3.15.76 \(\int e^{-8 x} (576 x^8-352 x^9-128 x^{10}+e^x (144 x^8-112 x^9)+e^{3 x} (-1792 x^6+1280 x^7+(448 x^6-320 x^7) \log (3))+e^{2 x} (-7168 x^6+4096 x^7+1536 x^8+(1792 x^6-1024 x^7-384 x^8) \log (3))+e^{5 x} (7680 x^4-4608 x^5+(-3840 x^4+2304 x^5) \log (3)+(480 x^4-288 x^5) \log ^2(3))+e^{4 x} (30720 x^4-15360 x^5-6144 x^6+(-15360 x^4+7680 x^5+3072 x^6) \log (3)+(1920 x^4-960 x^5-384 x^6) \log ^2(3))+e^{7 x} (-12288 x^2+4096 x^3+(9216 x^2-3072 x^3) \log (3)+(-2304 x^2+768 x^3) \log ^2(3)+(192 x^2-64 x^3) \log ^3(3))+e^{6 x} (-49152 x^2+16384 x^3+8192 x^4+(36864 x^2-12288 x^3-6144 x^4) \log (3)+(-9216 x^2+3072 x^3+1536 x^4) \log ^2(3)+(768 x^2-256 x^3-128 x^4) \log ^3(3))+e^{9 x} (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3))+e^{8 x} (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3))) \, dx\)

Optimal. Leaf size=24 \[ 16 x \left (4+e^x+x\right ) \left (-4+e^{-2 x} x^2+\log (3)\right )^4 \]

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Rubi [B]  time = 145.71, antiderivative size = 1259, normalized size of antiderivative = 52.46, number of steps used = 158, number of rules used = 6, integrand size = 462, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6688, 12, 6742, 2196, 2176, 2194} \begin {gather*} 16 e^{-8 x} x^{10}+64 e^{-8 x} x^9+16 e^{-7 x} x^9-64 e^{-6 x} (4-\log (3)) x^8-\frac {8}{3} e^{-6 x} (256-66 \log (3)+\log (9)) x^7-\frac {256}{3} e^{-6 x} (4-\log (3)) x^7-64 e^{-5 x} (4-\log (3)) x^7+\frac {8}{3} e^{-6 x} (448-108 \log (3)-\log (81)) x^6-\frac {28}{9} e^{-6 x} (256-66 \log (3)+\log (9)) x^6+96 e^{-4 x} (4-\log (3))^2 x^6-\frac {896}{9} e^{-6 x} (4-\log (3)) x^6+\frac {8}{3} e^{-6 x} (448-108 \log (3)-\log (81)) x^5+12 e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^5-\frac {28}{9} e^{-6 x} (256-66 \log (3)+\log (9)) x^5+144 e^{-4 x} (4-\log (3))^2 x^5+96 e^{-3 x} (4-\log (3))^2 x^5-\frac {896}{9} e^{-6 x} (4-\log (3)) x^5-12 e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^4+\frac {20}{9} e^{-6 x} (448-108 \log (3)-\log (81)) x^4+15 e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^4-\frac {70}{27} e^{-6 x} (256-66 \log (3)+\log (9)) x^4-64 e^{-2 x} (4-\log (3))^3 x^4+180 e^{-4 x} (4-\log (3))^2 x^4-\frac {2240}{27} e^{-6 x} (4-\log (3)) x^4-8 e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x^3-12 e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^3+\frac {40}{27} e^{-6 x} (448-108 \log (3)-\log (81)) x^3+15 e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^3-\frac {140}{81} e^{-6 x} (256-66 \log (3)+\log (9)) x^3-128 e^{-2 x} (4-\log (3))^3 x^3-64 e^{-x} (4-\log (3))^3 x^3+180 e^{-4 x} (4-\log (3))^2 x^3-\frac {4480}{81} e^{-6 x} (4-\log (3)) x^3-12 e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x^2+24 e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81)) x^2-9 e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^2+\frac {20}{27} e^{-6 x} (448-108 \log (3)-\log (81)) x^2+\frac {45}{4} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^2-\frac {70}{81} e^{-6 x} (256-66 \log (3)+\log (9)) x^2-192 e^{-2 x} (4-\log (3))^3 x^2+135 e^{-4 x} (4-\log (3))^2 x^2-\frac {2240}{81} e^{-6 x} (4-\log (3)) x^2-12 e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x+24 e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81)) x-\frac {9}{2} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x+\frac {20}{81} e^{-6 x} (448-108 \log (3)-\log (81)) x+\frac {45}{8} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x-\frac {70}{243} e^{-6 x} (256-66 \log (3)+\log (9)) x-192 e^{-2 x} (4-\log (3))^3 x+\frac {135}{2} e^{-4 x} (4-\log (3))^2 x-\frac {2240}{243} e^{-6 x} (4-\log (3)) x+\frac {8 (4-\log (3))^3 (-\log (9) x+8 x-\log (81)+16)^2}{8-\log (9)}-6 e^{-2 x} (4-\log (3))^2 (64-\log (43046721))+12 e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81))-\frac {9}{8} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81))+\frac {10}{243} e^{-6 x} (448-108 \log (3)-\log (81))+\frac {45}{32} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9))-\frac {35}{729} e^{-6 x} (256-66 \log (3)+\log (9))-16 e^x (4-\log (3))^4+16 e^x (x+1) (4-\log (3))^4-96 e^{-2 x} (4-\log (3))^3+\frac {135}{8} e^{-4 x} (4-\log (3))^2-\frac {1120}{729} e^{-6 x} (4-\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(576*x^8 - 352*x^9 - 128*x^10 + E^x*(144*x^8 - 112*x^9) + E^(3*x)*(-1792*x^6 + 1280*x^7 + (448*x^6 - 320*x
^7)*Log[3]) + E^(2*x)*(-7168*x^6 + 4096*x^7 + 1536*x^8 + (1792*x^6 - 1024*x^7 - 384*x^8)*Log[3]) + E^(5*x)*(76
80*x^4 - 4608*x^5 + (-3840*x^4 + 2304*x^5)*Log[3] + (480*x^4 - 288*x^5)*Log[3]^2) + E^(4*x)*(30720*x^4 - 15360
*x^5 - 6144*x^6 + (-15360*x^4 + 7680*x^5 + 3072*x^6)*Log[3] + (1920*x^4 - 960*x^5 - 384*x^6)*Log[3]^2) + E^(7*
x)*(-12288*x^2 + 4096*x^3 + (9216*x^2 - 3072*x^3)*Log[3] + (-2304*x^2 + 768*x^3)*Log[3]^2 + (192*x^2 - 64*x^3)
*Log[3]^3) + E^(6*x)*(-49152*x^2 + 16384*x^3 + 8192*x^4 + (36864*x^2 - 12288*x^3 - 6144*x^4)*Log[3] + (-9216*x
^2 + 3072*x^3 + 1536*x^4)*Log[3]^2 + (768*x^2 - 256*x^3 - 128*x^4)*Log[3]^3) + E^(9*x)*(4096 + 4096*x + (-4096
- 4096*x)*Log[3] + (1536 + 1536*x)*Log[3]^2 + (-256 - 256*x)*Log[3]^3 + (16 + 16*x)*Log[3]^4) + E^(8*x)*(1638
4 + 8192*x + (-16384 - 8192*x)*Log[3] + (6144 + 3072*x)*Log[3]^2 + (-1024 - 512*x)*Log[3]^3 + (64 + 32*x)*Log[
3]^4))/E^(8*x),x]

[Out]

(64*x^9)/E^(8*x) + (16*x^9)/E^(7*x) + (16*x^10)/E^(8*x) - (1120*(4 - Log[3]))/(729*E^(6*x)) - (2240*x*(4 - Log
[3]))/(243*E^(6*x)) - (2240*x^2*(4 - Log[3]))/(81*E^(6*x)) - (4480*x^3*(4 - Log[3]))/(81*E^(6*x)) - (2240*x^4*
(4 - Log[3]))/(27*E^(6*x)) - (896*x^5*(4 - Log[3]))/(9*E^(6*x)) - (896*x^6*(4 - Log[3]))/(9*E^(6*x)) - (256*x^
7*(4 - Log[3]))/(3*E^(6*x)) - (64*x^7*(4 - Log[3]))/E^(5*x) - (64*x^8*(4 - Log[3]))/E^(6*x) + (135*(4 - Log[3]
)^2)/(8*E^(4*x)) + (135*x*(4 - Log[3])^2)/(2*E^(4*x)) + (135*x^2*(4 - Log[3])^2)/E^(4*x) + (180*x^3*(4 - Log[3
])^2)/E^(4*x) + (180*x^4*(4 - Log[3])^2)/E^(4*x) + (144*x^5*(4 - Log[3])^2)/E^(4*x) + (96*x^5*(4 - Log[3])^2)/
E^(3*x) + (96*x^6*(4 - Log[3])^2)/E^(4*x) - (96*(4 - Log[3])^3)/E^(2*x) - (192*x*(4 - Log[3])^3)/E^(2*x) - (19
2*x^2*(4 - Log[3])^3)/E^(2*x) - (128*x^3*(4 - Log[3])^3)/E^(2*x) - (64*x^3*(4 - Log[3])^3)/E^x - (64*x^4*(4 -
Log[3])^3)/E^(2*x) - 16*E^x*(4 - Log[3])^4 + 16*E^x*(1 + x)*(4 - Log[3])^4 - (35*(256 - 66*Log[3] + Log[9]))/(
729*E^(6*x)) - (70*x*(256 - 66*Log[3] + Log[9]))/(243*E^(6*x)) - (70*x^2*(256 - 66*Log[3] + Log[9]))/(81*E^(6*
x)) - (140*x^3*(256 - 66*Log[3] + Log[9]))/(81*E^(6*x)) - (70*x^4*(256 - 66*Log[3] + Log[9]))/(27*E^(6*x)) - (
28*x^5*(256 - 66*Log[3] + Log[9]))/(9*E^(6*x)) - (28*x^6*(256 - 66*Log[3] + Log[9]))/(9*E^(6*x)) - (8*x^7*(256
- 66*Log[3] + Log[9]))/(3*E^(6*x)) + (45*(4 - Log[3])*(80 - 22*Log[3] + Log[9]))/(32*E^(4*x)) + (45*x*(4 - Lo
g[3])*(80 - 22*Log[3] + Log[9]))/(8*E^(4*x)) + (45*x^2*(4 - Log[3])*(80 - 22*Log[3] + Log[9]))/(4*E^(4*x)) + (
15*x^3*(4 - Log[3])*(80 - 22*Log[3] + Log[9]))/E^(4*x) + (15*x^4*(4 - Log[3])*(80 - 22*Log[3] + Log[9]))/E^(4*
x) + (12*x^5*(4 - Log[3])*(80 - 22*Log[3] + Log[9]))/E^(4*x) + (10*(448 - 108*Log[3] - Log[81]))/(243*E^(6*x))
+ (20*x*(448 - 108*Log[3] - Log[81]))/(81*E^(6*x)) + (20*x^2*(448 - 108*Log[3] - Log[81]))/(27*E^(6*x)) + (40
*x^3*(448 - 108*Log[3] - Log[81]))/(27*E^(6*x)) + (20*x^4*(448 - 108*Log[3] - Log[81]))/(9*E^(6*x)) + (8*x^5*(
448 - 108*Log[3] - Log[81]))/(3*E^(6*x)) + (8*x^6*(448 - 108*Log[3] - Log[81]))/(3*E^(6*x)) - (9*(4 - Log[3])*
(160 - 36*Log[3] - Log[81]))/(8*E^(4*x)) - (9*x*(4 - Log[3])*(160 - 36*Log[3] - Log[81]))/(2*E^(4*x)) - (9*x^2
*(4 - Log[3])*(160 - 36*Log[3] - Log[81]))/E^(4*x) - (12*x^3*(4 - Log[3])*(160 - 36*Log[3] - Log[81]))/E^(4*x)
- (12*x^4*(4 - Log[3])*(160 - 36*Log[3] - Log[81]))/E^(4*x) + (12*(4 - Log[3])^2*(64 - 12*Log[3] - Log[81]))/
E^(2*x) + (24*x*(4 - Log[3])^2*(64 - 12*Log[3] - Log[81]))/E^(2*x) + (24*x^2*(4 - Log[3])^2*(64 - 12*Log[3] -
Log[81]))/E^(2*x) + (8*(4 - Log[3])^3*(16 + 8*x - x*Log[9] - Log[81])^2)/(8 - Log[9]) - (6*(4 - Log[3])^2*(64
- Log[43046721]))/E^(2*x) - (12*x*(4 - Log[3])^2*(64 - Log[43046721]))/E^(2*x) - (12*x^2*(4 - Log[3])^2*(64 -
Log[43046721]))/E^(2*x) - (8*x^3*(4 - Log[3])^2*(64 - Log[43046721]))/E^(2*x)

Rule 12

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

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

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int 16 e^{-8 x} \left (x^2+e^{2 x} (-4+\log (3))\right )^3 \left (-e^x x^2 (-9+7 x)-2 x^2 \left (-18+11 x+4 x^2\right )+e^{3 x} (1+x) (-4+\log (3))+e^{2 x} (-16+x (-8+\log (9))+\log (81))\right ) \, dx\\ &=16 \int e^{-8 x} \left (x^2+e^{2 x} (-4+\log (3))\right )^3 \left (-e^x x^2 (-9+7 x)-2 x^2 \left (-18+11 x+4 x^2\right )+e^{3 x} (1+x) (-4+\log (3))+e^{2 x} (-16+x (-8+\log (9))+\log (81))\right ) \, dx\\ &=16 \int \left (-e^{-7 x} x^8 (-9+7 x)-2 e^{-8 x} x^8 \left (-18+11 x+4 x^2\right )-4 e^{-5 x} x^6 (-7+5 x) (-4+\log (3))-6 e^{-3 x} x^4 (-5+3 x) (-4+\log (3))^2-4 e^{-x} (-3+x) x^2 (-4+\log (3))^3+e^x (1+x) (-4+\log (3))^4+3 e^{-4 x} x^4 (4-\log (3)) \left (160-8 x^2 (4-\log (3))-36 \log (3)-x (80-22 \log (3)+\log (9))-\log (81)\right )+(-4+\log (3))^3 (-16-8 x+x \log (9)+\log (81))+e^{-6 x} x^6 \left (-448+24 x^2 (4-\log (3))+108 \log (3)+x (256-66 \log (3)+\log (9))+\log (81)\right )+e^{-2 x} x^2 (4-\log (3))^2 \left (8 x^2 (4-\log (3))-3 (64-12 \log (3)-\log (81))+x (64-\log (43046721))\right )\right ) \, dx\\ &=\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-16 \int e^{-7 x} x^8 (-9+7 x) \, dx+16 \int e^{-6 x} x^6 \left (-448+24 x^2 (4-\log (3))+108 \log (3)+x (256-66 \log (3)+\log (9))+\log (81)\right ) \, dx-32 \int e^{-8 x} x^8 \left (-18+11 x+4 x^2\right ) \, dx+(48 (4-\log (3))) \int e^{-4 x} x^4 \left (160-8 x^2 (4-\log (3))-36 \log (3)-x (80-22 \log (3)+\log (9))-\log (81)\right ) \, dx+(64 (4-\log (3))) \int e^{-5 x} x^6 (-7+5 x) \, dx+\left (16 (4-\log (3))^2\right ) \int e^{-2 x} x^2 \left (8 x^2 (4-\log (3))-3 (64-12 \log (3)-\log (81))+x (64-\log (43046721))\right ) \, dx-\left (96 (4-\log (3))^2\right ) \int e^{-3 x} x^4 (-5+3 x) \, dx+\left (64 (4-\log (3))^3\right ) \int e^{-x} (-3+x) x^2 \, dx+\left (16 (4-\log (3))^4\right ) \int e^x (1+x) \, dx\\ &=16 e^x (1+x) (4-\log (3))^4+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-16 \int \left (-9 e^{-7 x} x^8+7 e^{-7 x} x^9\right ) \, dx+16 \int \left (-24 e^{-6 x} x^8 (-4+\log (3))-e^{-6 x} x^7 (-256+66 \log (3)-\log (9))+e^{-6 x} x^6 (-448+108 \log (3)+\log (81))\right ) \, dx-32 \int \left (-18 e^{-8 x} x^8+11 e^{-8 x} x^9+4 e^{-8 x} x^{10}\right ) \, dx+(48 (4-\log (3))) \int \left (8 e^{-4 x} x^6 (-4+\log (3))+e^{-4 x} x^5 (-80+22 \log (3)-\log (9))-e^{-4 x} x^4 (-160+36 \log (3)+\log (81))\right ) \, dx+(64 (4-\log (3))) \int \left (-7 e^{-5 x} x^6+5 e^{-5 x} x^7\right ) \, dx+\left (16 (4-\log (3))^2\right ) \int \left (-8 e^{-2 x} x^4 (-4+\log (3))+3 e^{-2 x} x^2 (-64+12 \log (3)+\log (81))-e^{-2 x} x^3 (-64+\log (43046721))\right ) \, dx-\left (96 (4-\log (3))^2\right ) \int \left (-5 e^{-3 x} x^4+3 e^{-3 x} x^5\right ) \, dx+\left (64 (4-\log (3))^3\right ) \int \left (-3 e^{-x} x^2+e^{-x} x^3\right ) \, dx-\left (16 (4-\log (3))^4\right ) \int e^x \, dx\\ &=-16 e^x (4-\log (3))^4+16 e^x (1+x) (4-\log (3))^4+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-112 \int e^{-7 x} x^9 \, dx-128 \int e^{-8 x} x^{10} \, dx+144 \int e^{-7 x} x^8 \, dx-352 \int e^{-8 x} x^9 \, dx+576 \int e^{-8 x} x^8 \, dx+(320 (4-\log (3))) \int e^{-5 x} x^7 \, dx+(384 (4-\log (3))) \int e^{-6 x} x^8 \, dx-(448 (4-\log (3))) \int e^{-5 x} x^6 \, dx-\left (288 (4-\log (3))^2\right ) \int e^{-3 x} x^5 \, dx-\left (384 (4-\log (3))^2\right ) \int e^{-4 x} x^6 \, dx+\left (480 (4-\log (3))^2\right ) \int e^{-3 x} x^4 \, dx+\left (64 (4-\log (3))^3\right ) \int e^{-x} x^3 \, dx+\left (128 (4-\log (3))^3\right ) \int e^{-2 x} x^4 \, dx-\left (192 (4-\log (3))^3\right ) \int e^{-x} x^2 \, dx+(16 (256-66 \log (3)+\log (9))) \int e^{-6 x} x^7 \, dx-(48 (4-\log (3)) (80-22 \log (3)+\log (9))) \int e^{-4 x} x^5 \, dx-(16 (448-108 \log (3)-\log (81))) \int e^{-6 x} x^6 \, dx+(48 (4-\log (3)) (160-36 \log (3)-\log (81))) \int e^{-4 x} x^4 \, dx-\left (48 (4-\log (3))^2 (64-12 \log (3)-\log (81))\right ) \int e^{-2 x} x^2 \, dx+\left (16 (4-\log (3))^2 (64-\log (43046721))\right ) \int e^{-2 x} x^3 \, dx\\ &=-72 e^{-8 x} x^8-\frac {144}{7} e^{-7 x} x^8+44 e^{-8 x} x^9+16 e^{-7 x} x^9+16 e^{-8 x} x^{10}+\frac {448}{5} e^{-5 x} x^6 (4-\log (3))-64 e^{-5 x} x^7 (4-\log (3))-64 e^{-6 x} x^8 (4-\log (3))-160 e^{-3 x} x^4 (4-\log (3))^2+96 e^{-3 x} x^5 (4-\log (3))^2+96 e^{-4 x} x^6 (4-\log (3))^2+192 e^{-x} x^2 (4-\log (3))^3-64 e^{-x} x^3 (4-\log (3))^3-64 e^{-2 x} x^4 (4-\log (3))^3-16 e^x (4-\log (3))^4+16 e^x (1+x) (4-\log (3))^4-\frac {8}{3} e^{-6 x} x^7 (256-66 \log (3)+\log (9))+12 e^{-4 x} x^5 (4-\log (3)) (80-22 \log (3)+\log (9))+\frac {8}{3} e^{-6 x} x^6 (448-108 \log (3)-\log (81))-12 e^{-4 x} x^4 (4-\log (3)) (160-36 \log (3)-\log (81))+24 e^{-2 x} x^2 (4-\log (3))^2 (64-12 \log (3)-\log (81))+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-8 e^{-2 x} x^3 (4-\log (3))^2 (64-\log (43046721))-144 \int e^{-7 x} x^8 \, dx-160 \int e^{-8 x} x^9 \, dx+\frac {1152}{7} \int e^{-7 x} x^7 \, dx-396 \int e^{-8 x} x^8 \, dx+576 \int e^{-8 x} x^7 \, dx+(448 (4-\log (3))) \int e^{-5 x} x^6 \, dx+(512 (4-\log (3))) \int e^{-6 x} x^7 \, dx-\frac {1}{5} (2688 (4-\log (3))) \int e^{-5 x} x^5 \, dx-\left (480 (4-\log (3))^2\right ) \int e^{-3 x} x^4 \, dx-\left (576 (4-\log (3))^2\right ) \int e^{-4 x} x^5 \, dx+\left (640 (4-\log (3))^2\right ) \int e^{-3 x} x^3 \, dx+\left (192 (4-\log (3))^3\right ) \int e^{-x} x^2 \, dx+\left (256 (4-\log (3))^3\right ) \int e^{-2 x} x^3 \, dx-\left (384 (4-\log (3))^3\right ) \int e^{-x} x \, dx+\frac {1}{3} (56 (256-66 \log (3)+\log (9))) \int e^{-6 x} x^6 \, dx-(60 (4-\log (3)) (80-22 \log (3)+\log (9))) \int e^{-4 x} x^4 \, dx-(16 (448-108 \log (3)-\log (81))) \int e^{-6 x} x^5 \, dx+(48 (4-\log (3)) (160-36 \log (3)-\log (81))) \int e^{-4 x} x^3 \, dx-\left (48 (4-\log (3))^2 (64-12 \log (3)-\log (81))\right ) \int e^{-2 x} x \, dx+\left (24 (4-\log (3))^2 (64-\log (43046721))\right ) \int e^{-2 x} x^2 \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.28, size = 207, normalized size = 8.62 \begin {gather*} 16 \left (e^{-7 x} x^9+e^{-8 x} x^9 (4+x)+4 e^{-5 x} x^7 (-4+\log (3))+6 e^{-3 x} x^5 (-4+\log (3))^2+4 e^{-x} x^3 (-4+\log (3))^3+e^x x (-4+\log (3))^4+\frac {1}{2} e^{-2 x} x^3 (-4+\log (3))^2 (-128+8 x (-4+\log (3))+38 \log (3)-3 \log (9))+\frac {3}{4} e^{-4 x} x^5 (-4+\log (3)) (-128+8 x (-4+\log (3))+34 \log (3)-\log (9))+\frac {1}{6} e^{-6 x} x^7 (-384+24 x (-4+\log (3))+98 \log (3)-\log (9))+\frac {1}{2} x^2 (-4+\log (3))^3 (-8+\log (9))+x (-4+\log (3))^3 (-16+\log (81))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(576*x^8 - 352*x^9 - 128*x^10 + E^x*(144*x^8 - 112*x^9) + E^(3*x)*(-1792*x^6 + 1280*x^7 + (448*x^6 -
320*x^7)*Log[3]) + E^(2*x)*(-7168*x^6 + 4096*x^7 + 1536*x^8 + (1792*x^6 - 1024*x^7 - 384*x^8)*Log[3]) + E^(5*
x)*(7680*x^4 - 4608*x^5 + (-3840*x^4 + 2304*x^5)*Log[3] + (480*x^4 - 288*x^5)*Log[3]^2) + E^(4*x)*(30720*x^4 -
15360*x^5 - 6144*x^6 + (-15360*x^4 + 7680*x^5 + 3072*x^6)*Log[3] + (1920*x^4 - 960*x^5 - 384*x^6)*Log[3]^2) +
E^(7*x)*(-12288*x^2 + 4096*x^3 + (9216*x^2 - 3072*x^3)*Log[3] + (-2304*x^2 + 768*x^3)*Log[3]^2 + (192*x^2 - 6
4*x^3)*Log[3]^3) + E^(6*x)*(-49152*x^2 + 16384*x^3 + 8192*x^4 + (36864*x^2 - 12288*x^3 - 6144*x^4)*Log[3] + (-
9216*x^2 + 3072*x^3 + 1536*x^4)*Log[3]^2 + (768*x^2 - 256*x^3 - 128*x^4)*Log[3]^3) + E^(9*x)*(4096 + 4096*x +
(-4096 - 4096*x)*Log[3] + (1536 + 1536*x)*Log[3]^2 + (-256 - 256*x)*Log[3]^3 + (16 + 16*x)*Log[3]^4) + E^(8*x)
*(16384 + 8192*x + (-16384 - 8192*x)*Log[3] + (6144 + 3072*x)*Log[3]^2 + (-1024 - 512*x)*Log[3]^3 + (64 + 32*x
)*Log[3]^4))/E^(8*x),x]

[Out]

16*(x^9/E^(7*x) + (x^9*(4 + x))/E^(8*x) + (4*x^7*(-4 + Log[3]))/E^(5*x) + (6*x^5*(-4 + Log[3])^2)/E^(3*x) + (4
*x^3*(-4 + Log[3])^3)/E^x + E^x*x*(-4 + Log[3])^4 + (x^3*(-4 + Log[3])^2*(-128 + 8*x*(-4 + Log[3]) + 38*Log[3]
- 3*Log[9]))/(2*E^(2*x)) + (3*x^5*(-4 + Log[3])*(-128 + 8*x*(-4 + Log[3]) + 34*Log[3] - Log[9]))/(4*E^(4*x))
+ (x^7*(-384 + 24*x*(-4 + Log[3]) + 98*Log[3] - Log[9]))/(6*E^(6*x)) + (x^2*(-4 + Log[3])^3*(-8 + Log[9]))/2 +
x*(-4 + Log[3])^3*(-16 + Log[81]))

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fricas [B]  time = 0.74, size = 333, normalized size = 13.88 \begin {gather*} 16 \, {\left (x^{10} + x^{9} e^{x} + 4 \, x^{9} + {\left (x \log \relax (3)^{4} - 16 \, x \log \relax (3)^{3} + 96 \, x \log \relax (3)^{2} - 256 \, x \log \relax (3) + 256 \, x\right )} e^{\left (9 \, x\right )} + {\left ({\left (x^{2} + 4 \, x\right )} \log \relax (3)^{4} - 16 \, {\left (x^{2} + 4 \, x\right )} \log \relax (3)^{3} + 96 \, {\left (x^{2} + 4 \, x\right )} \log \relax (3)^{2} + 256 \, x^{2} - 256 \, {\left (x^{2} + 4 \, x\right )} \log \relax (3) + 1024 \, x\right )} e^{\left (8 \, x\right )} + 4 \, {\left (x^{3} \log \relax (3)^{3} - 12 \, x^{3} \log \relax (3)^{2} + 48 \, x^{3} \log \relax (3) - 64 \, x^{3}\right )} e^{\left (7 \, x\right )} - 4 \, {\left (64 \, x^{4} - {\left (x^{4} + 4 \, x^{3}\right )} \log \relax (3)^{3} + 256 \, x^{3} + 12 \, {\left (x^{4} + 4 \, x^{3}\right )} \log \relax (3)^{2} - 48 \, {\left (x^{4} + 4 \, x^{3}\right )} \log \relax (3)\right )} e^{\left (6 \, x\right )} + 6 \, {\left (x^{5} \log \relax (3)^{2} - 8 \, x^{5} \log \relax (3) + 16 \, x^{5}\right )} e^{\left (5 \, x\right )} + 6 \, {\left (16 \, x^{6} + 64 \, x^{5} + {\left (x^{6} + 4 \, x^{5}\right )} \log \relax (3)^{2} - 8 \, {\left (x^{6} + 4 \, x^{5}\right )} \log \relax (3)\right )} e^{\left (4 \, x\right )} + 4 \, {\left (x^{7} \log \relax (3) - 4 \, x^{7}\right )} e^{\left (3 \, x\right )} - 4 \, {\left (4 \, x^{8} + 16 \, x^{7} - {\left (x^{8} + 4 \, x^{7}\right )} \log \relax (3)\right )} e^{\left (2 \, x\right )}\right )} e^{\left (-8 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x+16)*log(3)^4+(-256*x-256)*log(3)^3+(1536*x+1536)*log(3)^2+(-4096*x-4096)*log(3)+4096*x+4096)
*exp(x)^9+((32*x+64)*log(3)^4+(-512*x-1024)*log(3)^3+(3072*x+6144)*log(3)^2+(-8192*x-16384)*log(3)+8192*x+1638
4)*exp(x)^8+((-64*x^3+192*x^2)*log(3)^3+(768*x^3-2304*x^2)*log(3)^2+(-3072*x^3+9216*x^2)*log(3)+4096*x^3-12288
*x^2)*exp(x)^7+((-128*x^4-256*x^3+768*x^2)*log(3)^3+(1536*x^4+3072*x^3-9216*x^2)*log(3)^2+(-6144*x^4-12288*x^3
+36864*x^2)*log(3)+8192*x^4+16384*x^3-49152*x^2)*exp(x)^6+((-288*x^5+480*x^4)*log(3)^2+(2304*x^5-3840*x^4)*log
(3)-4608*x^5+7680*x^4)*exp(x)^5+((-384*x^6-960*x^5+1920*x^4)*log(3)^2+(3072*x^6+7680*x^5-15360*x^4)*log(3)-614
4*x^6-15360*x^5+30720*x^4)*exp(x)^4+((-320*x^7+448*x^6)*log(3)+1280*x^7-1792*x^6)*exp(x)^3+((-384*x^8-1024*x^7
+1792*x^6)*log(3)+1536*x^8+4096*x^7-7168*x^6)*exp(x)^2+(-112*x^9+144*x^8)*exp(x)-128*x^10-352*x^9+576*x^8)/exp
(x)^8,x, algorithm="fricas")

[Out]

16*(x^10 + x^9*e^x + 4*x^9 + (x*log(3)^4 - 16*x*log(3)^3 + 96*x*log(3)^2 - 256*x*log(3) + 256*x)*e^(9*x) + ((x
^2 + 4*x)*log(3)^4 - 16*(x^2 + 4*x)*log(3)^3 + 96*(x^2 + 4*x)*log(3)^2 + 256*x^2 - 256*(x^2 + 4*x)*log(3) + 10
24*x)*e^(8*x) + 4*(x^3*log(3)^3 - 12*x^3*log(3)^2 + 48*x^3*log(3) - 64*x^3)*e^(7*x) - 4*(64*x^4 - (x^4 + 4*x^3
)*log(3)^3 + 256*x^3 + 12*(x^4 + 4*x^3)*log(3)^2 - 48*(x^4 + 4*x^3)*log(3))*e^(6*x) + 6*(x^5*log(3)^2 - 8*x^5*
log(3) + 16*x^5)*e^(5*x) + 6*(16*x^6 + 64*x^5 + (x^6 + 4*x^5)*log(3)^2 - 8*(x^6 + 4*x^5)*log(3))*e^(4*x) + 4*(
x^7*log(3) - 4*x^7)*e^(3*x) - 4*(4*x^8 + 16*x^7 - (x^8 + 4*x^7)*log(3))*e^(2*x))*e^(-8*x)

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giac [B]  time = 0.42, size = 432, normalized size = 18.00 \begin {gather*} 16 \, x^{10} e^{\left (-8 \, x\right )} + 16 \, x^{9} e^{\left (-7 \, x\right )} + 64 \, x^{9} e^{\left (-8 \, x\right )} + 64 \, x^{8} e^{\left (-6 \, x\right )} \log \relax (3) - 256 \, x^{8} e^{\left (-6 \, x\right )} + 64 \, x^{7} e^{\left (-5 \, x\right )} \log \relax (3) + 256 \, x^{7} e^{\left (-6 \, x\right )} \log \relax (3) + 96 \, x^{6} e^{\left (-4 \, x\right )} \log \relax (3)^{2} - 256 \, x^{7} e^{\left (-5 \, x\right )} - 1024 \, x^{7} e^{\left (-6 \, x\right )} - 768 \, x^{6} e^{\left (-4 \, x\right )} \log \relax (3) + 96 \, x^{5} e^{\left (-3 \, x\right )} \log \relax (3)^{2} + 384 \, x^{5} e^{\left (-4 \, x\right )} \log \relax (3)^{2} + 64 \, x^{4} e^{\left (-2 \, x\right )} \log \relax (3)^{3} + 1536 \, x^{6} e^{\left (-4 \, x\right )} - 768 \, x^{5} e^{\left (-3 \, x\right )} \log \relax (3) - 3072 \, x^{5} e^{\left (-4 \, x\right )} \log \relax (3) - 768 \, x^{4} e^{\left (-2 \, x\right )} \log \relax (3)^{2} + 64 \, x^{3} e^{\left (-x\right )} \log \relax (3)^{3} + 256 \, x^{3} e^{\left (-2 \, x\right )} \log \relax (3)^{3} + 1536 \, x^{5} e^{\left (-3 \, x\right )} + 6144 \, x^{5} e^{\left (-4 \, x\right )} + 3072 \, x^{4} e^{\left (-2 \, x\right )} \log \relax (3) - 768 \, x^{3} e^{\left (-x\right )} \log \relax (3)^{2} - 3072 \, x^{3} e^{\left (-2 \, x\right )} \log \relax (3)^{2} + 16 \, x^{2} \log \relax (3)^{4} + 16 \, x e^{x} \log \relax (3)^{4} - 4096 \, x^{4} e^{\left (-2 \, x\right )} + 3072 \, x^{3} e^{\left (-x\right )} \log \relax (3) + 12288 \, x^{3} e^{\left (-2 \, x\right )} \log \relax (3) - 256 \, x^{2} \log \relax (3)^{3} - 256 \, x e^{x} \log \relax (3)^{3} + 64 \, x \log \relax (3)^{4} - 4096 \, x^{3} e^{\left (-x\right )} - 16384 \, x^{3} e^{\left (-2 \, x\right )} + 1536 \, x^{2} \log \relax (3)^{2} + 1536 \, x e^{x} \log \relax (3)^{2} - 1024 \, x \log \relax (3)^{3} - 4096 \, x^{2} \log \relax (3) - 4096 \, x e^{x} \log \relax (3) + 6144 \, x \log \relax (3)^{2} + 4096 \, x^{2} + 4096 \, x e^{x} - 16384 \, x \log \relax (3) + 16384 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x+16)*log(3)^4+(-256*x-256)*log(3)^3+(1536*x+1536)*log(3)^2+(-4096*x-4096)*log(3)+4096*x+4096)
*exp(x)^9+((32*x+64)*log(3)^4+(-512*x-1024)*log(3)^3+(3072*x+6144)*log(3)^2+(-8192*x-16384)*log(3)+8192*x+1638
4)*exp(x)^8+((-64*x^3+192*x^2)*log(3)^3+(768*x^3-2304*x^2)*log(3)^2+(-3072*x^3+9216*x^2)*log(3)+4096*x^3-12288
*x^2)*exp(x)^7+((-128*x^4-256*x^3+768*x^2)*log(3)^3+(1536*x^4+3072*x^3-9216*x^2)*log(3)^2+(-6144*x^4-12288*x^3
+36864*x^2)*log(3)+8192*x^4+16384*x^3-49152*x^2)*exp(x)^6+((-288*x^5+480*x^4)*log(3)^2+(2304*x^5-3840*x^4)*log
(3)-4608*x^5+7680*x^4)*exp(x)^5+((-384*x^6-960*x^5+1920*x^4)*log(3)^2+(3072*x^6+7680*x^5-15360*x^4)*log(3)-614
4*x^6-15360*x^5+30720*x^4)*exp(x)^4+((-320*x^7+448*x^6)*log(3)+1280*x^7-1792*x^6)*exp(x)^3+((-384*x^8-1024*x^7
+1792*x^6)*log(3)+1536*x^8+4096*x^7-7168*x^6)*exp(x)^2+(-112*x^9+144*x^8)*exp(x)-128*x^10-352*x^9+576*x^8)/exp
(x)^8,x, algorithm="giac")

[Out]

16*x^10*e^(-8*x) + 16*x^9*e^(-7*x) + 64*x^9*e^(-8*x) + 64*x^8*e^(-6*x)*log(3) - 256*x^8*e^(-6*x) + 64*x^7*e^(-
5*x)*log(3) + 256*x^7*e^(-6*x)*log(3) + 96*x^6*e^(-4*x)*log(3)^2 - 256*x^7*e^(-5*x) - 1024*x^7*e^(-6*x) - 768*
x^6*e^(-4*x)*log(3) + 96*x^5*e^(-3*x)*log(3)^2 + 384*x^5*e^(-4*x)*log(3)^2 + 64*x^4*e^(-2*x)*log(3)^3 + 1536*x
^6*e^(-4*x) - 768*x^5*e^(-3*x)*log(3) - 3072*x^5*e^(-4*x)*log(3) - 768*x^4*e^(-2*x)*log(3)^2 + 64*x^3*e^(-x)*l
og(3)^3 + 256*x^3*e^(-2*x)*log(3)^3 + 1536*x^5*e^(-3*x) + 6144*x^5*e^(-4*x) + 3072*x^4*e^(-2*x)*log(3) - 768*x
^3*e^(-x)*log(3)^2 - 3072*x^3*e^(-2*x)*log(3)^2 + 16*x^2*log(3)^4 + 16*x*e^x*log(3)^4 - 4096*x^4*e^(-2*x) + 30
72*x^3*e^(-x)*log(3) + 12288*x^3*e^(-2*x)*log(3) - 256*x^2*log(3)^3 - 256*x*e^x*log(3)^3 + 64*x*log(3)^4 - 409
6*x^3*e^(-x) - 16384*x^3*e^(-2*x) + 1536*x^2*log(3)^2 + 1536*x*e^x*log(3)^2 - 1024*x*log(3)^3 - 4096*x^2*log(3
) - 4096*x*e^x*log(3) + 6144*x*log(3)^2 + 4096*x^2 + 4096*x*e^x - 16384*x*log(3) + 16384*x

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maple [B]  time = 0.14, size = 323, normalized size = 13.46

method	result	size
risch	\(16 x^{2} \ln \relax (3)^{4}+64 x \ln \relax (3)^{4}-256 \ln \relax (3)^{3} x^{2}-1024 x \ln \relax (3)^{3}+1536 x^{2} \ln \relax (3)^{2}+6144 x \ln \relax (3)^{2}-4096 x^{2} \ln \relax (3)-16384 x \ln \relax (3)+4096 x^{2}+16384 x +16 \left (\ln \relax (3)^{4}-16 \ln \relax (3)^{3}+96 \ln \relax (3)^{2}-256 \ln \relax (3)+256\right ) x \,{\mathrm e}^{x}+64 \left (\ln \relax (3)^{3}-12 \ln \relax (3)^{2}+48 \ln \relax (3)-64\right ) x^{3} {\mathrm e}^{-x}+\left (64 x^{4} \ln \relax (3)^{3}+256 x^{3} \ln \relax (3)^{3}-768 x^{4} \ln \relax (3)^{2}-3072 x^{3} \ln \relax (3)^{2}+3072 x^{4} \ln \relax (3)+12288 x^{3} \ln \relax (3)-4096 x^{4}-16384 x^{3}\right ) {\mathrm e}^{-2 x}+96 \left (\ln \relax (3)^{2}-8 \ln \relax (3)+16\right ) x^{5} {\mathrm e}^{-3 x}+\left (96 x^{6} \ln \relax (3)^{2}+384 x^{5} \ln \relax (3)^{2}-768 x^{6} \ln \relax (3)-3072 x^{5} \ln \relax (3)+1536 x^{6}+6144 x^{5}\right ) {\mathrm e}^{-4 x}+64 \left (-4+\ln \relax (3)\right ) x^{7} {\mathrm e}^{-5 x}+\left (64 x^{8} \ln \relax (3)+256 \ln \relax (3) x^{7}-256 x^{8}-1024 x^{7}\right ) {\mathrm e}^{-6 x}+16 \,{\mathrm e}^{-7 x} x^{9}+\left (16 x^{10}+64 x^{9}\right ) {\mathrm e}^{-8 x}\)	\(323\)
default	\(16384 x +1536 x \ln \relax (3)^{2} {\mathrm e}^{x}-4096 x^{2} \ln \relax (3)+4096 x^{2}-1024 x \ln \relax (3)^{3}+6144 x \ln \relax (3)^{2}-16384 x \ln \relax (3)+64 x \ln \relax (3)^{4}+4096 \,{\mathrm e}^{x} x -4096 x^{3} {\mathrm e}^{-x}+1536 x^{5} {\mathrm e}^{-3 x}-256 x^{7} {\mathrm e}^{-5 x}-4096 x \ln \relax (3) {\mathrm e}^{x}+16 x^{2} \ln \relax (3)^{4}+1536 x^{2} \ln \relax (3)^{2}+16 \,{\mathrm e}^{-7 x} x^{9}-4096 x^{4} {\mathrm e}^{-2 x}-1024 \,{\mathrm e}^{-6 x} x^{7}-256 \ln \relax (3)^{3} x^{2}-256 \,{\mathrm e}^{-6 x} x^{8}+16 \,{\mathrm e}^{-8 x} x^{10}+64 \,{\mathrm e}^{-8 x} x^{9}-16384 \,{\mathrm e}^{-2 x} x^{3}+1536 \,{\mathrm e}^{-4 x} x^{6}+6144 \,{\mathrm e}^{-4 x} x^{5}+256 \,{\mathrm e}^{-2 x} \ln \relax (3)^{3} x^{3}-768 \,{\mathrm e}^{-2 x} \ln \relax (3)^{2} x^{4}+96 \,{\mathrm e}^{-3 x} \ln \relax (3)^{2} x^{5}+96 \,{\mathrm e}^{-4 x} \ln \relax (3)^{2} x^{6}+3072 \,{\mathrm e}^{-x} \ln \relax (3) x^{3}-3072 \,{\mathrm e}^{-2 x} \ln \relax (3)^{2} x^{3}+3072 \,{\mathrm e}^{-2 x} \ln \relax (3) x^{4}-768 \,{\mathrm e}^{-3 x} \ln \relax (3) x^{5}+384 \,{\mathrm e}^{-4 x} \ln \relax (3)^{2} x^{5}-768 \,{\mathrm e}^{-4 x} \ln \relax (3) x^{6}+64 \,{\mathrm e}^{-5 x} \ln \relax (3) x^{7}+64 \,{\mathrm e}^{-6 x} \ln \relax (3) x^{8}+12288 \,{\mathrm e}^{-2 x} \ln \relax (3) x^{3}-3072 \,{\mathrm e}^{-4 x} \ln \relax (3) x^{5}+256 \,{\mathrm e}^{-6 x} \ln \relax (3) x^{7}+64 \,{\mathrm e}^{-x} \ln \relax (3)^{3} x^{3}+64 \,{\mathrm e}^{-2 x} \ln \relax (3)^{3} x^{4}-768 \,{\mathrm e}^{-x} \ln \relax (3)^{2} x^{3}+16 \,{\mathrm e}^{x} \ln \relax (3)^{4} x -256 \,{\mathrm e}^{x} \ln \relax (3)^{3} x\)	\(433\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((16*x+16)*ln(3)^4+(-256*x-256)*ln(3)^3+(1536*x+1536)*ln(3)^2+(-4096*x-4096)*ln(3)+4096*x+4096)*exp(x)^9+
((32*x+64)*ln(3)^4+(-512*x-1024)*ln(3)^3+(3072*x+6144)*ln(3)^2+(-8192*x-16384)*ln(3)+8192*x+16384)*exp(x)^8+((
-64*x^3+192*x^2)*ln(3)^3+(768*x^3-2304*x^2)*ln(3)^2+(-3072*x^3+9216*x^2)*ln(3)+4096*x^3-12288*x^2)*exp(x)^7+((
-128*x^4-256*x^3+768*x^2)*ln(3)^3+(1536*x^4+3072*x^3-9216*x^2)*ln(3)^2+(-6144*x^4-12288*x^3+36864*x^2)*ln(3)+8
192*x^4+16384*x^3-49152*x^2)*exp(x)^6+((-288*x^5+480*x^4)*ln(3)^2+(2304*x^5-3840*x^4)*ln(3)-4608*x^5+7680*x^4)
*exp(x)^5+((-384*x^6-960*x^5+1920*x^4)*ln(3)^2+(3072*x^6+7680*x^5-15360*x^4)*ln(3)-6144*x^6-15360*x^5+30720*x^
4)*exp(x)^4+((-320*x^7+448*x^6)*ln(3)+1280*x^7-1792*x^6)*exp(x)^3+((-384*x^8-1024*x^7+1792*x^6)*ln(3)+1536*x^8
+4096*x^7-7168*x^6)*exp(x)^2+(-112*x^9+144*x^8)*exp(x)-128*x^10-352*x^9+576*x^8)/exp(x)^8,x,method=_RETURNVERB
OSE)

[Out]

16*x^2*ln(3)^4+64*x*ln(3)^4-256*ln(3)^3*x^2-1024*x*ln(3)^3+1536*x^2*ln(3)^2+6144*x*ln(3)^2-4096*x^2*ln(3)-1638
4*x*ln(3)+4096*x^2+16384*x+16*(ln(3)^4-16*ln(3)^3+96*ln(3)^2-256*ln(3)+256)*x*exp(x)+64*(ln(3)^3-12*ln(3)^2+48
*ln(3)-64)*x^3*exp(-x)+(64*x^4*ln(3)^3+256*x^3*ln(3)^3-768*x^4*ln(3)^2-3072*x^3*ln(3)^2+3072*x^4*ln(3)+12288*x
^3*ln(3)-4096*x^4-16384*x^3)*exp(-2*x)+96*(ln(3)^2-8*ln(3)+16)*x^5*exp(-3*x)+(96*x^6*ln(3)^2+384*x^5*ln(3)^2-7
68*x^6*ln(3)-3072*x^5*ln(3)+1536*x^6+6144*x^5)*exp(-4*x)+64*(-4+ln(3))*x^7*exp(-5*x)+(64*x^8*ln(3)+256*ln(3)*x
^7-256*x^8-1024*x^7)*exp(-6*x)+16*exp(-7*x)*x^9+(16*x^10+64*x^9)*exp(-8*x)

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maxima [B]  time = 0.76, size = 1726, normalized size = 71.92 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x+16)*log(3)^4+(-256*x-256)*log(3)^3+(1536*x+1536)*log(3)^2+(-4096*x-4096)*log(3)+4096*x+4096)
*exp(x)^9+((32*x+64)*log(3)^4+(-512*x-1024)*log(3)^3+(3072*x+6144)*log(3)^2+(-8192*x-16384)*log(3)+8192*x+1638
4)*exp(x)^8+((-64*x^3+192*x^2)*log(3)^3+(768*x^3-2304*x^2)*log(3)^2+(-3072*x^3+9216*x^2)*log(3)+4096*x^3-12288
*x^2)*exp(x)^7+((-128*x^4-256*x^3+768*x^2)*log(3)^3+(1536*x^4+3072*x^3-9216*x^2)*log(3)^2+(-6144*x^4-12288*x^3
+36864*x^2)*log(3)+8192*x^4+16384*x^3-49152*x^2)*exp(x)^6+((-288*x^5+480*x^4)*log(3)^2+(2304*x^5-3840*x^4)*log
(3)-4608*x^5+7680*x^4)*exp(x)^5+((-384*x^6-960*x^5+1920*x^4)*log(3)^2+(3072*x^6+7680*x^5-15360*x^4)*log(3)-614
4*x^6-15360*x^5+30720*x^4)*exp(x)^4+((-320*x^7+448*x^6)*log(3)+1280*x^7-1792*x^6)*exp(x)^3+((-384*x^8-1024*x^7
+1792*x^6)*log(3)+1536*x^8+4096*x^7-7168*x^6)*exp(x)^2+(-112*x^9+144*x^8)*exp(x)-128*x^10-352*x^9+576*x^8)/exp
(x)^8,x, algorithm="maxima")

[Out]

16*x^2*log(3)^4 + 16*(x - 1)*e^x*log(3)^4 - 256*x^2*log(3)^3 + 64*(x^3 + 3*x^2 + 6*x + 6)*e^(-x)*log(3)^3 - 19
2*(x^2 + 2*x + 2)*e^(-x)*log(3)^3 + 32*(2*x^4 + 4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3)^3 + 32*(4*x^3 + 6*x^2
+ 6*x + 3)*e^(-2*x)*log(3)^3 - 192*(2*x^2 + 2*x + 1)*e^(-2*x)*log(3)^3 - 256*(x - 1)*e^x*log(3)^3 + 64*x*log(
3)^4 + 16*e^x*log(3)^4 + 1536*x^2*log(3)^2 - 768*(x^3 + 3*x^2 + 6*x + 6)*e^(-x)*log(3)^2 + 2304*(x^2 + 2*x + 2
)*e^(-x)*log(3)^2 - 384*(2*x^4 + 4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3)^2 - 384*(4*x^3 + 6*x^2 + 6*x + 3)*e^
(-2*x)*log(3)^2 + 2304*(2*x^2 + 2*x + 1)*e^(-2*x)*log(3)^2 + 32/27*(81*x^5 + 135*x^4 + 180*x^3 + 180*x^2 + 120
*x + 40)*e^(-3*x)*log(3)^2 - 160/27*(27*x^4 + 36*x^3 + 36*x^2 + 24*x + 8)*e^(-3*x)*log(3)^2 + 3/8*(256*x^6 + 3
84*x^5 + 480*x^4 + 480*x^3 + 360*x^2 + 180*x + 45)*e^(-4*x)*log(3)^2 + 15/8*(128*x^5 + 160*x^4 + 160*x^3 + 120
*x^2 + 60*x + 15)*e^(-4*x)*log(3)^2 - 15*(32*x^4 + 32*x^3 + 24*x^2 + 12*x + 3)*e^(-4*x)*log(3)^2 + 1536*(x - 1
)*e^x*log(3)^2 - 1024*x*log(3)^3 - 256*e^x*log(3)^3 - 4096*x^2*log(3) + 3072*(x^3 + 3*x^2 + 6*x + 6)*e^(-x)*lo
g(3) - 9216*(x^2 + 2*x + 2)*e^(-x)*log(3) + 1536*(2*x^4 + 4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3) + 1536*(4*x
^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3) - 9216*(2*x^2 + 2*x + 1)*e^(-2*x)*log(3) - 256/27*(81*x^5 + 135*x^4 + 18
0*x^3 + 180*x^2 + 120*x + 40)*e^(-3*x)*log(3) + 1280/27*(27*x^4 + 36*x^3 + 36*x^2 + 24*x + 8)*e^(-3*x)*log(3)
- 3*(256*x^6 + 384*x^5 + 480*x^4 + 480*x^3 + 360*x^2 + 180*x + 45)*e^(-4*x)*log(3) - 15*(128*x^5 + 160*x^4 + 1
60*x^3 + 120*x^2 + 60*x + 15)*e^(-4*x)*log(3) + 120*(32*x^4 + 32*x^3 + 24*x^2 + 12*x + 3)*e^(-4*x)*log(3) + 64
/15625*(15625*x^7 + 21875*x^6 + 26250*x^5 + 26250*x^4 + 21000*x^3 + 12600*x^2 + 5040*x + 1008)*e^(-5*x)*log(3)
- 448/15625*(3125*x^6 + 3750*x^5 + 3750*x^4 + 3000*x^3 + 1800*x^2 + 720*x + 144)*e^(-5*x)*log(3) + 32/729*(14
58*x^8 + 1944*x^7 + 2268*x^6 + 2268*x^5 + 1890*x^4 + 1260*x^3 + 630*x^2 + 210*x + 35)*e^(-6*x)*log(3) + 64/729
*(1944*x^7 + 2268*x^6 + 2268*x^5 + 1890*x^4 + 1260*x^3 + 630*x^2 + 210*x + 35)*e^(-6*x)*log(3) - 224/243*(324*
x^6 + 324*x^5 + 270*x^4 + 180*x^3 + 90*x^2 + 30*x + 5)*e^(-6*x)*log(3) - 4096*(x - 1)*e^x*log(3) + 6144*x*log(
3)^2 + 1536*e^x*log(3)^2 + 4096*x^2 - 4096*(x^3 + 3*x^2 + 6*x + 6)*e^(-x) + 12288*(x^2 + 2*x + 2)*e^(-x) - 204
8*(2*x^4 + 4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x) - 2048*(4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x) + 12288*(2*x^2 + 2*x +
1)*e^(-2*x) + 512/27*(81*x^5 + 135*x^4 + 180*x^3 + 180*x^2 + 120*x + 40)*e^(-3*x) - 2560/27*(27*x^4 + 36*x^3 +
36*x^2 + 24*x + 8)*e^(-3*x) + 6*(256*x^6 + 384*x^5 + 480*x^4 + 480*x^3 + 360*x^2 + 180*x + 45)*e^(-4*x) + 30*
(128*x^5 + 160*x^4 + 160*x^3 + 120*x^2 + 60*x + 15)*e^(-4*x) - 240*(32*x^4 + 32*x^3 + 24*x^2 + 12*x + 3)*e^(-4
*x) - 256/15625*(15625*x^7 + 21875*x^6 + 26250*x^5 + 26250*x^4 + 21000*x^3 + 12600*x^2 + 5040*x + 1008)*e^(-5*
x) + 1792/15625*(3125*x^6 + 3750*x^5 + 3750*x^4 + 3000*x^3 + 1800*x^2 + 720*x + 144)*e^(-5*x) - 128/729*(1458*
x^8 + 1944*x^7 + 2268*x^6 + 2268*x^5 + 1890*x^4 + 1260*x^3 + 630*x^2 + 210*x + 35)*e^(-6*x) - 256/729*(1944*x^
7 + 2268*x^6 + 2268*x^5 + 1890*x^4 + 1260*x^3 + 630*x^2 + 210*x + 35)*e^(-6*x) + 896/243*(324*x^6 + 324*x^5 +
270*x^4 + 180*x^3 + 90*x^2 + 30*x + 5)*e^(-6*x) + 16/5764801*(5764801*x^9 + 7411887*x^8 + 8470728*x^7 + 847072
8*x^6 + 7260624*x^5 + 5186160*x^4 + 2963520*x^3 + 1270080*x^2 + 362880*x + 51840)*e^(-7*x) - 144/5764801*(8235
43*x^8 + 941192*x^7 + 941192*x^6 + 806736*x^5 + 576240*x^4 + 329280*x^3 + 141120*x^2 + 40320*x + 5760)*e^(-7*x
) + 1/262144*(4194304*x^10 + 5242880*x^9 + 5898240*x^8 + 5898240*x^7 + 5160960*x^6 + 3870720*x^5 + 2419200*x^4
+ 1209600*x^3 + 453600*x^2 + 113400*x + 14175)*e^(-8*x) + 11/262144*(1048576*x^9 + 1179648*x^8 + 1179648*x^7
+ 1032192*x^6 + 774144*x^5 + 483840*x^4 + 241920*x^3 + 90720*x^2 + 22680*x + 2835)*e^(-8*x) - 9/16384*(131072*
x^8 + 131072*x^7 + 114688*x^6 + 86016*x^5 + 53760*x^4 + 26880*x^3 + 10080*x^2 + 2520*x + 315)*e^(-8*x) + 4096*
(x - 1)*e^x - 16384*x*log(3) - 4096*e^x*log(3) + 16384*x + 4096*e^x

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mupad [B]  time = 1.65, size = 183, normalized size = 7.62 \begin {gather*} 64\,x\,{\left (\ln \relax (3)-4\right )}^4+16\,x^2\,{\left (\ln \relax (3)-4\right )}^4+{\mathrm {e}}^{-8\,x}\,\left (16\,x^{10}+64\,x^9\right )+16\,x^9\,{\mathrm {e}}^{-7\,x}+{\mathrm {e}}^{-6\,x}\,\left (\left (64\,\ln \relax (3)-256\right )\,x^8+\left (256\,\ln \relax (3)-1024\right )\,x^7\right )+{\mathrm {e}}^{-2\,x}\,\left (64\,{\left (\ln \relax (3)-4\right )}^3\,x^4+256\,{\left (\ln \relax (3)-4\right )}^3\,x^3\right )+{\mathrm {e}}^{-4\,x}\,\left (96\,{\left (\ln \relax (3)-4\right )}^2\,x^6+384\,{\left (\ln \relax (3)-4\right )}^2\,x^5\right )+x^7\,{\mathrm {e}}^{-5\,x}\,\left (64\,\ln \relax (3)-256\right )+64\,x^3\,{\mathrm {e}}^{-x}\,{\left (\ln \relax (3)-4\right )}^3+96\,x^5\,{\mathrm {e}}^{-3\,x}\,{\left (\ln \relax (3)-4\right )}^2+16\,x\,{\mathrm {e}}^x\,{\left (\ln \relax (3)-4\right )}^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-8*x)*(exp(3*x)*(log(3)*(448*x^6 - 320*x^7) - 1792*x^6 + 1280*x^7) + exp(x)*(144*x^8 - 112*x^9) - exp(
2*x)*(log(3)*(1024*x^7 - 1792*x^6 + 384*x^8) + 7168*x^6 - 4096*x^7 - 1536*x^8) - exp(4*x)*(log(3)^2*(960*x^5 -
1920*x^4 + 384*x^6) - log(3)*(7680*x^5 - 15360*x^4 + 3072*x^6) - 30720*x^4 + 15360*x^5 + 6144*x^6) - exp(6*x)
*(log(3)^3*(256*x^3 - 768*x^2 + 128*x^4) - log(3)^2*(3072*x^3 - 9216*x^2 + 1536*x^4) + log(3)*(12288*x^3 - 368
64*x^2 + 6144*x^4) + 49152*x^2 - 16384*x^3 - 8192*x^4) + 576*x^8 - 352*x^9 - 128*x^10 + exp(7*x)*(log(3)*(9216
*x^2 - 3072*x^3) - 12288*x^2 + 4096*x^3 + log(3)^3*(192*x^2 - 64*x^3) - log(3)^2*(2304*x^2 - 768*x^3)) - exp(5
*x)*(log(3)*(3840*x^4 - 2304*x^5) - 7680*x^4 + 4608*x^5 - log(3)^2*(480*x^4 - 288*x^5)) + exp(9*x)*(4096*x - l
og(3)*(4096*x + 4096) + log(3)^4*(16*x + 16) - log(3)^3*(256*x + 256) + log(3)^2*(1536*x + 1536) + 4096) + exp
(8*x)*(8192*x - log(3)*(8192*x + 16384) + log(3)^4*(32*x + 64) - log(3)^3*(512*x + 1024) + log(3)^2*(3072*x +
6144) + 16384)),x)

[Out]

64*x*(log(3) - 4)^4 + 16*x^2*(log(3) - 4)^4 + exp(-8*x)*(64*x^9 + 16*x^10) + 16*x^9*exp(-7*x) + exp(-6*x)*(x^8
*(64*log(3) - 256) + x^7*(256*log(3) - 1024)) + exp(-2*x)*(256*x^3*(log(3) - 4)^3 + 64*x^4*(log(3) - 4)^3) + e
xp(-4*x)*(384*x^5*(log(3) - 4)^2 + 96*x^6*(log(3) - 4)^2) + x^7*exp(-5*x)*(64*log(3) - 256) + 64*x^3*exp(-x)*(
log(3) - 4)^3 + 96*x^5*exp(-3*x)*(log(3) - 4)^2 + 16*x*exp(x)*(log(3) - 4)^4

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sympy [B]  time = 0.85, size = 366, normalized size = 15.25 \begin {gather*} 16 x^{9} e^{- 7 x} + x^{2} \left (- 4096 \log {\relax (3 )} - 256 \log {\relax (3 )}^{3} + 16 \log {\relax (3 )}^{4} + 1536 \log {\relax (3 )}^{2} + 4096\right ) + x \left (- 16384 \log {\relax (3 )} - 1024 \log {\relax (3 )}^{3} + 64 \log {\relax (3 )}^{4} + 6144 \log {\relax (3 )}^{2} + 16384\right ) + \left (- 256 x^{7} + 64 x^{7} \log {\relax (3 )}\right ) e^{- 5 x} + \left (16 x^{10} + 64 x^{9}\right ) e^{- 8 x} + \left (- 768 x^{5} \log {\relax (3 )} + 96 x^{5} \log {\relax (3 )}^{2} + 1536 x^{5}\right ) e^{- 3 x} + \left (- 4096 x^{3} - 768 x^{3} \log {\relax (3 )}^{2} + 64 x^{3} \log {\relax (3 )}^{3} + 3072 x^{3} \log {\relax (3 )}\right ) e^{- x} + \left (- 256 x^{8} + 64 x^{8} \log {\relax (3 )} - 1024 x^{7} + 256 x^{7} \log {\relax (3 )}\right ) e^{- 6 x} + \left (- 4096 x \log {\relax (3 )} - 256 x \log {\relax (3 )}^{3} + 16 x \log {\relax (3 )}^{4} + 1536 x \log {\relax (3 )}^{2} + 4096 x\right ) e^{x} + \left (- 768 x^{6} \log {\relax (3 )} + 96 x^{6} \log {\relax (3 )}^{2} + 1536 x^{6} - 3072 x^{5} \log {\relax (3 )} + 384 x^{5} \log {\relax (3 )}^{2} + 6144 x^{5}\right ) e^{- 4 x} + \left (- 4096 x^{4} - 768 x^{4} \log {\relax (3 )}^{2} + 64 x^{4} \log {\relax (3 )}^{3} + 3072 x^{4} \log {\relax (3 )} - 16384 x^{3} - 3072 x^{3} \log {\relax (3 )}^{2} + 256 x^{3} \log {\relax (3 )}^{3} + 12288 x^{3} \log {\relax (3 )}\right ) e^{- 2 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x+16)*ln(3)**4+(-256*x-256)*ln(3)**3+(1536*x+1536)*ln(3)**2+(-4096*x-4096)*ln(3)+4096*x+4096)*
exp(x)**9+((32*x+64)*ln(3)**4+(-512*x-1024)*ln(3)**3+(3072*x+6144)*ln(3)**2+(-8192*x-16384)*ln(3)+8192*x+16384
)*exp(x)**8+((-64*x**3+192*x**2)*ln(3)**3+(768*x**3-2304*x**2)*ln(3)**2+(-3072*x**3+9216*x**2)*ln(3)+4096*x**3
-12288*x**2)*exp(x)**7+((-128*x**4-256*x**3+768*x**2)*ln(3)**3+(1536*x**4+3072*x**3-9216*x**2)*ln(3)**2+(-6144
*x**4-12288*x**3+36864*x**2)*ln(3)+8192*x**4+16384*x**3-49152*x**2)*exp(x)**6+((-288*x**5+480*x**4)*ln(3)**2+(
2304*x**5-3840*x**4)*ln(3)-4608*x**5+7680*x**4)*exp(x)**5+((-384*x**6-960*x**5+1920*x**4)*ln(3)**2+(3072*x**6+
7680*x**5-15360*x**4)*ln(3)-6144*x**6-15360*x**5+30720*x**4)*exp(x)**4+((-320*x**7+448*x**6)*ln(3)+1280*x**7-1
792*x**6)*exp(x)**3+((-384*x**8-1024*x**7+1792*x**6)*ln(3)+1536*x**8+4096*x**7-7168*x**6)*exp(x)**2+(-112*x**9
+144*x**8)*exp(x)-128*x**10-352*x**9+576*x**8)/exp(x)**8,x)

[Out]

16*x**9*exp(-7*x) + x**2*(-4096*log(3) - 256*log(3)**3 + 16*log(3)**4 + 1536*log(3)**2 + 4096) + x*(-16384*log
(3) - 1024*log(3)**3 + 64*log(3)**4 + 6144*log(3)**2 + 16384) + (-256*x**7 + 64*x**7*log(3))*exp(-5*x) + (16*x
**10 + 64*x**9)*exp(-8*x) + (-768*x**5*log(3) + 96*x**5*log(3)**2 + 1536*x**5)*exp(-3*x) + (-4096*x**3 - 768*x
**3*log(3)**2 + 64*x**3*log(3)**3 + 3072*x**3*log(3))*exp(-x) + (-256*x**8 + 64*x**8*log(3) - 1024*x**7 + 256*
x**7*log(3))*exp(-6*x) + (-4096*x*log(3) - 256*x*log(3)**3 + 16*x*log(3)**4 + 1536*x*log(3)**2 + 4096*x)*exp(x
) + (-768*x**6*log(3) + 96*x**6*log(3)**2 + 1536*x**6 - 3072*x**5*log(3) + 384*x**5*log(3)**2 + 6144*x**5)*exp
(-4*x) + (-4096*x**4 - 768*x**4*log(3)**2 + 64*x**4*log(3)**3 + 3072*x**4*log(3) - 16384*x**3 - 3072*x**3*log(
3)**2 + 256*x**3*log(3)**3 + 12288*x**3*log(3))*exp(-2*x)

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