3.9.28 \(\int \frac {1}{16} (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} (5 x^4+16 x^5)+e^{14 x} (-80 x^4-320 x^5-224 x^6)+e^{12 x} (560 x^4+2688 x^5+3472 x^6+1344 x^7)+e^{10 x} (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8)+e^{8 x} (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9)+e^{6 x} (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10})+e^{4 x} (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11})+e^{2 x} (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12})) \, dx\)

Optimal. Leaf size=30 \[ \frac {1}{16} x^3 \left (3-x+x \left (2-e^{2 x}+2 x\right )^4\right )^2 \]

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Rubi [B]  time = 5.04, antiderivative size = 468, normalized size of antiderivative = 15.60, number of steps used = 376, number of rules used = 6, integrand size = 356, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {12, 1593, 2196, 2176, 2194, 1594} \begin {gather*} 16 x^{13}-64 e^{2 x} x^{12}+128 x^{12}-448 e^{2 x} x^{11}+112 e^{4 x} x^{11}+448 x^{11}-1344 e^{2 x} x^{10}+672 e^{4 x} x^{10}-112 e^{6 x} x^{10}+896 x^{10}-2240 e^{2 x} x^9+1680 e^{4 x} x^9-560 e^{6 x} x^9+70 e^{8 x} x^9+1118 x^9-2236 e^{2 x} x^8+2240 e^{4 x} x^8-1120 e^{6 x} x^8+280 e^{8 x} x^8-28 e^{10 x} x^8+894 x^8-1344 e^{2 x} x^7+1677 e^{4 x} x^7-1120 e^{6 x} x^7+420 e^{8 x} x^7-84 e^{10 x} x^7+7 e^{12 x} x^7+460 x^7-472 e^{2 x} x^6+675 e^{4 x} x^6-559 e^{6 x} x^6+280 e^{8 x} x^6-84 e^{10 x} x^6+14 e^{12 x} x^6-e^{14 x} x^6+156 x^6-96 e^{2 x} x^5+127 e^{4 x} x^5-114 e^{6 x} x^5+\frac {559}{8} e^{8 x} x^5-28 e^{10 x} x^5+7 e^{12 x} x^5-e^{14 x} x^5+\frac {1}{16} e^{16 x} x^5+\frac {609 x^5}{16}-12 e^{2 x} x^4+9 e^{4 x} x^4-3 e^{6 x} x^4+\frac {3}{8} e^{8 x} x^4+\frac {45 x^4}{8}+\frac {9 x^3}{16} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(27*x^2 + 360*x^3 + 3045*x^4 + 14976*x^5 + 51520*x^6 + 114432*x^7 + 160992*x^8 + 143360*x^9 + 78848*x^10 +
24576*x^11 + 3328*x^12 + E^(16*x)*(5*x^4 + 16*x^5) + E^(14*x)*(-80*x^4 - 320*x^5 - 224*x^6) + E^(12*x)*(560*x
^4 + 2688*x^5 + 3472*x^6 + 1344*x^7) + E^(10*x)*(-2240*x^4 - 12544*x^5 - 22848*x^6 - 17024*x^7 - 4480*x^8) + E
^(8*x)*(24*x^3 + 5638*x^4 + 35824*x^5 + 82880*x^6 + 89600*x^7 + 45920*x^8 + 8960*x^9) + E^(6*x)*(-192*x^3 - 94
08*x^4 - 64608*x^5 - 179104*x^6 - 250880*x^7 - 188160*x^8 - 71680*x^9 - 10752*x^10) + E^(4*x)*(576*x^3 + 10736
*x^4 + 72928*x^5 + 231024*x^6 + 394048*x^7 + 385280*x^8 + 215040*x^9 + 62720*x^10 + 7168*x^11) + E^(2*x)*(-768
*x^3 - 8064*x^4 - 48384*x^5 - 165632*x^6 - 329216*x^7 - 394112*x^8 - 286720*x^9 - 121856*x^10 - 26624*x^11 - 2
048*x^12))/16,x]

[Out]

(9*x^3)/16 + (45*x^4)/8 - 12*E^(2*x)*x^4 + 9*E^(4*x)*x^4 - 3*E^(6*x)*x^4 + (3*E^(8*x)*x^4)/8 + (609*x^5)/16 -
96*E^(2*x)*x^5 + 127*E^(4*x)*x^5 - 114*E^(6*x)*x^5 + (559*E^(8*x)*x^5)/8 - 28*E^(10*x)*x^5 + 7*E^(12*x)*x^5 -
E^(14*x)*x^5 + (E^(16*x)*x^5)/16 + 156*x^6 - 472*E^(2*x)*x^6 + 675*E^(4*x)*x^6 - 559*E^(6*x)*x^6 + 280*E^(8*x)
*x^6 - 84*E^(10*x)*x^6 + 14*E^(12*x)*x^6 - E^(14*x)*x^6 + 460*x^7 - 1344*E^(2*x)*x^7 + 1677*E^(4*x)*x^7 - 1120
*E^(6*x)*x^7 + 420*E^(8*x)*x^7 - 84*E^(10*x)*x^7 + 7*E^(12*x)*x^7 + 894*x^8 - 2236*E^(2*x)*x^8 + 2240*E^(4*x)*
x^8 - 1120*E^(6*x)*x^8 + 280*E^(8*x)*x^8 - 28*E^(10*x)*x^8 + 1118*x^9 - 2240*E^(2*x)*x^9 + 1680*E^(4*x)*x^9 -
560*E^(6*x)*x^9 + 70*E^(8*x)*x^9 + 896*x^10 - 1344*E^(2*x)*x^10 + 672*E^(4*x)*x^10 - 112*E^(6*x)*x^10 + 448*x^
11 - 448*E^(2*x)*x^11 + 112*E^(4*x)*x^11 + 128*x^12 - 64*E^(2*x)*x^12 + 16*x^13

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 1593

Int[(u_.)*((a_.)*(x_)^(p_.) + (b_.)*(x_)^(q_.))^(n_.), x_Symbol] :> Int[u*x^(n*p)*(a + b*x^(q - p))^n, x] /; F
reeQ[{a, b, p, q}, x] && IntegerQ[n] && PosQ[q - p]

Rule 1594

Int[(u_.)*((a_.)*(x_)^(p_.) + (b_.)*(x_)^(q_.) + (c_.)*(x_)^(r_.))^(n_.), x_Symbol] :> Int[u*x^(n*p)*(a + b*x^
(q - p) + c*x^(r - p))^n, x] /; FreeQ[{a, b, c, p, q, r}, x] && IntegerQ[n] && PosQ[q - p] && PosQ[r - p]

Rule 2176

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m
*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !$UseGamma === True

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rule 2196

Int[(F_)^((c_.)*(v_))*(u_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), u, x], x] /; FreeQ[{F, c
}, x] && PolynomialQ[u, x] && LinearQ[v, x] &&  !$UseGamma === True

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx\\ &=\frac {9 x^3}{16}+\frac {45 x^4}{8}+\frac {609 x^5}{16}+156 x^6+460 x^7+894 x^8+1118 x^9+896 x^{10}+448 x^{11}+128 x^{12}+16 x^{13}+\frac {1}{16} \int e^{16 x} \left (5 x^4+16 x^5\right ) \, dx+\frac {1}{16} \int e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right ) \, dx+\frac {1}{16} \int e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right ) \, dx+\frac {1}{16} \int e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right ) \, dx+\frac {1}{16} \int e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right ) \, dx+\frac {1}{16} \int e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right ) \, dx+\frac {1}{16} \int e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right ) \, dx+\frac {1}{16} \int e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right ) \, dx\\ &=\frac {9 x^3}{16}+\frac {45 x^4}{8}+\frac {609 x^5}{16}+156 x^6+460 x^7+894 x^8+1118 x^9+896 x^{10}+448 x^{11}+128 x^{12}+16 x^{13}+\frac {1}{16} \int e^{16 x} x^4 (5+16 x) \, dx+\frac {1}{16} \int e^{14 x} x^4 \left (-80-320 x-224 x^2\right ) \, dx+\frac {1}{16} \int \left (560 e^{12 x} x^4+2688 e^{12 x} x^5+3472 e^{12 x} x^6+1344 e^{12 x} x^7\right ) \, dx+\frac {1}{16} \int \left (-2240 e^{10 x} x^4-12544 e^{10 x} x^5-22848 e^{10 x} x^6-17024 e^{10 x} x^7-4480 e^{10 x} x^8\right ) \, dx+\frac {1}{16} \int \left (24 e^{8 x} x^3+5638 e^{8 x} x^4+35824 e^{8 x} x^5+82880 e^{8 x} x^6+89600 e^{8 x} x^7+45920 e^{8 x} x^8+8960 e^{8 x} x^9\right ) \, dx+\frac {1}{16} \int \left (-192 e^{6 x} x^3-9408 e^{6 x} x^4-64608 e^{6 x} x^5-179104 e^{6 x} x^6-250880 e^{6 x} x^7-188160 e^{6 x} x^8-71680 e^{6 x} x^9-10752 e^{6 x} x^{10}\right ) \, dx+\frac {1}{16} \int \left (576 e^{4 x} x^3+10736 e^{4 x} x^4+72928 e^{4 x} x^5+231024 e^{4 x} x^6+394048 e^{4 x} x^7+385280 e^{4 x} x^8+215040 e^{4 x} x^9+62720 e^{4 x} x^{10}+7168 e^{4 x} x^{11}\right ) \, dx+\frac {1}{16} \int \left (-768 e^{2 x} x^3-8064 e^{2 x} x^4-48384 e^{2 x} x^5-165632 e^{2 x} x^6-329216 e^{2 x} x^7-394112 e^{2 x} x^8-286720 e^{2 x} x^9-121856 e^{2 x} x^{10}-26624 e^{2 x} x^{11}-2048 e^{2 x} x^{12}\right ) \, dx\\ &=\frac {9 x^3}{16}+\frac {45 x^4}{8}+\frac {609 x^5}{16}+156 x^6+460 x^7+894 x^8+1118 x^9+896 x^{10}+448 x^{11}+128 x^{12}+16 x^{13}+\frac {1}{16} \int \left (5 e^{16 x} x^4+16 e^{16 x} x^5\right ) \, dx+\frac {1}{16} \int \left (-80 e^{14 x} x^4-320 e^{14 x} x^5-224 e^{14 x} x^6\right ) \, dx+\frac {3}{2} \int e^{8 x} x^3 \, dx-12 \int e^{6 x} x^3 \, dx+35 \int e^{12 x} x^4 \, dx+36 \int e^{4 x} x^3 \, dx-48 \int e^{2 x} x^3 \, dx+84 \int e^{12 x} x^7 \, dx-128 \int e^{2 x} x^{12} \, dx-140 \int e^{10 x} x^4 \, dx+168 \int e^{12 x} x^5 \, dx+217 \int e^{12 x} x^6 \, dx-280 \int e^{10 x} x^8 \, dx+\frac {2819}{8} \int e^{8 x} x^4 \, dx+448 \int e^{4 x} x^{11} \, dx-504 \int e^{2 x} x^4 \, dx+560 \int e^{8 x} x^9 \, dx-588 \int e^{6 x} x^4 \, dx+671 \int e^{4 x} x^4 \, dx-672 \int e^{6 x} x^{10} \, dx-784 \int e^{10 x} x^5 \, dx-1064 \int e^{10 x} x^7 \, dx-1428 \int e^{10 x} x^6 \, dx-1664 \int e^{2 x} x^{11} \, dx+2239 \int e^{8 x} x^5 \, dx+2870 \int e^{8 x} x^8 \, dx-3024 \int e^{2 x} x^5 \, dx+3920 \int e^{4 x} x^{10} \, dx-4038 \int e^{6 x} x^5 \, dx-4480 \int e^{6 x} x^9 \, dx+4558 \int e^{4 x} x^5 \, dx+5180 \int e^{8 x} x^6 \, dx+5600 \int e^{8 x} x^7 \, dx-7616 \int e^{2 x} x^{10} \, dx-10352 \int e^{2 x} x^6 \, dx-11194 \int e^{6 x} x^6 \, dx-11760 \int e^{6 x} x^8 \, dx+13440 \int e^{4 x} x^9 \, dx+14439 \int e^{4 x} x^6 \, dx-15680 \int e^{6 x} x^7 \, dx-17920 \int e^{2 x} x^9 \, dx-20576 \int e^{2 x} x^7 \, dx+24080 \int e^{4 x} x^8 \, dx+24628 \int e^{4 x} x^7 \, dx-24632 \int e^{2 x} x^8 \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.73, size = 86, normalized size = 2.87 \begin {gather*} \frac {1}{16} x^3 \left (3+\left (15-32 e^{2 x}+24 e^{4 x}-8 e^{6 x}+e^{8 x}\right ) x-8 \left (-2+e^{2 x}\right )^3 x^2+24 \left (-2+e^{2 x}\right )^2 x^3-32 \left (-2+e^{2 x}\right ) x^4+16 x^5\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(27*x^2 + 360*x^3 + 3045*x^4 + 14976*x^5 + 51520*x^6 + 114432*x^7 + 160992*x^8 + 143360*x^9 + 78848*
x^10 + 24576*x^11 + 3328*x^12 + E^(16*x)*(5*x^4 + 16*x^5) + E^(14*x)*(-80*x^4 - 320*x^5 - 224*x^6) + E^(12*x)*
(560*x^4 + 2688*x^5 + 3472*x^6 + 1344*x^7) + E^(10*x)*(-2240*x^4 - 12544*x^5 - 22848*x^6 - 17024*x^7 - 4480*x^
8) + E^(8*x)*(24*x^3 + 5638*x^4 + 35824*x^5 + 82880*x^6 + 89600*x^7 + 45920*x^8 + 8960*x^9) + E^(6*x)*(-192*x^
3 - 9408*x^4 - 64608*x^5 - 179104*x^6 - 250880*x^7 - 188160*x^8 - 71680*x^9 - 10752*x^10) + E^(4*x)*(576*x^3 +
10736*x^4 + 72928*x^5 + 231024*x^6 + 394048*x^7 + 385280*x^8 + 215040*x^9 + 62720*x^10 + 7168*x^11) + E^(2*x)
*(-768*x^3 - 8064*x^4 - 48384*x^5 - 165632*x^6 - 329216*x^7 - 394112*x^8 - 286720*x^9 - 121856*x^10 - 26624*x^
11 - 2048*x^12))/16,x]

[Out]

(x^3*(3 + (15 - 32*E^(2*x) + 24*E^(4*x) - 8*E^(6*x) + E^(8*x))*x - 8*(-2 + E^(2*x))^3*x^2 + 24*(-2 + E^(2*x))^
2*x^3 - 32*(-2 + E^(2*x))*x^4 + 16*x^5)^2)/16

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fricas [B]  time = 0.96, size = 296, normalized size = 9.87 \begin {gather*} 16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/16*(16*x^5+5*x^4)*exp(2*x)^8+1/16*(-224*x^6-320*x^5-80*x^4)*exp(2*x)^7+1/16*(1344*x^7+3472*x^6+268
8*x^5+560*x^4)*exp(2*x)^6+1/16*(-4480*x^8-17024*x^7-22848*x^6-12544*x^5-2240*x^4)*exp(2*x)^5+1/16*(8960*x^9+45
920*x^8+89600*x^7+82880*x^6+35824*x^5+5638*x^4+24*x^3)*exp(2*x)^4+1/16*(-10752*x^10-71680*x^9-188160*x^8-25088
0*x^7-179104*x^6-64608*x^5-9408*x^4-192*x^3)*exp(2*x)^3+1/16*(7168*x^11+62720*x^10+215040*x^9+385280*x^8+39404
8*x^7+231024*x^6+72928*x^5+10736*x^4+576*x^3)*exp(2*x)^2+1/16*(-2048*x^12-26624*x^11-121856*x^10-286720*x^9-39
4112*x^8-329216*x^7-165632*x^6-48384*x^5-8064*x^4-768*x^3)*exp(2*x)+208*x^12+1536*x^11+4928*x^10+8960*x^9+1006
2*x^8+7152*x^7+3220*x^6+936*x^5+3045/16*x^4+45/2*x^3+27/16*x^2,x, algorithm="fricas")

[Out]

16*x^13 + 128*x^12 + 448*x^11 + 896*x^10 + 1118*x^9 + 894*x^8 + 460*x^7 + 156*x^6 + 1/16*x^5*e^(16*x) + 609/16
*x^5 + 45/8*x^4 + 9/16*x^3 - (x^6 + x^5)*e^(14*x) + 7*(x^7 + 2*x^6 + x^5)*e^(12*x) - 28*(x^8 + 3*x^7 + 3*x^6 +
x^5)*e^(10*x) + 1/8*(560*x^9 + 2240*x^8 + 3360*x^7 + 2240*x^6 + 559*x^5 + 3*x^4)*e^(8*x) - (112*x^10 + 560*x^
9 + 1120*x^8 + 1120*x^7 + 559*x^6 + 114*x^5 + 3*x^4)*e^(6*x) + (112*x^11 + 672*x^10 + 1680*x^9 + 2240*x^8 + 16
77*x^7 + 675*x^6 + 127*x^5 + 9*x^4)*e^(4*x) - 4*(16*x^12 + 112*x^11 + 336*x^10 + 560*x^9 + 559*x^8 + 336*x^7 +
118*x^6 + 24*x^5 + 3*x^4)*e^(2*x)

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giac [B]  time = 0.34, size = 296, normalized size = 9.87 \begin {gather*} 16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/16*(16*x^5+5*x^4)*exp(2*x)^8+1/16*(-224*x^6-320*x^5-80*x^4)*exp(2*x)^7+1/16*(1344*x^7+3472*x^6+268
8*x^5+560*x^4)*exp(2*x)^6+1/16*(-4480*x^8-17024*x^7-22848*x^6-12544*x^5-2240*x^4)*exp(2*x)^5+1/16*(8960*x^9+45
920*x^8+89600*x^7+82880*x^6+35824*x^5+5638*x^4+24*x^3)*exp(2*x)^4+1/16*(-10752*x^10-71680*x^9-188160*x^8-25088
0*x^7-179104*x^6-64608*x^5-9408*x^4-192*x^3)*exp(2*x)^3+1/16*(7168*x^11+62720*x^10+215040*x^9+385280*x^8+39404
8*x^7+231024*x^6+72928*x^5+10736*x^4+576*x^3)*exp(2*x)^2+1/16*(-2048*x^12-26624*x^11-121856*x^10-286720*x^9-39
4112*x^8-329216*x^7-165632*x^6-48384*x^5-8064*x^4-768*x^3)*exp(2*x)+208*x^12+1536*x^11+4928*x^10+8960*x^9+1006
2*x^8+7152*x^7+3220*x^6+936*x^5+3045/16*x^4+45/2*x^3+27/16*x^2,x, algorithm="giac")

[Out]

16*x^13 + 128*x^12 + 448*x^11 + 896*x^10 + 1118*x^9 + 894*x^8 + 460*x^7 + 156*x^6 + 1/16*x^5*e^(16*x) + 609/16
*x^5 + 45/8*x^4 + 9/16*x^3 - (x^6 + x^5)*e^(14*x) + 7*(x^7 + 2*x^6 + x^5)*e^(12*x) - 28*(x^8 + 3*x^7 + 3*x^6 +
x^5)*e^(10*x) + 1/8*(560*x^9 + 2240*x^8 + 3360*x^7 + 2240*x^6 + 559*x^5 + 3*x^4)*e^(8*x) - (112*x^10 + 560*x^
9 + 1120*x^8 + 1120*x^7 + 559*x^6 + 114*x^5 + 3*x^4)*e^(6*x) + (112*x^11 + 672*x^10 + 1680*x^9 + 2240*x^8 + 16
77*x^7 + 675*x^6 + 127*x^5 + 9*x^4)*e^(4*x) - 4*(16*x^12 + 112*x^11 + 336*x^10 + 560*x^9 + 559*x^8 + 336*x^7 +
118*x^6 + 24*x^5 + 3*x^4)*e^(2*x)

________________________________________________________________________________________

maple [B]  time = 0.17, size = 310, normalized size = 10.33

method	result	size
risch	\(\frac {{\mathrm e}^{16 x} x^{5}}{16}+\frac {\left (-16 x^{6}-16 x^{5}\right ) {\mathrm e}^{14 x}}{16}+\frac {\left (112 x^{7}+224 x^{6}+112 x^{5}\right ) {\mathrm e}^{12 x}}{16}+\frac {\left (-448 x^{8}-1344 x^{7}-1344 x^{6}-448 x^{5}\right ) {\mathrm e}^{10 x}}{16}+\frac {\left (1120 x^{9}+4480 x^{8}+6720 x^{7}+4480 x^{6}+1118 x^{5}+6 x^{4}\right ) {\mathrm e}^{8 x}}{16}+\frac {\left (-1792 x^{10}-8960 x^{9}-17920 x^{8}-17920 x^{7}-8944 x^{6}-1824 x^{5}-48 x^{4}\right ) {\mathrm e}^{6 x}}{16}+\frac {\left (1792 x^{11}+10752 x^{10}+26880 x^{9}+35840 x^{8}+26832 x^{7}+10800 x^{6}+2032 x^{5}+144 x^{4}\right ) {\mathrm e}^{4 x}}{16}+\frac {\left (-1024 x^{12}-7168 x^{11}-21504 x^{10}-35840 x^{9}-35776 x^{8}-21504 x^{7}-7552 x^{6}-1536 x^{5}-192 x^{4}\right ) {\mathrm e}^{2 x}}{16}+16 x^{13}+128 x^{12}+448 x^{11}+896 x^{10}+1118 x^{9}+894 x^{8}+460 x^{7}+156 x^{6}+\frac {609 x^{5}}{16}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}\)	\(310\)
derivativedivides	\(448 x^{11}+128 x^{12}+16 x^{13}+460 x^{7}+894 x^{8}+896 x^{10}+1118 x^{9}+156 x^{6}+\frac {609 x^{5}}{16}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}-96 x^{5} {\mathrm e}^{2 x}+\frac {{\mathrm e}^{16 x} x^{5}}{16}-448 \,{\mathrm e}^{2 x} x^{11}-1344 \,{\mathrm e}^{2 x} x^{10}-2240 \,{\mathrm e}^{2 x} x^{9}-2236 \,{\mathrm e}^{2 x} x^{8}-1344 \,{\mathrm e}^{2 x} x^{7}-472 \,{\mathrm e}^{2 x} x^{6}-12 \,{\mathrm e}^{2 x} x^{4}+9 x^{4} {\mathrm e}^{4 x}+\frac {3 x^{4} {\mathrm e}^{8 x}}{8}-{\mathrm e}^{14 x} x^{5}+14 \,{\mathrm e}^{12 x} x^{6}-84 \,{\mathrm e}^{10 x} x^{7}+280 \,{\mathrm e}^{8 x} x^{8}-560 \,{\mathrm e}^{6 x} x^{9}+672 \,{\mathrm e}^{4 x} x^{10}+7 \,{\mathrm e}^{12 x} x^{5}-84 \,{\mathrm e}^{10 x} x^{6}+420 \,{\mathrm e}^{8 x} x^{7}-1120 \,{\mathrm e}^{6 x} x^{8}+1680 \,{\mathrm e}^{4 x} x^{9}-28 \,{\mathrm e}^{10 x} x^{5}+280 \,{\mathrm e}^{8 x} x^{6}-1120 \,{\mathrm e}^{6 x} x^{7}+2240 \,{\mathrm e}^{4 x} x^{8}+\frac {559 \,{\mathrm e}^{8 x} x^{5}}{8}-559 \,{\mathrm e}^{6 x} x^{6}+1677 \,{\mathrm e}^{4 x} x^{7}-114 \,{\mathrm e}^{6 x} x^{5}+675 \,{\mathrm e}^{4 x} x^{6}-3 \,{\mathrm e}^{6 x} x^{4}+127 \,{\mathrm e}^{4 x} x^{5}-112 \,{\mathrm e}^{6 x} x^{10}+70 \,{\mathrm e}^{8 x} x^{9}-{\mathrm e}^{14 x} x^{6}+7 \,{\mathrm e}^{12 x} x^{7}-28 \,{\mathrm e}^{10 x} x^{8}+112 \,{\mathrm e}^{4 x} x^{11}-64 \,{\mathrm e}^{2 x} x^{12}\)	\(479\)
default	\(448 x^{11}+128 x^{12}+16 x^{13}+460 x^{7}+894 x^{8}+896 x^{10}+1118 x^{9}+156 x^{6}+\frac {609 x^{5}}{16}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}-96 x^{5} {\mathrm e}^{2 x}+\frac {{\mathrm e}^{16 x} x^{5}}{16}-448 \,{\mathrm e}^{2 x} x^{11}-1344 \,{\mathrm e}^{2 x} x^{10}-2240 \,{\mathrm e}^{2 x} x^{9}-2236 \,{\mathrm e}^{2 x} x^{8}-1344 \,{\mathrm e}^{2 x} x^{7}-472 \,{\mathrm e}^{2 x} x^{6}-12 \,{\mathrm e}^{2 x} x^{4}+9 x^{4} {\mathrm e}^{4 x}+\frac {3 x^{4} {\mathrm e}^{8 x}}{8}-{\mathrm e}^{14 x} x^{5}+14 \,{\mathrm e}^{12 x} x^{6}-84 \,{\mathrm e}^{10 x} x^{7}+280 \,{\mathrm e}^{8 x} x^{8}-560 \,{\mathrm e}^{6 x} x^{9}+672 \,{\mathrm e}^{4 x} x^{10}+7 \,{\mathrm e}^{12 x} x^{5}-84 \,{\mathrm e}^{10 x} x^{6}+420 \,{\mathrm e}^{8 x} x^{7}-1120 \,{\mathrm e}^{6 x} x^{8}+1680 \,{\mathrm e}^{4 x} x^{9}-28 \,{\mathrm e}^{10 x} x^{5}+280 \,{\mathrm e}^{8 x} x^{6}-1120 \,{\mathrm e}^{6 x} x^{7}+2240 \,{\mathrm e}^{4 x} x^{8}+\frac {559 \,{\mathrm e}^{8 x} x^{5}}{8}-559 \,{\mathrm e}^{6 x} x^{6}+1677 \,{\mathrm e}^{4 x} x^{7}-114 \,{\mathrm e}^{6 x} x^{5}+675 \,{\mathrm e}^{4 x} x^{6}-3 \,{\mathrm e}^{6 x} x^{4}+127 \,{\mathrm e}^{4 x} x^{5}-112 \,{\mathrm e}^{6 x} x^{10}+70 \,{\mathrm e}^{8 x} x^{9}-{\mathrm e}^{14 x} x^{6}+7 \,{\mathrm e}^{12 x} x^{7}-28 \,{\mathrm e}^{10 x} x^{8}+112 \,{\mathrm e}^{4 x} x^{11}-64 \,{\mathrm e}^{2 x} x^{12}\)	\(479\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/16*(16*x^5+5*x^4)*exp(2*x)^8+1/16*(-224*x^6-320*x^5-80*x^4)*exp(2*x)^7+1/16*(1344*x^7+3472*x^6+2688*x^5+
560*x^4)*exp(2*x)^6+1/16*(-4480*x^8-17024*x^7-22848*x^6-12544*x^5-2240*x^4)*exp(2*x)^5+1/16*(8960*x^9+45920*x^
8+89600*x^7+82880*x^6+35824*x^5+5638*x^4+24*x^3)*exp(2*x)^4+1/16*(-10752*x^10-71680*x^9-188160*x^8-250880*x^7-
179104*x^6-64608*x^5-9408*x^4-192*x^3)*exp(2*x)^3+1/16*(7168*x^11+62720*x^10+215040*x^9+385280*x^8+394048*x^7+
231024*x^6+72928*x^5+10736*x^4+576*x^3)*exp(2*x)^2+1/16*(-2048*x^12-26624*x^11-121856*x^10-286720*x^9-394112*x
^8-329216*x^7-165632*x^6-48384*x^5-8064*x^4-768*x^3)*exp(2*x)+208*x^12+1536*x^11+4928*x^10+8960*x^9+10062*x^8+
7152*x^7+3220*x^6+936*x^5+3045/16*x^4+45/2*x^3+27/16*x^2,x,method=_RETURNVERBOSE)

[Out]

1/16*exp(16*x)*x^5+1/16*(-16*x^6-16*x^5)*exp(14*x)+1/16*(112*x^7+224*x^6+112*x^5)*exp(12*x)+1/16*(-448*x^8-134
4*x^7-1344*x^6-448*x^5)*exp(10*x)+1/16*(1120*x^9+4480*x^8+6720*x^7+4480*x^6+1118*x^5+6*x^4)*exp(8*x)+1/16*(-17
92*x^10-8960*x^9-17920*x^8-17920*x^7-8944*x^6-1824*x^5-48*x^4)*exp(6*x)+1/16*(1792*x^11+10752*x^10+26880*x^9+3
5840*x^8+26832*x^7+10800*x^6+2032*x^5+144*x^4)*exp(4*x)+1/16*(-1024*x^12-7168*x^11-21504*x^10-35840*x^9-35776*
x^8-21504*x^7-7552*x^6-1536*x^5-192*x^4)*exp(2*x)+16*x^13+128*x^12+448*x^11+896*x^10+1118*x^9+894*x^8+460*x^7+
156*x^6+609/16*x^5+45/8*x^4+9/16*x^3

________________________________________________________________________________________

maxima [B]  time = 0.50, size = 296, normalized size = 9.87 \begin {gather*} 16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/16*(16*x^5+5*x^4)*exp(2*x)^8+1/16*(-224*x^6-320*x^5-80*x^4)*exp(2*x)^7+1/16*(1344*x^7+3472*x^6+268
8*x^5+560*x^4)*exp(2*x)^6+1/16*(-4480*x^8-17024*x^7-22848*x^6-12544*x^5-2240*x^4)*exp(2*x)^5+1/16*(8960*x^9+45
920*x^8+89600*x^7+82880*x^6+35824*x^5+5638*x^4+24*x^3)*exp(2*x)^4+1/16*(-10752*x^10-71680*x^9-188160*x^8-25088
0*x^7-179104*x^6-64608*x^5-9408*x^4-192*x^3)*exp(2*x)^3+1/16*(7168*x^11+62720*x^10+215040*x^9+385280*x^8+39404
8*x^7+231024*x^6+72928*x^5+10736*x^4+576*x^3)*exp(2*x)^2+1/16*(-2048*x^12-26624*x^11-121856*x^10-286720*x^9-39
4112*x^8-329216*x^7-165632*x^6-48384*x^5-8064*x^4-768*x^3)*exp(2*x)+208*x^12+1536*x^11+4928*x^10+8960*x^9+1006
2*x^8+7152*x^7+3220*x^6+936*x^5+3045/16*x^4+45/2*x^3+27/16*x^2,x, algorithm="maxima")

[Out]

16*x^13 + 128*x^12 + 448*x^11 + 896*x^10 + 1118*x^9 + 894*x^8 + 460*x^7 + 156*x^6 + 1/16*x^5*e^(16*x) + 609/16
*x^5 + 45/8*x^4 + 9/16*x^3 - (x^6 + x^5)*e^(14*x) + 7*(x^7 + 2*x^6 + x^5)*e^(12*x) - 28*(x^8 + 3*x^7 + 3*x^6 +
x^5)*e^(10*x) + 1/8*(560*x^9 + 2240*x^8 + 3360*x^7 + 2240*x^6 + 559*x^5 + 3*x^4)*e^(8*x) - (112*x^10 + 560*x^
9 + 1120*x^8 + 1120*x^7 + 559*x^6 + 114*x^5 + 3*x^4)*e^(6*x) + (112*x^11 + 672*x^10 + 1680*x^9 + 2240*x^8 + 16
77*x^7 + 675*x^6 + 127*x^5 + 9*x^4)*e^(4*x) - 4*(16*x^12 + 112*x^11 + 336*x^10 + 560*x^9 + 559*x^8 + 336*x^7 +
118*x^6 + 24*x^5 + 3*x^4)*e^(2*x)

________________________________________________________________________________________

mupad [B]  time = 4.52, size = 416, normalized size = 13.87 \begin {gather*} 9\,x^4\,{\mathrm {e}}^{4\,x}-96\,x^5\,{\mathrm {e}}^{2\,x}-12\,x^4\,{\mathrm {e}}^{2\,x}-472\,x^6\,{\mathrm {e}}^{2\,x}+127\,x^5\,{\mathrm {e}}^{4\,x}-1344\,x^7\,{\mathrm {e}}^{2\,x}-3\,x^4\,{\mathrm {e}}^{6\,x}+675\,x^6\,{\mathrm {e}}^{4\,x}-2236\,x^8\,{\mathrm {e}}^{2\,x}-114\,x^5\,{\mathrm {e}}^{6\,x}+1677\,x^7\,{\mathrm {e}}^{4\,x}-2240\,x^9\,{\mathrm {e}}^{2\,x}+\frac {3\,x^4\,{\mathrm {e}}^{8\,x}}{8}-559\,x^6\,{\mathrm {e}}^{6\,x}+2240\,x^8\,{\mathrm {e}}^{4\,x}-1344\,x^{10}\,{\mathrm {e}}^{2\,x}+\frac {559\,x^5\,{\mathrm {e}}^{8\,x}}{8}-1120\,x^7\,{\mathrm {e}}^{6\,x}+1680\,x^9\,{\mathrm {e}}^{4\,x}-448\,x^{11}\,{\mathrm {e}}^{2\,x}+280\,x^6\,{\mathrm {e}}^{8\,x}-1120\,x^8\,{\mathrm {e}}^{6\,x}+672\,x^{10}\,{\mathrm {e}}^{4\,x}-64\,x^{12}\,{\mathrm {e}}^{2\,x}-28\,x^5\,{\mathrm {e}}^{10\,x}+420\,x^7\,{\mathrm {e}}^{8\,x}-560\,x^9\,{\mathrm {e}}^{6\,x}+112\,x^{11}\,{\mathrm {e}}^{4\,x}-84\,x^6\,{\mathrm {e}}^{10\,x}+280\,x^8\,{\mathrm {e}}^{8\,x}-112\,x^{10}\,{\mathrm {e}}^{6\,x}+7\,x^5\,{\mathrm {e}}^{12\,x}-84\,x^7\,{\mathrm {e}}^{10\,x}+70\,x^9\,{\mathrm {e}}^{8\,x}+14\,x^6\,{\mathrm {e}}^{12\,x}-28\,x^8\,{\mathrm {e}}^{10\,x}-x^5\,{\mathrm {e}}^{14\,x}+7\,x^7\,{\mathrm {e}}^{12\,x}-x^6\,{\mathrm {e}}^{14\,x}+\frac {x^5\,{\mathrm {e}}^{16\,x}}{16}+\frac {9\,x^3}{16}+\frac {45\,x^4}{8}+\frac {609\,x^5}{16}+156\,x^6+460\,x^7+894\,x^8+1118\,x^9+896\,x^{10}+448\,x^{11}+128\,x^{12}+16\,x^{13} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(16*x)*(5*x^4 + 16*x^5))/16 - (exp(2*x)*(768*x^3 + 8064*x^4 + 48384*x^5 + 165632*x^6 + 329216*x^7 + 39
4112*x^8 + 286720*x^9 + 121856*x^10 + 26624*x^11 + 2048*x^12))/16 - (exp(10*x)*(2240*x^4 + 12544*x^5 + 22848*x
^6 + 17024*x^7 + 4480*x^8))/16 + (exp(8*x)*(24*x^3 + 5638*x^4 + 35824*x^5 + 82880*x^6 + 89600*x^7 + 45920*x^8
+ 8960*x^9))/16 - (exp(14*x)*(80*x^4 + 320*x^5 + 224*x^6))/16 - (exp(6*x)*(192*x^3 + 9408*x^4 + 64608*x^5 + 17
9104*x^6 + 250880*x^7 + 188160*x^8 + 71680*x^9 + 10752*x^10))/16 + (exp(12*x)*(560*x^4 + 2688*x^5 + 3472*x^6 +
1344*x^7))/16 + (27*x^2)/16 + (45*x^3)/2 + (3045*x^4)/16 + 936*x^5 + 3220*x^6 + 7152*x^7 + 10062*x^8 + 8960*x
^9 + 4928*x^10 + 1536*x^11 + 208*x^12 + (exp(4*x)*(576*x^3 + 10736*x^4 + 72928*x^5 + 231024*x^6 + 394048*x^7 +
385280*x^8 + 215040*x^9 + 62720*x^10 + 7168*x^11))/16,x)

[Out]

9*x^4*exp(4*x) - 96*x^5*exp(2*x) - 12*x^4*exp(2*x) - 472*x^6*exp(2*x) + 127*x^5*exp(4*x) - 1344*x^7*exp(2*x) -
3*x^4*exp(6*x) + 675*x^6*exp(4*x) - 2236*x^8*exp(2*x) - 114*x^5*exp(6*x) + 1677*x^7*exp(4*x) - 2240*x^9*exp(2
*x) + (3*x^4*exp(8*x))/8 - 559*x^6*exp(6*x) + 2240*x^8*exp(4*x) - 1344*x^10*exp(2*x) + (559*x^5*exp(8*x))/8 -
1120*x^7*exp(6*x) + 1680*x^9*exp(4*x) - 448*x^11*exp(2*x) + 280*x^6*exp(8*x) - 1120*x^8*exp(6*x) + 672*x^10*ex
p(4*x) - 64*x^12*exp(2*x) - 28*x^5*exp(10*x) + 420*x^7*exp(8*x) - 560*x^9*exp(6*x) + 112*x^11*exp(4*x) - 84*x^
6*exp(10*x) + 280*x^8*exp(8*x) - 112*x^10*exp(6*x) + 7*x^5*exp(12*x) - 84*x^7*exp(10*x) + 70*x^9*exp(8*x) + 14
*x^6*exp(12*x) - 28*x^8*exp(10*x) - x^5*exp(14*x) + 7*x^7*exp(12*x) - x^6*exp(14*x) + (x^5*exp(16*x))/16 + (9*
x^3)/16 + (45*x^4)/8 + (609*x^5)/16 + 156*x^6 + 460*x^7 + 894*x^8 + 1118*x^9 + 896*x^10 + 448*x^11 + 128*x^12
+ 16*x^13

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sympy [B]  time = 0.52, size = 323, normalized size = 10.77 \begin {gather*} 16 x^{13} + 128 x^{12} + 448 x^{11} + 896 x^{10} + 1118 x^{9} + 894 x^{8} + 460 x^{7} + 156 x^{6} + \frac {x^{5} e^{16 x}}{16} + \frac {609 x^{5}}{16} + \frac {45 x^{4}}{8} + \frac {9 x^{3}}{16} + \frac {\left (- 128 x^{6} - 128 x^{5}\right ) e^{14 x}}{128} + \frac {\left (896 x^{7} + 1792 x^{6} + 896 x^{5}\right ) e^{12 x}}{128} + \frac {\left (- 3584 x^{8} - 10752 x^{7} - 10752 x^{6} - 3584 x^{5}\right ) e^{10 x}}{128} + \frac {\left (8960 x^{9} + 35840 x^{8} + 53760 x^{7} + 35840 x^{6} + 8944 x^{5} + 48 x^{4}\right ) e^{8 x}}{128} + \frac {\left (- 14336 x^{10} - 71680 x^{9} - 143360 x^{8} - 143360 x^{7} - 71552 x^{6} - 14592 x^{5} - 384 x^{4}\right ) e^{6 x}}{128} + \frac {\left (14336 x^{11} + 86016 x^{10} + 215040 x^{9} + 286720 x^{8} + 214656 x^{7} + 86400 x^{6} + 16256 x^{5} + 1152 x^{4}\right ) e^{4 x}}{128} + \frac {\left (- 8192 x^{12} - 57344 x^{11} - 172032 x^{10} - 286720 x^{9} - 286208 x^{8} - 172032 x^{7} - 60416 x^{6} - 12288 x^{5} - 1536 x^{4}\right ) e^{2 x}}{128} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/16*(16*x**5+5*x**4)*exp(2*x)**8+1/16*(-224*x**6-320*x**5-80*x**4)*exp(2*x)**7+1/16*(1344*x**7+3472
*x**6+2688*x**5+560*x**4)*exp(2*x)**6+1/16*(-4480*x**8-17024*x**7-22848*x**6-12544*x**5-2240*x**4)*exp(2*x)**5
+1/16*(8960*x**9+45920*x**8+89600*x**7+82880*x**6+35824*x**5+5638*x**4+24*x**3)*exp(2*x)**4+1/16*(-10752*x**10
-71680*x**9-188160*x**8-250880*x**7-179104*x**6-64608*x**5-9408*x**4-192*x**3)*exp(2*x)**3+1/16*(7168*x**11+62
720*x**10+215040*x**9+385280*x**8+394048*x**7+231024*x**6+72928*x**5+10736*x**4+576*x**3)*exp(2*x)**2+1/16*(-2
048*x**12-26624*x**11-121856*x**10-286720*x**9-394112*x**8-329216*x**7-165632*x**6-48384*x**5-8064*x**4-768*x*
*3)*exp(2*x)+208*x**12+1536*x**11+4928*x**10+8960*x**9+10062*x**8+7152*x**7+3220*x**6+936*x**5+3045/16*x**4+45
/2*x**3+27/16*x**2,x)

[Out]

16*x**13 + 128*x**12 + 448*x**11 + 896*x**10 + 1118*x**9 + 894*x**8 + 460*x**7 + 156*x**6 + x**5*exp(16*x)/16
+ 609*x**5/16 + 45*x**4/8 + 9*x**3/16 + (-128*x**6 - 128*x**5)*exp(14*x)/128 + (896*x**7 + 1792*x**6 + 896*x**
5)*exp(12*x)/128 + (-3584*x**8 - 10752*x**7 - 10752*x**6 - 3584*x**5)*exp(10*x)/128 + (8960*x**9 + 35840*x**8
+ 53760*x**7 + 35840*x**6 + 8944*x**5 + 48*x**4)*exp(8*x)/128 + (-14336*x**10 - 71680*x**9 - 143360*x**8 - 143
360*x**7 - 71552*x**6 - 14592*x**5 - 384*x**4)*exp(6*x)/128 + (14336*x**11 + 86016*x**10 + 215040*x**9 + 28672
0*x**8 + 214656*x**7 + 86400*x**6 + 16256*x**5 + 1152*x**4)*exp(4*x)/128 + (-8192*x**12 - 57344*x**11 - 172032
*x**10 - 286720*x**9 - 286208*x**8 - 172032*x**7 - 60416*x**6 - 12288*x**5 - 1536*x**4)*exp(2*x)/128

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