - 48*x^4
+ 48*x^5 - 16*x^6) - 32) - exp(x)*(32*x - exp(3)*(4*x^4 - 16*x^5 + 24*x^6 - 16*x^7 + 4*x^8) - 80*x^2 + 32*x^3
+ 412*x^4 - 1664*x^5 + 2700*x^6 - 2080*x^7 + 740*x^8 - 96*x^9 + 4*x^10) + exp(4*x)*(exp(3)*(16*x - 16*x^2) -
1584*x + 1904*x^2 - 336*x^3 + 16*x^4) + exp(5*x)*(80*x + 4*exp(3) - 4*x^2 - 396) - exp(3*x)*(2376*x^2 - exp(3)
*(24*x^2 - 48*x^3 + 24*x^4) - 5232*x^3 + 3360*x^4 - 528*x^5 + 24*x^6 + 48))/(exp(2*x)*(exp(6)*(6*x^2 - 12*x^3
+ 6*x^4) - exp(3)*(972*x^2 - 2160*x^3 + 1416*x^4 - 240*x^5 + 12*x^6 + 8) - 144*x + 39374*x^2 - 96228*x^3 + 772
74*x^4 - 23544*x^5 + 3354*x^6 - 228*x^7 + 6*x^8 + 648) - exp(3)*(8*x^2 - 16*x^3 + 170*x^4 - 684*x^5 + 1118*x^6
- 872*x^7 + 318*x^8 - 44*x^9 + 2*x^10) + exp(6)*(x^4 - 4*x^5 + 6*x^6 - 4*x^7 + x^8) + exp(4*x)*(exp(6) - 2916
*x - exp(3)*(2*x^2 - 36*x + 162) + 486*x^2 - 36*x^3 + x^4 + 6561) + exp(3*x)*(26244*x + exp(6)*(4*x - 4*x^2) -
exp(3)*(648*x - 792*x^2 + 152*x^3 - 8*x^4) - 37908*x^2 + 13608*x^3 - 2088*x^4 + 148*x^5 - 4*x^6) + 648*x^2 -
1440*x^3 + 7505*x^4 - 29320*x^5 + 51524*x^6 - 45720*x^7 + 21286*x^8 - 5080*x^9 + 636*x^10 - 40*x^11 + x^12 + e
xp(x)*(1296*x - exp(3)*(16*x - 16*x^2 + 648*x^3 - 2088*x^4 + 2384*x^5 - 1104*x^6 + 168*x^7 - 8*x^8) - 1584*x^2
+ 26548*x^3 - 90412*x^4 + 115668*x^5 - 67212*x^6 + 17932*x^7 - 2388*x^8 + 156*x^9 - 4*x^10 + exp(6)*(4*x^3 -
12*x^4 + 12*x^5 - 4*x^6)) + 16), x)
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sympy [B] time = 3.33, size = 257, normalized size = 7.56 \begin {gather*} \frac {16 e^{x}}{x^{8} - 38 x^{7} - 2 x^{6} e^{3} + 559 x^{6} - 3924 x^{5} + 40 x^{5} e^{3} - 236 x^{4} e^{3} + x^{4} e^{6} + 12879 x^{4} - 16038 x^{3} - 2 x^{3} e^{6} + 360 x^{3} e^{3} - 162 x^{2} e^{3} + x^{2} e^{6} + 6565 x^{2} - 72 x + \left (x^{4} - 36 x^{3} - 2 x^{2} e^{3} + 486 x^{2} - 2916 x + 36 x e^{3} - 162 e^{3} + e^{6} + 6561\right ) e^{2 x} + \left (- 2 x^{6} + 74 x^{5} - 1044 x^{4} + 4 x^{4} e^{3} - 76 x^{3} e^{3} + 6804 x^{3} - 18954 x^{2} - 2 x^{2} e^{6} + 396 x^{2} e^{3} - 324 x e^{3} + 2 x e^{6} + 13122 x\right ) e^{x} - 4 e^{3} + 324} - \frac {4 e^{x}}{x^{2} - 18 x - e^{3} + 81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*exp(3)-4*x**2+80*x-396)*exp(x)**5+((-16*x**2+16*x)*exp(3)+16*x**4-336*x**3+1904*x**2-1584*x)*exp
(x)**4+((24*x**4-48*x**3+24*x**2)*exp(3)-24*x**6+528*x**5-3360*x**4+5232*x**3-2376*x**2-48)*exp(x)**3+((-16*x*
*6+48*x**5-48*x**4+16*x**3)*exp(3)+16*x**8-368*x**7+2592*x**6-5728*x**5+5072*x**4-1584*x**3+64*x**2-32)*exp(x)
**2+((4*x**8-16*x**7+24*x**6-16*x**5+4*x**4)*exp(3)-4*x**10+96*x**9-740*x**8+2080*x**7-2700*x**6+1664*x**5-412
*x**4-32*x**3+80*x**2-32*x)*exp(x))/((exp(3)**2+(-2*x**2+36*x-162)*exp(3)+x**4-36*x**3+486*x**2-2916*x+6561)*e
xp(x)**4+((-4*x**2+4*x)*exp(3)**2+(8*x**4-152*x**3+792*x**2-648*x)*exp(3)-4*x**6+148*x**5-2088*x**4+13608*x**3
-37908*x**2+26244*x)*exp(x)**3+((6*x**4-12*x**3+6*x**2)*exp(3)**2+(-12*x**6+240*x**5-1416*x**4+2160*x**3-972*x
**2-8)*exp(3)+6*x**8-228*x**7+3354*x**6-23544*x**5+77274*x**4-96228*x**3+39374*x**2-144*x+648)*exp(x)**2+((-4*
x**6+12*x**5-12*x**4+4*x**3)*exp(3)**2+(8*x**8-168*x**7+1104*x**6-2384*x**5+2088*x**4-648*x**3+16*x**2-16*x)*e
xp(3)-4*x**10+156*x**9-2388*x**8+17932*x**7-67212*x**6+115668*x**5-90412*x**4+26548*x**3-1584*x**2+1296*x)*exp
(x)+(x**8-4*x**7+6*x**6-4*x**5+x**4)*exp(3)**2+(-2*x**10+44*x**9-318*x**8+872*x**7-1118*x**6+684*x**5-170*x**4
+16*x**3-8*x**2)*exp(3)+x**12-40*x**11+636*x**10-5080*x**9+21286*x**8-45720*x**7+51524*x**6-29320*x**5+7505*x*
*4-1440*x**3+648*x**2+16),x)
[Out]
16*exp(x)/(x**8 - 38*x**7 - 2*x**6*exp(3) + 559*x**6 - 3924*x**5 + 40*x**5*exp(3) - 236*x**4*exp(3) + x**4*exp
(6) + 12879*x**4 - 16038*x**3 - 2*x**3*exp(6) + 360*x**3*exp(3) - 162*x**2*exp(3) + x**2*exp(6) + 6565*x**2 -
72*x + (x**4 - 36*x**3 - 2*x**2*exp(3) + 486*x**2 - 2916*x + 36*x*exp(3) - 162*exp(3) + exp(6) + 6561)*exp(2*x
) + (-2*x**6 + 74*x**5 - 1044*x**4 + 4*x**4*exp(3) - 76*x**3*exp(3) + 6804*x**3 - 18954*x**2 - 2*x**2*exp(6) +
396*x**2*exp(3) - 324*x*exp(3) + 2*x*exp(6) + 13122*x)*exp(x) - 4*exp(3) + 324) - 4*exp(x)/(x**2 - 18*x - exp
(3) + 81)
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