3.35.1 \(\int (1152+1800 x+2032 x^2+1130 x^3+934 x^4+526 x^5+114 x^6+8 x^7+e^8 (8 x-4 x^2+4 x^3)+e^6 (16+112 x-12 x^2+40 x^3+20 x^4)+e^4 (200+616 x+218 x^2+192 x^3+202 x^4+36 x^5)+e^2 (832+1632 x+1312 x^2+664 x^3+716 x^4+272 x^5+28 x^6)+(1024+1792 x+1740 x^2+1914 x^3+1006 x^4+206 x^5+14 x^6+e^8 (4-2 x+6 x^2)+e^6 (64+80 x^2+32 x^3)+e^4 (384+208 x+448 x^2+364 x^3+60 x^4)+e^2 (1024+1152 x+1328 x^2+1416 x^3+488 x^4+48 x^5)) \log (x)+(512 x+2 e^8 x+864 x^2+452 x^3+90 x^4+6 x^5+e^6 (32 x+12 x^2)+e^4 (192 x+150 x^2+24 x^3)+e^2 (512 x+624 x^2+208 x^3+20 x^4)) \log ^2(x)) \, dx\)

Optimal. Leaf size=29 \[ 5+\left (x+\left (4+e^2+x\right )^2\right )^2 \left (2-x+x^2+x \log (x)\right )^2 \]

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Rubi [B]  time = 0.49, antiderivative size = 711, normalized size of antiderivative = 24.52, number of steps used = 27, number of rules used = 5, integrand size = 345, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {2356, 2295, 2304, 6, 2305} \begin {gather*} x^8+4 e^2 x^7+16 x^7+2 x^7 \log (x)-\frac {1}{18} \left (103+24 e^2\right ) x^6+6 e^4 x^6+\frac {136 e^2 x^6}{3}+\frac {1579 x^6}{18}+x^6 \log ^2(x)+\frac {1}{3} \left (103+24 e^2\right ) x^6 \log (x)-\frac {1}{3} x^6 \log (x)-\frac {2}{25} \left (503+244 e^2+30 e^4\right ) x^5+\frac {4}{25} \left (9+2 e^2\right ) x^5+4 e^6 x^5+\frac {202 e^4 x^5}{5}+\frac {716 e^2 x^5}{5}+\frac {934 x^5}{5}+2 \left (9+2 e^2\right ) x^5 \log ^2(x)+\frac {2}{5} \left (503+244 e^2+30 e^4\right ) x^5 \log (x)-\frac {4}{5} \left (9+2 e^2\right ) x^5 \log (x)-\frac {1}{8} \left (957+708 e^2+182 e^4+16 e^6\right ) x^4+\frac {1}{8} \left (113+52 e^2+6 e^4\right ) x^4+e^8 x^4+10 e^6 x^4+48 e^4 x^4+166 e^2 x^4+\frac {565 x^4}{2}+\left (113+52 e^2+6 e^4\right ) x^4 \log ^2(x)+\frac {1}{2} \left (957+708 e^2+182 e^4+16 e^6\right ) x^4 \log (x)-\frac {1}{2} \left (113+52 e^2+6 e^4\right ) x^4 \log (x)-\frac {2}{9} \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^3+\frac {4}{9} \left (4+e^2\right )^2 \left (9+2 e^2\right ) x^3-\frac {4 e^8 x^3}{3}-4 e^6 x^3+\frac {218 e^4 x^3}{3}+\frac {1312 e^2 x^3}{3}+\frac {2032 x^3}{3}+2 \left (4+e^2\right )^2 \left (9+2 e^2\right ) x^3 \log ^2(x)+\frac {2}{3} \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^3 \log (x)-\frac {4}{3} \left (4+e^2\right )^2 \left (9+2 e^2\right ) x^3 \log (x)-\frac {1}{2} \left (4+e^2\right )^2 \left (56+8 e^2-e^4\right ) x^2+\frac {1}{2} \left (4+e^2\right )^4 x^2+4 e^8 x^2+56 e^6 x^2+308 e^4 x^2+816 e^2 x^2+900 x^2+\left (4+e^2\right )^4 x^2 \log ^2(x)+\left (4+e^2\right )^2 \left (56+8 e^2-e^4\right ) x^2 \log (x)-\left (4+e^2\right )^4 x^2 \log (x)-4 \left (4+e^2\right )^4 x+16 e^6 x+200 e^4 x+832 e^2 x+1152 x+4 \left (4+e^2\right )^4 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1152 + 1800*x + 2032*x^2 + 1130*x^3 + 934*x^4 + 526*x^5 + 114*x^6 + 8*x^7 + E^8*(8*x - 4*x^2 + 4*x^3) + E^
6*(16 + 112*x - 12*x^2 + 40*x^3 + 20*x^4) + E^4*(200 + 616*x + 218*x^2 + 192*x^3 + 202*x^4 + 36*x^5) + E^2*(83
2 + 1632*x + 1312*x^2 + 664*x^3 + 716*x^4 + 272*x^5 + 28*x^6) + (1024 + 1792*x + 1740*x^2 + 1914*x^3 + 1006*x^
4 + 206*x^5 + 14*x^6 + E^8*(4 - 2*x + 6*x^2) + E^6*(64 + 80*x^2 + 32*x^3) + E^4*(384 + 208*x + 448*x^2 + 364*x
^3 + 60*x^4) + E^2*(1024 + 1152*x + 1328*x^2 + 1416*x^3 + 488*x^4 + 48*x^5))*Log[x] + (512*x + 2*E^8*x + 864*x
^2 + 452*x^3 + 90*x^4 + 6*x^5 + E^6*(32*x + 12*x^2) + E^4*(192*x + 150*x^2 + 24*x^3) + E^2*(512*x + 624*x^2 +
208*x^3 + 20*x^4))*Log[x]^2,x]

[Out]

1152*x + 832*E^2*x + 200*E^4*x + 16*E^6*x - 4*(4 + E^2)^4*x + 900*x^2 + 816*E^2*x^2 + 308*E^4*x^2 + 56*E^6*x^2
+ 4*E^8*x^2 + ((4 + E^2)^4*x^2)/2 - ((4 + E^2)^2*(56 + 8*E^2 - E^4)*x^2)/2 + (2032*x^3)/3 + (1312*E^2*x^3)/3
+ (218*E^4*x^3)/3 - 4*E^6*x^3 - (4*E^8*x^3)/3 + (4*(4 + E^2)^2*(9 + 2*E^2)*x^3)/9 - (2*(870 + 664*E^2 + 224*E^
4 + 40*E^6 + 3*E^8)*x^3)/9 + (565*x^4)/2 + 166*E^2*x^4 + 48*E^4*x^4 + 10*E^6*x^4 + E^8*x^4 + ((113 + 52*E^2 +
6*E^4)*x^4)/8 - ((957 + 708*E^2 + 182*E^4 + 16*E^6)*x^4)/8 + (934*x^5)/5 + (716*E^2*x^5)/5 + (202*E^4*x^5)/5 +
4*E^6*x^5 + (4*(9 + 2*E^2)*x^5)/25 - (2*(503 + 244*E^2 + 30*E^4)*x^5)/25 + (1579*x^6)/18 + (136*E^2*x^6)/3 +
6*E^4*x^6 - ((103 + 24*E^2)*x^6)/18 + 16*x^7 + 4*E^2*x^7 + x^8 + 4*(4 + E^2)^4*x*Log[x] - (4 + E^2)^4*x^2*Log[
x] + (4 + E^2)^2*(56 + 8*E^2 - E^4)*x^2*Log[x] - (4*(4 + E^2)^2*(9 + 2*E^2)*x^3*Log[x])/3 + (2*(870 + 664*E^2
+ 224*E^4 + 40*E^6 + 3*E^8)*x^3*Log[x])/3 - ((113 + 52*E^2 + 6*E^4)*x^4*Log[x])/2 + ((957 + 708*E^2 + 182*E^4
+ 16*E^6)*x^4*Log[x])/2 - (4*(9 + 2*E^2)*x^5*Log[x])/5 + (2*(503 + 244*E^2 + 30*E^4)*x^5*Log[x])/5 - (x^6*Log[
x])/3 + ((103 + 24*E^2)*x^6*Log[x])/3 + 2*x^7*Log[x] + (4 + E^2)^4*x^2*Log[x]^2 + 2*(4 + E^2)^2*(9 + 2*E^2)*x^
3*Log[x]^2 + (113 + 52*E^2 + 6*E^4)*x^4*Log[x]^2 + 2*(9 + 2*E^2)*x^5*Log[x]^2 + x^6*Log[x]^2

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2305

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Lo
g[c*x^n])^p)/(d*(m + 1)), x] - Dist[(b*n*p)/(m + 1), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]

Rule 2356

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Polyx*(a + b*Log[c*
x^n])^p, x], x] /; FreeQ[{a, b, c, n, p}, x] && PolynomialQ[Polyx, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=1152 x+900 x^2+\frac {2032 x^3}{3}+\frac {565 x^4}{2}+\frac {934 x^5}{5}+\frac {263 x^6}{3}+\frac {114 x^7}{7}+x^8+e^2 \int \left (832+1632 x+1312 x^2+664 x^3+716 x^4+272 x^5+28 x^6\right ) \, dx+e^4 \int \left (200+616 x+218 x^2+192 x^3+202 x^4+36 x^5\right ) \, dx+e^6 \int \left (16+112 x-12 x^2+40 x^3+20 x^4\right ) \, dx+e^8 \int \left (8 x-4 x^2+4 x^3\right ) \, dx+\int \left (1024+1792 x+1740 x^2+1914 x^3+1006 x^4+206 x^5+14 x^6+e^8 \left (4-2 x+6 x^2\right )+e^6 \left (64+80 x^2+32 x^3\right )+e^4 \left (384+208 x+448 x^2+364 x^3+60 x^4\right )+e^2 \left (1024+1152 x+1328 x^2+1416 x^3+488 x^4+48 x^5\right )\right ) \log (x) \, dx+\int \left (512 x+2 e^8 x+864 x^2+452 x^3+90 x^4+6 x^5+e^6 \left (32 x+12 x^2\right )+e^4 \left (192 x+150 x^2+24 x^3\right )+e^2 \left (512 x+624 x^2+208 x^3+20 x^4\right )\right ) \log ^2(x) \, dx\\ &=1152 x+832 e^2 x+200 e^4 x+16 e^6 x+900 x^2+816 e^2 x^2+308 e^4 x^2+56 e^6 x^2+4 e^8 x^2+\frac {2032 x^3}{3}+\frac {1312 e^2 x^3}{3}+\frac {218 e^4 x^3}{3}-4 e^6 x^3-\frac {4 e^8 x^3}{3}+\frac {565 x^4}{2}+166 e^2 x^4+48 e^4 x^4+10 e^6 x^4+e^8 x^4+\frac {934 x^5}{5}+\frac {716 e^2 x^5}{5}+\frac {202 e^4 x^5}{5}+4 e^6 x^5+\frac {263 x^6}{3}+\frac {136 e^2 x^6}{3}+6 e^4 x^6+\frac {114 x^7}{7}+4 e^2 x^7+x^8+\int \left (\left (512+2 e^8\right ) x+864 x^2+452 x^3+90 x^4+6 x^5+e^6 \left (32 x+12 x^2\right )+e^4 \left (192 x+150 x^2+24 x^3\right )+e^2 \left (512 x+624 x^2+208 x^3+20 x^4\right )\right ) \log ^2(x) \, dx+\int \left (4 \left (4+e^2\right )^4 \log (x)-2 \left (4+e^2\right )^2 \left (-56-8 e^2+e^4\right ) x \log (x)+2 \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^2 \log (x)+2 \left (957+708 e^2+182 e^4+16 e^6\right ) x^3 \log (x)+2 \left (503+244 e^2+30 e^4\right ) x^4 \log (x)+2 \left (103+24 e^2\right ) x^5 \log (x)+14 x^6 \log (x)\right ) \, dx\\ &=1152 x+832 e^2 x+200 e^4 x+16 e^6 x+900 x^2+816 e^2 x^2+308 e^4 x^2+56 e^6 x^2+4 e^8 x^2+\frac {2032 x^3}{3}+\frac {1312 e^2 x^3}{3}+\frac {218 e^4 x^3}{3}-4 e^6 x^3-\frac {4 e^8 x^3}{3}+\frac {565 x^4}{2}+166 e^2 x^4+48 e^4 x^4+10 e^6 x^4+e^8 x^4+\frac {934 x^5}{5}+\frac {716 e^2 x^5}{5}+\frac {202 e^4 x^5}{5}+4 e^6 x^5+\frac {263 x^6}{3}+\frac {136 e^2 x^6}{3}+6 e^4 x^6+\frac {114 x^7}{7}+4 e^2 x^7+x^8+14 \int x^6 \log (x) \, dx+\left (4 \left (4+e^2\right )^4\right ) \int \log (x) \, dx+\left (2 \left (103+24 e^2\right )\right ) \int x^5 \log (x) \, dx+\left (2 \left (4+e^2\right )^2 \left (56+8 e^2-e^4\right )\right ) \int x \log (x) \, dx+\left (2 \left (503+244 e^2+30 e^4\right )\right ) \int x^4 \log (x) \, dx+\left (2 \left (957+708 e^2+182 e^4+16 e^6\right )\right ) \int x^3 \log (x) \, dx+\left (2 \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right )\right ) \int x^2 \log (x) \, dx+\int \left (2 \left (4+e^2\right )^4 x \log ^2(x)+6 \left (4+e^2\right )^2 \left (9+2 e^2\right ) x^2 \log ^2(x)+4 \left (113+52 e^2+6 e^4\right ) x^3 \log ^2(x)+10 \left (9+2 e^2\right ) x^4 \log ^2(x)+6 x^5 \log ^2(x)\right ) \, dx\\ &=1152 x+832 e^2 x+200 e^4 x+16 e^6 x-4 \left (4+e^2\right )^4 x+900 x^2+816 e^2 x^2+308 e^4 x^2+56 e^6 x^2+4 e^8 x^2-\frac {1}{2} \left (4+e^2\right )^2 \left (56+8 e^2-e^4\right ) x^2+\frac {2032 x^3}{3}+\frac {1312 e^2 x^3}{3}+\frac {218 e^4 x^3}{3}-4 e^6 x^3-\frac {4 e^8 x^3}{3}-\frac {2}{9} \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^3+\frac {565 x^4}{2}+166 e^2 x^4+48 e^4 x^4+10 e^6 x^4+e^8 x^4-\frac {1}{8} \left (957+708 e^2+182 e^4+16 e^6\right ) x^4+\frac {934 x^5}{5}+\frac {716 e^2 x^5}{5}+\frac {202 e^4 x^5}{5}+4 e^6 x^5-\frac {2}{25} \left (503+244 e^2+30 e^4\right ) x^5+\frac {263 x^6}{3}+\frac {136 e^2 x^6}{3}+6 e^4 x^6-\frac {1}{18} \left (103+24 e^2\right ) x^6+16 x^7+4 e^2 x^7+x^8+4 \left (4+e^2\right )^4 x \log (x)+\left (4+e^2\right )^2 \left (56+8 e^2-e^4\right ) x^2 \log (x)+\frac {2}{3} \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^3 \log (x)+\frac {1}{2} \left (957+708 e^2+182 e^4+16 e^6\right ) x^4 \log (x)+\frac {2}{5} \left (503+244 e^2+30 e^4\right ) x^5 \log (x)+\frac {1}{3} \left (103+24 e^2\right ) x^6 \log (x)+2 x^7 \log (x)+6 \int x^5 \log ^2(x) \, dx+\left (2 \left (4+e^2\right )^4\right ) \int x \log ^2(x) \, dx+\left (10 \left (9+2 e^2\right )\right ) \int x^4 \log ^2(x) \, dx+\left (6 \left (4+e^2\right )^2 \left (9+2 e^2\right )\right ) \int x^2 \log ^2(x) \, dx+\left (4 \left (113+52 e^2+6 e^4\right )\right ) \int x^3 \log ^2(x) \, dx\\ &=1152 x+832 e^2 x+200 e^4 x+16 e^6 x-4 \left (4+e^2\right )^4 x+900 x^2+816 e^2 x^2+308 e^4 x^2+56 e^6 x^2+4 e^8 x^2-\frac {1}{2} \left (4+e^2\right )^2 \left (56+8 e^2-e^4\right ) x^2+\frac {2032 x^3}{3}+\frac {1312 e^2 x^3}{3}+\frac {218 e^4 x^3}{3}-4 e^6 x^3-\frac {4 e^8 x^3}{3}-\frac {2}{9} \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^3+\frac {565 x^4}{2}+166 e^2 x^4+48 e^4 x^4+10 e^6 x^4+e^8 x^4-\frac {1}{8} \left (957+708 e^2+182 e^4+16 e^6\right ) x^4+\frac {934 x^5}{5}+\frac {716 e^2 x^5}{5}+\frac {202 e^4 x^5}{5}+4 e^6 x^5-\frac {2}{25} \left (503+244 e^2+30 e^4\right ) x^5+\frac {263 x^6}{3}+\frac {136 e^2 x^6}{3}+6 e^4 x^6-\frac {1}{18} \left (103+24 e^2\right ) x^6+16 x^7+4 e^2 x^7+x^8+4 \left (4+e^2\right )^4 x \log (x)+\left (4+e^2\right )^2 \left (56+8 e^2-e^4\right ) x^2 \log (x)+\frac {2}{3} \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^3 \log (x)+\frac {1}{2} \left (957+708 e^2+182 e^4+16 e^6\right ) x^4 \log (x)+\frac {2}{5} \left (503+244 e^2+30 e^4\right ) x^5 \log (x)+\frac {1}{3} \left (103+24 e^2\right ) x^6 \log (x)+2 x^7 \log (x)+\left (4+e^2\right )^4 x^2 \log ^2(x)+2 \left (4+e^2\right )^2 \left (9+2 e^2\right ) x^3 \log ^2(x)+\left (113+52 e^2+6 e^4\right ) x^4 \log ^2(x)+2 \left (9+2 e^2\right ) x^5 \log ^2(x)+x^6 \log ^2(x)-2 \int x^5 \log (x) \, dx-\left (2 \left (4+e^2\right )^4\right ) \int x \log (x) \, dx-\left (4 \left (9+2 e^2\right )\right ) \int x^4 \log (x) \, dx-\left (4 \left (4+e^2\right )^2 \left (9+2 e^2\right )\right ) \int x^2 \log (x) \, dx-\left (2 \left (113+52 e^2+6 e^4\right )\right ) \int x^3 \log (x) \, dx\\ &=1152 x+832 e^2 x+200 e^4 x+16 e^6 x-4 \left (4+e^2\right )^4 x+900 x^2+816 e^2 x^2+308 e^4 x^2+56 e^6 x^2+4 e^8 x^2+\frac {1}{2} \left (4+e^2\right )^4 x^2-\frac {1}{2} \left (4+e^2\right )^2 \left (56+8 e^2-e^4\right ) x^2+\frac {2032 x^3}{3}+\frac {1312 e^2 x^3}{3}+\frac {218 e^4 x^3}{3}-4 e^6 x^3-\frac {4 e^8 x^3}{3}+\frac {4}{9} \left (4+e^2\right )^2 \left (9+2 e^2\right ) x^3-\frac {2}{9} \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^3+\frac {565 x^4}{2}+166 e^2 x^4+48 e^4 x^4+10 e^6 x^4+e^8 x^4+\frac {1}{8} \left (113+52 e^2+6 e^4\right ) x^4-\frac {1}{8} \left (957+708 e^2+182 e^4+16 e^6\right ) x^4+\frac {934 x^5}{5}+\frac {716 e^2 x^5}{5}+\frac {202 e^4 x^5}{5}+4 e^6 x^5+\frac {4}{25} \left (9+2 e^2\right ) x^5-\frac {2}{25} \left (503+244 e^2+30 e^4\right ) x^5+\frac {1579 x^6}{18}+\frac {136 e^2 x^6}{3}+6 e^4 x^6-\frac {1}{18} \left (103+24 e^2\right ) x^6+16 x^7+4 e^2 x^7+x^8+4 \left (4+e^2\right )^4 x \log (x)-\left (4+e^2\right )^4 x^2 \log (x)+\left (4+e^2\right )^2 \left (56+8 e^2-e^4\right ) x^2 \log (x)-\frac {4}{3} \left (4+e^2\right )^2 \left (9+2 e^2\right ) x^3 \log (x)+\frac {2}{3} \left (870+664 e^2+224 e^4+40 e^6+3 e^8\right ) x^3 \log (x)-\frac {1}{2} \left (113+52 e^2+6 e^4\right ) x^4 \log (x)+\frac {1}{2} \left (957+708 e^2+182 e^4+16 e^6\right ) x^4 \log (x)-\frac {4}{5} \left (9+2 e^2\right ) x^5 \log (x)+\frac {2}{5} \left (503+244 e^2+30 e^4\right ) x^5 \log (x)-\frac {1}{3} x^6 \log (x)+\frac {1}{3} \left (103+24 e^2\right ) x^6 \log (x)+2 x^7 \log (x)+\left (4+e^2\right )^4 x^2 \log ^2(x)+2 \left (4+e^2\right )^2 \left (9+2 e^2\right ) x^3 \log ^2(x)+\left (113+52 e^2+6 e^4\right ) x^4 \log ^2(x)+2 \left (9+2 e^2\right ) x^5 \log ^2(x)+x^6 \log ^2(x)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.11, size = 207, normalized size = 7.14 \begin {gather*} x \left (-4 \left (4+e^2\right )^2 \left (-2+4 e^2+e^4\right )+\left (580+656 e^2+304 e^4+64 e^6+5 e^8\right ) x-2 \left (-274-168 e^2-17 e^4+6 e^6+e^8\right ) x^2+\left (177+84 e^2+26 e^4+8 e^6+e^8\right ) x^3+2 \left (74+62 e^2+19 e^4+2 e^6\right ) x^4+2 \left (41+22 e^2+3 e^4\right ) x^5+4 \left (4+e^2\right ) x^6+x^7+2 \left (2-x+x^2\right ) \left (16+e^4+9 x+x^2+2 e^2 (4+x)\right )^2 \log (x)+x \left (16+e^4+9 x+x^2+2 e^2 (4+x)\right )^2 \log ^2(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1152 + 1800*x + 2032*x^2 + 1130*x^3 + 934*x^4 + 526*x^5 + 114*x^6 + 8*x^7 + E^8*(8*x - 4*x^2 + 4*x^3
) + E^6*(16 + 112*x - 12*x^2 + 40*x^3 + 20*x^4) + E^4*(200 + 616*x + 218*x^2 + 192*x^3 + 202*x^4 + 36*x^5) + E
^2*(832 + 1632*x + 1312*x^2 + 664*x^3 + 716*x^4 + 272*x^5 + 28*x^6) + (1024 + 1792*x + 1740*x^2 + 1914*x^3 + 1
006*x^4 + 206*x^5 + 14*x^6 + E^8*(4 - 2*x + 6*x^2) + E^6*(64 + 80*x^2 + 32*x^3) + E^4*(384 + 208*x + 448*x^2 +
364*x^3 + 60*x^4) + E^2*(1024 + 1152*x + 1328*x^2 + 1416*x^3 + 488*x^4 + 48*x^5))*Log[x] + (512*x + 2*E^8*x +
864*x^2 + 452*x^3 + 90*x^4 + 6*x^5 + E^6*(32*x + 12*x^2) + E^4*(192*x + 150*x^2 + 24*x^3) + E^2*(512*x + 624*
x^2 + 208*x^3 + 20*x^4))*Log[x]^2,x]

[Out]

x*(-4*(4 + E^2)^2*(-2 + 4*E^2 + E^4) + (580 + 656*E^2 + 304*E^4 + 64*E^6 + 5*E^8)*x - 2*(-274 - 168*E^2 - 17*E
^4 + 6*E^6 + E^8)*x^2 + (177 + 84*E^2 + 26*E^4 + 8*E^6 + E^8)*x^3 + 2*(74 + 62*E^2 + 19*E^4 + 2*E^6)*x^4 + 2*(
41 + 22*E^2 + 3*E^4)*x^5 + 4*(4 + E^2)*x^6 + x^7 + 2*(2 - x + x^2)*(16 + E^4 + 9*x + x^2 + 2*E^2*(4 + x))^2*Lo
g[x] + x*(16 + E^4 + 9*x + x^2 + 2*E^2*(4 + x))^2*Log[x]^2)

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fricas [B]  time = 0.59, size = 374, normalized size = 12.90 \begin {gather*} x^{8} + 16 \, x^{7} + 82 \, x^{6} + 148 \, x^{5} + 177 \, x^{4} + 548 \, x^{3} + {\left (x^{6} + 18 \, x^{5} + 113 \, x^{4} + 288 \, x^{3} + x^{2} e^{8} + 256 \, x^{2} + 4 \, {\left (x^{3} + 4 \, x^{2}\right )} e^{6} + 2 \, {\left (3 \, x^{4} + 25 \, x^{3} + 48 \, x^{2}\right )} e^{4} + 4 \, {\left (x^{5} + 13 \, x^{4} + 52 \, x^{3} + 64 \, x^{2}\right )} e^{2}\right )} \log \relax (x)^{2} + 580 \, x^{2} + {\left (x^{4} - 2 \, x^{3} + 5 \, x^{2} - 4 \, x\right )} e^{8} + 4 \, {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3} + 16 \, x^{2} - 12 \, x\right )} e^{6} + 2 \, {\left (3 \, x^{6} + 19 \, x^{5} + 13 \, x^{4} + 17 \, x^{3} + 152 \, x^{2} - 92 \, x\right )} e^{4} + 4 \, {\left (x^{7} + 11 \, x^{6} + 31 \, x^{5} + 21 \, x^{4} + 84 \, x^{3} + 164 \, x^{2} - 48 \, x\right )} e^{2} + 2 \, {\left (x^{7} + 17 \, x^{6} + 97 \, x^{5} + 211 \, x^{4} + 194 \, x^{3} + 320 \, x^{2} + {\left (x^{3} - x^{2} + 2 \, x\right )} e^{8} + 4 \, {\left (x^{4} + 3 \, x^{3} - 2 \, x^{2} + 8 \, x\right )} e^{6} + 2 \, {\left (3 \, x^{5} + 22 \, x^{4} + 29 \, x^{3} + 2 \, x^{2} + 96 \, x\right )} e^{4} + 4 \, {\left (x^{6} + 12 \, x^{5} + 41 \, x^{4} + 38 \, x^{3} + 40 \, x^{2} + 128 \, x\right )} e^{2} + 512 \, x\right )} \log \relax (x) + 128 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*exp(2)^4+(12*x^2+32*x)*exp(2)^3+(24*x^3+150*x^2+192*x)*exp(2)^2+(20*x^4+208*x^3+624*x^2+512*x)*
exp(2)+6*x^5+90*x^4+452*x^3+864*x^2+512*x)*log(x)^2+((6*x^2-2*x+4)*exp(2)^4+(32*x^3+80*x^2+64)*exp(2)^3+(60*x^
4+364*x^3+448*x^2+208*x+384)*exp(2)^2+(48*x^5+488*x^4+1416*x^3+1328*x^2+1152*x+1024)*exp(2)+14*x^6+206*x^5+100
6*x^4+1914*x^3+1740*x^2+1792*x+1024)*log(x)+(4*x^3-4*x^2+8*x)*exp(2)^4+(20*x^4+40*x^3-12*x^2+112*x+16)*exp(2)^
3+(36*x^5+202*x^4+192*x^3+218*x^2+616*x+200)*exp(2)^2+(28*x^6+272*x^5+716*x^4+664*x^3+1312*x^2+1632*x+832)*exp
(2)+8*x^7+114*x^6+526*x^5+934*x^4+1130*x^3+2032*x^2+1800*x+1152,x, algorithm="fricas")

[Out]

x^8 + 16*x^7 + 82*x^6 + 148*x^5 + 177*x^4 + 548*x^3 + (x^6 + 18*x^5 + 113*x^4 + 288*x^3 + x^2*e^8 + 256*x^2 +
4*(x^3 + 4*x^2)*e^6 + 2*(3*x^4 + 25*x^3 + 48*x^2)*e^4 + 4*(x^5 + 13*x^4 + 52*x^3 + 64*x^2)*e^2)*log(x)^2 + 580
*x^2 + (x^4 - 2*x^3 + 5*x^2 - 4*x)*e^8 + 4*(x^5 + 2*x^4 - 3*x^3 + 16*x^2 - 12*x)*e^6 + 2*(3*x^6 + 19*x^5 + 13*
x^4 + 17*x^3 + 152*x^2 - 92*x)*e^4 + 4*(x^7 + 11*x^6 + 31*x^5 + 21*x^4 + 84*x^3 + 164*x^2 - 48*x)*e^2 + 2*(x^7
+ 17*x^6 + 97*x^5 + 211*x^4 + 194*x^3 + 320*x^2 + (x^3 - x^2 + 2*x)*e^8 + 4*(x^4 + 3*x^3 - 2*x^2 + 8*x)*e^6 +
2*(3*x^5 + 22*x^4 + 29*x^3 + 2*x^2 + 96*x)*e^4 + 4*(x^6 + 12*x^5 + 41*x^4 + 38*x^3 + 40*x^2 + 128*x)*e^2 + 51
2*x)*log(x) + 128*x

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giac [B]  time = 0.19, size = 627, normalized size = 21.62 \begin {gather*} x^{8} + 2 \, x^{7} \log \relax (x) + 8 \, x^{6} e^{2} \log \relax (x) + x^{6} \log \relax (x)^{2} + 4 \, x^{5} e^{2} \log \relax (x)^{2} + 16 \, x^{7} - \frac {4}{3} \, x^{6} e^{2} + 34 \, x^{6} \log \relax (x) + 12 \, x^{5} e^{4} \log \relax (x) + 96 \, x^{5} e^{2} \log \relax (x) + 18 \, x^{5} \log \relax (x)^{2} + 6 \, x^{4} e^{4} \log \relax (x)^{2} + 52 \, x^{4} e^{2} \log \relax (x)^{2} + 82 \, x^{6} - \frac {12}{5} \, x^{5} e^{4} - \frac {96}{5} \, x^{5} e^{2} + 194 \, x^{5} \log \relax (x) + 8 \, x^{4} e^{6} \log \relax (x) + 88 \, x^{4} e^{4} \log \relax (x) + 328 \, x^{4} e^{2} \log \relax (x) + 113 \, x^{4} \log \relax (x)^{2} + 4 \, x^{3} e^{6} \log \relax (x)^{2} + 50 \, x^{3} e^{4} \log \relax (x)^{2} + 208 \, x^{3} e^{2} \log \relax (x)^{2} + 148 \, x^{5} - 2 \, x^{4} e^{6} - 22 \, x^{4} e^{4} - 82 \, x^{4} e^{2} + 422 \, x^{4} \log \relax (x) + 2 \, x^{3} e^{8} \log \relax (x) + 24 \, x^{3} e^{6} \log \relax (x) + 116 \, x^{3} e^{4} \log \relax (x) + 304 \, x^{3} e^{2} \log \relax (x) + 288 \, x^{3} \log \relax (x)^{2} + x^{2} e^{8} \log \relax (x)^{2} + 16 \, x^{2} e^{6} \log \relax (x)^{2} + 96 \, x^{2} e^{4} \log \relax (x)^{2} + 256 \, x^{2} e^{2} \log \relax (x)^{2} + 177 \, x^{4} - \frac {2}{3} \, x^{3} e^{8} - 8 \, x^{3} e^{6} - \frac {116}{3} \, x^{3} e^{4} - \frac {304}{3} \, x^{3} e^{2} + 388 \, x^{3} \log \relax (x) - 2 \, x^{2} e^{8} \log \relax (x) - 16 \, x^{2} e^{6} \log \relax (x) + 8 \, x^{2} e^{4} \log \relax (x) + 320 \, x^{2} e^{2} \log \relax (x) + 256 \, x^{2} \log \relax (x)^{2} + 548 \, x^{3} + x^{2} e^{8} + 8 \, x^{2} e^{6} - 4 \, x^{2} e^{4} - 160 \, x^{2} e^{2} + 640 \, x^{2} \log \relax (x) + 4 \, x e^{8} \log \relax (x) + 64 \, x e^{6} \log \relax (x) + 384 \, x e^{4} \log \relax (x) + 1024 \, x e^{2} \log \relax (x) + 580 \, x^{2} + \frac {1}{3} \, {\left (3 \, x^{4} - 4 \, x^{3} + 12 \, x^{2}\right )} e^{8} - 4 \, x e^{8} + 2 \, {\left (2 \, x^{5} + 5 \, x^{4} - 2 \, x^{3} + 28 \, x^{2} + 8 \, x\right )} e^{6} - 64 \, x e^{6} + \frac {2}{15} \, {\left (45 \, x^{6} + 303 \, x^{5} + 360 \, x^{4} + 545 \, x^{3} + 2310 \, x^{2} + 1500 \, x\right )} e^{4} - 384 \, x e^{4} + \frac {2}{15} \, {\left (30 \, x^{7} + 340 \, x^{6} + 1074 \, x^{5} + 1245 \, x^{4} + 3280 \, x^{3} + 6120 \, x^{2} + 6240 \, x\right )} e^{2} - 1024 \, x e^{2} + 1024 \, x \log \relax (x) + 128 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*exp(2)^4+(12*x^2+32*x)*exp(2)^3+(24*x^3+150*x^2+192*x)*exp(2)^2+(20*x^4+208*x^3+624*x^2+512*x)*
exp(2)+6*x^5+90*x^4+452*x^3+864*x^2+512*x)*log(x)^2+((6*x^2-2*x+4)*exp(2)^4+(32*x^3+80*x^2+64)*exp(2)^3+(60*x^
4+364*x^3+448*x^2+208*x+384)*exp(2)^2+(48*x^5+488*x^4+1416*x^3+1328*x^2+1152*x+1024)*exp(2)+14*x^6+206*x^5+100
6*x^4+1914*x^3+1740*x^2+1792*x+1024)*log(x)+(4*x^3-4*x^2+8*x)*exp(2)^4+(20*x^4+40*x^3-12*x^2+112*x+16)*exp(2)^
3+(36*x^5+202*x^4+192*x^3+218*x^2+616*x+200)*exp(2)^2+(28*x^6+272*x^5+716*x^4+664*x^3+1312*x^2+1632*x+832)*exp
(2)+8*x^7+114*x^6+526*x^5+934*x^4+1130*x^3+2032*x^2+1800*x+1152,x, algorithm="giac")

[Out]

x^8 + 2*x^7*log(x) + 8*x^6*e^2*log(x) + x^6*log(x)^2 + 4*x^5*e^2*log(x)^2 + 16*x^7 - 4/3*x^6*e^2 + 34*x^6*log(
x) + 12*x^5*e^4*log(x) + 96*x^5*e^2*log(x) + 18*x^5*log(x)^2 + 6*x^4*e^4*log(x)^2 + 52*x^4*e^2*log(x)^2 + 82*x
^6 - 12/5*x^5*e^4 - 96/5*x^5*e^2 + 194*x^5*log(x) + 8*x^4*e^6*log(x) + 88*x^4*e^4*log(x) + 328*x^4*e^2*log(x)
+ 113*x^4*log(x)^2 + 4*x^3*e^6*log(x)^2 + 50*x^3*e^4*log(x)^2 + 208*x^3*e^2*log(x)^2 + 148*x^5 - 2*x^4*e^6 - 2
2*x^4*e^4 - 82*x^4*e^2 + 422*x^4*log(x) + 2*x^3*e^8*log(x) + 24*x^3*e^6*log(x) + 116*x^3*e^4*log(x) + 304*x^3*
e^2*log(x) + 288*x^3*log(x)^2 + x^2*e^8*log(x)^2 + 16*x^2*e^6*log(x)^2 + 96*x^2*e^4*log(x)^2 + 256*x^2*e^2*log
(x)^2 + 177*x^4 - 2/3*x^3*e^8 - 8*x^3*e^6 - 116/3*x^3*e^4 - 304/3*x^3*e^2 + 388*x^3*log(x) - 2*x^2*e^8*log(x)
- 16*x^2*e^6*log(x) + 8*x^2*e^4*log(x) + 320*x^2*e^2*log(x) + 256*x^2*log(x)^2 + 548*x^3 + x^2*e^8 + 8*x^2*e^6
- 4*x^2*e^4 - 160*x^2*e^2 + 640*x^2*log(x) + 4*x*e^8*log(x) + 64*x*e^6*log(x) + 384*x*e^4*log(x) + 1024*x*e^2
*log(x) + 580*x^2 + 1/3*(3*x^4 - 4*x^3 + 12*x^2)*e^8 - 4*x*e^8 + 2*(2*x^5 + 5*x^4 - 2*x^3 + 28*x^2 + 8*x)*e^6
- 64*x*e^6 + 2/15*(45*x^6 + 303*x^5 + 360*x^4 + 545*x^3 + 2310*x^2 + 1500*x)*e^4 - 384*x*e^4 + 2/15*(30*x^7 +
340*x^6 + 1074*x^5 + 1245*x^4 + 3280*x^3 + 6120*x^2 + 6240*x)*e^2 - 1024*x*e^2 + 1024*x*log(x) + 128*x

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maple [B]  time = 0.09, size = 408, normalized size = 14.07

method	result	size
norman	\(x^{8}+x^{6} \ln \relax (x )^{2}+\left (16+4 \,{\mathrm e}^{2}\right ) x^{7}+\left (82+44 \,{\mathrm e}^{2}+6 \,{\mathrm e}^{4}\right ) x^{6}+\left (148+124 \,{\mathrm e}^{2}+38 \,{\mathrm e}^{4}+4 \,{\mathrm e}^{6}\right ) x^{5}+\left (128-48 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{8}-184 \,{\mathrm e}^{4}-192 \,{\mathrm e}^{2}\right ) x +\left (177+26 \,{\mathrm e}^{4}+84 \,{\mathrm e}^{2}+8 \,{\mathrm e}^{6}+{\mathrm e}^{8}\right ) x^{4}+\left (548-12 \,{\mathrm e}^{6}+34 \,{\mathrm e}^{4}+336 \,{\mathrm e}^{2}-2 \,{\mathrm e}^{8}\right ) x^{3}+\left (580+5 \,{\mathrm e}^{8}+64 \,{\mathrm e}^{6}+304 \,{\mathrm e}^{4}+656 \,{\mathrm e}^{2}\right ) x^{2}+\left (18+4 \,{\mathrm e}^{2}\right ) x^{5} \ln \relax (x )^{2}+\left (34+8 \,{\mathrm e}^{2}\right ) x^{6} \ln \relax (x )+\left (194+96 \,{\mathrm e}^{2}+12 \,{\mathrm e}^{4}\right ) x^{5} \ln \relax (x )+\left (6 \,{\mathrm e}^{4}+52 \,{\mathrm e}^{2}+113\right ) x^{4} \ln \relax (x )^{2}+\left (422+88 \,{\mathrm e}^{4}+328 \,{\mathrm e}^{2}+8 \,{\mathrm e}^{6}\right ) x^{4} \ln \relax (x )+\left (4 \,{\mathrm e}^{6}+50 \,{\mathrm e}^{4}+208 \,{\mathrm e}^{2}+288\right ) x^{3} \ln \relax (x )^{2}+\left (388+24 \,{\mathrm e}^{6}+116 \,{\mathrm e}^{4}+304 \,{\mathrm e}^{2}+2 \,{\mathrm e}^{8}\right ) x^{3} \ln \relax (x )+\left (640-2 \,{\mathrm e}^{8}-16 \,{\mathrm e}^{6}+8 \,{\mathrm e}^{4}+320 \,{\mathrm e}^{2}\right ) x^{2} \ln \relax (x )+\left (1024+64 \,{\mathrm e}^{6}+4 \,{\mathrm e}^{8}+384 \,{\mathrm e}^{4}+1024 \,{\mathrm e}^{2}\right ) x \ln \relax (x )+\left ({\mathrm e}^{8}+16 \,{\mathrm e}^{6}+96 \,{\mathrm e}^{4}+256 \,{\mathrm e}^{2}+256\right ) x^{2} \ln \relax (x )^{2}+2 x^{7} \ln \relax (x )\)	\(408\)
risch	\(128 x -192 \,{\mathrm e}^{2} x +124 \,{\mathrm e}^{2} x^{5}-4 x \,{\mathrm e}^{8}+64 x^{2} {\mathrm e}^{6}-12 x^{3} {\mathrm e}^{6}+5 x^{2} {\mathrm e}^{8}-184 x \,{\mathrm e}^{4}+16 x^{7}+x^{8}+82 x^{6}+148 x^{5}+177 x^{4}+548 x^{3}+580 x^{2}+44 x^{6} {\mathrm e}^{2}+34 x^{3} {\mathrm e}^{4}+304 x^{2} {\mathrm e}^{4}-48 x \,{\mathrm e}^{6}+336 x^{3} {\mathrm e}^{2}+656 x^{2} {\mathrm e}^{2}+84 x^{4} {\mathrm e}^{2}+\left (-\frac {x^{6}}{3}-\frac {8 \,{\mathrm e}^{2} x^{5}}{5}-\frac {36 x^{5}}{5}-3 x^{4} {\mathrm e}^{4}-26 x^{4} {\mathrm e}^{2}-\frac {113 x^{4}}{2}-\frac {8 x^{3} {\mathrm e}^{6}}{3}-\frac {100 x^{3} {\mathrm e}^{4}}{3}-\frac {416 x^{3} {\mathrm e}^{2}}{3}-192 x^{3}-x^{2} {\mathrm e}^{8}-16 x^{2} {\mathrm e}^{6}-96 x^{2} {\mathrm e}^{4}-256 x^{2} {\mathrm e}^{2}-256 x^{2}\right ) \ln \relax (x )+\left (x^{2} {\mathrm e}^{8}+4 x^{3} {\mathrm e}^{6}+6 x^{4} {\mathrm e}^{4}+4 \,{\mathrm e}^{2} x^{5}+x^{6}+16 x^{2} {\mathrm e}^{6}+50 x^{3} {\mathrm e}^{4}+52 x^{4} {\mathrm e}^{2}+18 x^{5}+96 x^{2} {\mathrm e}^{4}+208 x^{3} {\mathrm e}^{2}+113 x^{4}+256 x^{2} {\mathrm e}^{2}+288 x^{3}+256 x^{2}\right ) \ln \relax (x )^{2}+4 \,{\mathrm e}^{6} x^{5}+\left (2 x^{3} {\mathrm e}^{8}+8 x^{4} {\mathrm e}^{6}+12 x^{5} {\mathrm e}^{4}+8 x^{6} {\mathrm e}^{2}+2 x^{7}-x^{2} {\mathrm e}^{8}+\frac {80 x^{3} {\mathrm e}^{6}}{3}+91 x^{4} {\mathrm e}^{4}+\frac {488 \,{\mathrm e}^{2} x^{5}}{5}+\frac {103 x^{6}}{3}+4 x \,{\mathrm e}^{8}+\frac {448 x^{3} {\mathrm e}^{4}}{3}+354 x^{4} {\mathrm e}^{2}+\frac {1006 x^{5}}{5}+64 x \,{\mathrm e}^{6}+104 x^{2} {\mathrm e}^{4}+\frac {1328 x^{3} {\mathrm e}^{2}}{3}+\frac {957 x^{4}}{2}+384 x \,{\mathrm e}^{4}+576 x^{2} {\mathrm e}^{2}+580 x^{3}+1024 \,{\mathrm e}^{2} x +896 x^{2}+1024 x \right ) \ln \relax (x )+8 x^{4} {\mathrm e}^{6}+4 \,{\mathrm e}^{2} x^{7}+x^{4} {\mathrm e}^{8}-2 x^{3} {\mathrm e}^{8}+26 x^{4} {\mathrm e}^{4}+38 x^{5} {\mathrm e}^{4}+6 x^{6} {\mathrm e}^{4}\)	\(528\)
default	\(128 x -1024 \,{\mathrm e}^{2} x +50 x^{3} {\mathrm e}^{4} \ln \relax (x )^{2}+64 x \,{\mathrm e}^{6} \ln \relax (x )+304 x^{3} {\mathrm e}^{2} \ln \relax (x )-\frac {96 \,{\mathrm e}^{2} x^{5}}{5}+640 x^{2} \ln \relax (x )+1024 x \,{\mathrm e}^{2} \ln \relax (x )+320 x^{2} {\mathrm e}^{2} \ln \relax (x )-4 x \,{\mathrm e}^{8}+8 x^{2} {\mathrm e}^{6}-8 x^{3} {\mathrm e}^{6}+x^{2} {\mathrm e}^{8}-384 x \,{\mathrm e}^{4}+256 x^{2} \ln \relax (x )^{2}+16 x^{7}+x^{8}+82 x^{6}+148 x^{5}+177 x^{4}+548 x^{3}+580 x^{2}+388 x^{3} \ln \relax (x )+8 x^{2} {\mathrm e}^{4} \ln \relax (x )+52 \,{\mathrm e}^{2} \ln \relax (x )^{2} x^{4}+96 \,{\mathrm e}^{2} \ln \relax (x ) x^{5}+208 \,{\mathrm e}^{2} \ln \relax (x )^{2} x^{3}+328 \,{\mathrm e}^{2} \ln \relax (x ) x^{4}+256 \,{\mathrm e}^{2} \ln \relax (x )^{2} x^{2}-\frac {4 x^{6} {\mathrm e}^{2}}{3}+x^{6} \ln \relax (x )^{2}+34 x^{6} \ln \relax (x )+2 x^{7} \ln \relax (x )+194 x^{5} \ln \relax (x )+113 x^{4} \ln \relax (x )^{2}-\frac {116 x^{3} {\mathrm e}^{4}}{3}-4 x^{2} {\mathrm e}^{4}-64 x \,{\mathrm e}^{6}-\frac {304 x^{3} {\mathrm e}^{2}}{3}-160 x^{2} {\mathrm e}^{2}+422 x^{4} \ln \relax (x )-82 x^{4} {\mathrm e}^{2}+1024 x \ln \relax (x )+{\mathrm e}^{4} \left (6 x^{6}+\frac {202}{5} x^{5}+48 x^{4}+\frac {218}{3} x^{3}+308 x^{2}+200 x \right )+{\mathrm e}^{6} \left (4 x^{5}+10 x^{4}-4 x^{3}+56 x^{2}+16 x \right )+{\mathrm e}^{8} \left (x^{4}-\frac {4}{3} x^{3}+4 x^{2}\right )+96 x^{2} {\mathrm e}^{4} \ln \relax (x )^{2}-2 x^{4} {\mathrm e}^{6}-\frac {2 x^{3} {\mathrm e}^{8}}{3}+{\mathrm e}^{2} \left (4 x^{7}+\frac {136}{3} x^{6}+\frac {716}{5} x^{5}+166 x^{4}+\frac {1312}{3} x^{3}+816 x^{2}+832 x \right )+18 x^{5} \ln \relax (x )^{2}+384 x \,{\mathrm e}^{4} \ln \relax (x )-22 x^{4} {\mathrm e}^{4}-\frac {12 x^{5} {\mathrm e}^{4}}{5}+288 x^{3} \ln \relax (x )^{2}+4 \,{\mathrm e}^{2} x^{5} \ln \relax (x )^{2}+8 \,{\mathrm e}^{2} x^{6} \ln \relax (x )+116 x^{3} {\mathrm e}^{4} \ln \relax (x )-2 \,{\mathrm e}^{8} \ln \relax (x ) x^{2}+16 \,{\mathrm e}^{6} \ln \relax (x )^{2} x^{2}+24 \,{\mathrm e}^{6} \ln \relax (x ) x^{3}+88 \,{\mathrm e}^{4} \ln \relax (x ) x^{4}+4 \,{\mathrm e}^{8} \ln \relax (x ) x -16 \,{\mathrm e}^{6} \ln \relax (x ) x^{2}+6 \,{\mathrm e}^{4} x^{4} \ln \relax (x )^{2}+4 \,{\mathrm e}^{6} x^{3} \ln \relax (x )^{2}+{\mathrm e}^{8} x^{2} \ln \relax (x )^{2}+8 \,{\mathrm e}^{6} x^{4} \ln \relax (x )+12 \,{\mathrm e}^{4} x^{5} \ln \relax (x )+2 \,{\mathrm e}^{8} x^{3} \ln \relax (x )\)	\(688\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x*exp(2)^4+(12*x^2+32*x)*exp(2)^3+(24*x^3+150*x^2+192*x)*exp(2)^2+(20*x^4+208*x^3+624*x^2+512*x)*exp(2)
+6*x^5+90*x^4+452*x^3+864*x^2+512*x)*ln(x)^2+((6*x^2-2*x+4)*exp(2)^4+(32*x^3+80*x^2+64)*exp(2)^3+(60*x^4+364*x
^3+448*x^2+208*x+384)*exp(2)^2+(48*x^5+488*x^4+1416*x^3+1328*x^2+1152*x+1024)*exp(2)+14*x^6+206*x^5+1006*x^4+1
914*x^3+1740*x^2+1792*x+1024)*ln(x)+(4*x^3-4*x^2+8*x)*exp(2)^4+(20*x^4+40*x^3-12*x^2+112*x+16)*exp(2)^3+(36*x^
5+202*x^4+192*x^3+218*x^2+616*x+200)*exp(2)^2+(28*x^6+272*x^5+716*x^4+664*x^3+1312*x^2+1632*x+832)*exp(2)+8*x^
7+114*x^6+526*x^5+934*x^4+1130*x^3+2032*x^2+1800*x+1152,x,method=_RETURNVERBOSE)

[Out]

x^8+x^6*ln(x)^2+(16+4*exp(2))*x^7+(82+44*exp(2)+6*exp(2)^2)*x^6+(148+124*exp(2)+38*exp(2)^2+4*exp(2)^3)*x^5+(1
28-48*exp(2)^3-4*exp(2)^4-184*exp(2)^2-192*exp(2))*x+(177+26*exp(2)^2+84*exp(2)+8*exp(2)^3+exp(2)^4)*x^4+(548-
12*exp(2)^3+34*exp(2)^2+336*exp(2)-2*exp(2)^4)*x^3+(580+5*exp(2)^4+64*exp(2)^3+304*exp(2)^2+656*exp(2))*x^2+(1
8+4*exp(2))*x^5*ln(x)^2+(34+8*exp(2))*x^6*ln(x)+(194+96*exp(2)+12*exp(2)^2)*x^5*ln(x)+(6*exp(2)^2+52*exp(2)+11
3)*x^4*ln(x)^2+(422+88*exp(2)^2+328*exp(2)+8*exp(2)^3)*x^4*ln(x)+(4*exp(2)^3+50*exp(2)^2+208*exp(2)+288)*x^3*l
n(x)^2+(388+24*exp(2)^3+116*exp(2)^2+304*exp(2)+2*exp(2)^4)*x^3*ln(x)+(640-2*exp(2)^4-16*exp(2)^3+8*exp(2)^2+3
20*exp(2))*x^2*ln(x)+(1024+64*exp(2)^3+4*exp(2)^4+384*exp(2)^2+1024*exp(2))*x*ln(x)+(exp(2)^4+16*exp(2)^3+96*e
xp(2)^2+256*exp(2)+256)*x^2*ln(x)^2+2*x^7*ln(x)

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maxima [B]  time = 0.55, size = 610, normalized size = 21.03 \begin {gather*} x^{8} + \frac {1}{18} \, {\left (18 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 1\right )} x^{6} + 16 \, x^{7} - \frac {1}{18} \, x^{6} {\left (24 \, e^{2} + 103\right )} + \frac {2}{25} \, {\left (25 \, {\left (2 \, e^{2} + 9\right )} \log \relax (x)^{2} - 10 \, {\left (2 \, e^{2} + 9\right )} \log \relax (x) + 4 \, e^{2} + 18\right )} x^{5} + \frac {263}{3} \, x^{6} - \frac {2}{25} \, x^{5} {\left (30 \, e^{4} + 244 \, e^{2} + 503\right )} + \frac {1}{8} \, {\left (8 \, {\left (6 \, e^{4} + 52 \, e^{2} + 113\right )} \log \relax (x)^{2} - 4 \, {\left (6 \, e^{4} + 52 \, e^{2} + 113\right )} \log \relax (x) + 6 \, e^{4} + 52 \, e^{2} + 113\right )} x^{4} + \frac {934}{5} \, x^{5} - \frac {1}{8} \, x^{4} {\left (16 \, e^{6} + 182 \, e^{4} + 708 \, e^{2} + 957\right )} + \frac {2}{9} \, {\left (9 \, {\left (2 \, e^{6} + 25 \, e^{4} + 104 \, e^{2} + 144\right )} \log \relax (x)^{2} - 6 \, {\left (2 \, e^{6} + 25 \, e^{4} + 104 \, e^{2} + 144\right )} \log \relax (x) + 4 \, e^{6} + 50 \, e^{4} + 208 \, e^{2} + 288\right )} x^{3} + \frac {565}{2} \, x^{4} - \frac {2}{9} \, x^{3} {\left (3 \, e^{8} + 40 \, e^{6} + 224 \, e^{4} + 664 \, e^{2} + 870\right )} + \frac {1}{2} \, {\left (2 \, {\left (e^{8} + 16 \, e^{6} + 96 \, e^{4} + 256 \, e^{2} + 256\right )} \log \relax (x)^{2} - 2 \, {\left (e^{8} + 16 \, e^{6} + 96 \, e^{4} + 256 \, e^{2} + 256\right )} \log \relax (x) + e^{8} + 16 \, e^{6} + 96 \, e^{4} + 256 \, e^{2} + 256\right )} x^{2} + \frac {2032}{3} \, x^{3} + \frac {1}{2} \, x^{2} {\left (e^{8} - 104 \, e^{4} - 576 \, e^{2} - 896\right )} + 900 \, x^{2} - 4 \, x {\left (e^{8} + 16 \, e^{6} + 96 \, e^{4} + 256 \, e^{2} + 256\right )} + \frac {1}{3} \, {\left (3 \, x^{4} - 4 \, x^{3} + 12 \, x^{2}\right )} e^{8} + 2 \, {\left (2 \, x^{5} + 5 \, x^{4} - 2 \, x^{3} + 28 \, x^{2} + 8 \, x\right )} e^{6} + \frac {2}{15} \, {\left (45 \, x^{6} + 303 \, x^{5} + 360 \, x^{4} + 545 \, x^{3} + 2310 \, x^{2} + 1500 \, x\right )} e^{4} + \frac {2}{15} \, {\left (30 \, x^{7} + 340 \, x^{6} + 1074 \, x^{5} + 1245 \, x^{4} + 3280 \, x^{3} + 6120 \, x^{2} + 6240 \, x\right )} e^{2} + \frac {1}{30} \, {\left (60 \, x^{7} + 1030 \, x^{6} + 6036 \, x^{5} + 14355 \, x^{4} + 17400 \, x^{3} + 26880 \, x^{2} + 30 \, {\left (2 \, x^{3} - x^{2} + 4 \, x\right )} e^{8} + 80 \, {\left (3 \, x^{4} + 10 \, x^{3} + 24 \, x\right )} e^{6} + 10 \, {\left (36 \, x^{5} + 273 \, x^{4} + 448 \, x^{3} + 312 \, x^{2} + 1152 \, x\right )} e^{4} + 4 \, {\left (60 \, x^{6} + 732 \, x^{5} + 2655 \, x^{4} + 3320 \, x^{3} + 4320 \, x^{2} + 7680 \, x\right )} e^{2} + 30720 \, x\right )} \log \relax (x) + 1152 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*exp(2)^4+(12*x^2+32*x)*exp(2)^3+(24*x^3+150*x^2+192*x)*exp(2)^2+(20*x^4+208*x^3+624*x^2+512*x)*
exp(2)+6*x^5+90*x^4+452*x^3+864*x^2+512*x)*log(x)^2+((6*x^2-2*x+4)*exp(2)^4+(32*x^3+80*x^2+64)*exp(2)^3+(60*x^
4+364*x^3+448*x^2+208*x+384)*exp(2)^2+(48*x^5+488*x^4+1416*x^3+1328*x^2+1152*x+1024)*exp(2)+14*x^6+206*x^5+100
6*x^4+1914*x^3+1740*x^2+1792*x+1024)*log(x)+(4*x^3-4*x^2+8*x)*exp(2)^4+(20*x^4+40*x^3-12*x^2+112*x+16)*exp(2)^
3+(36*x^5+202*x^4+192*x^3+218*x^2+616*x+200)*exp(2)^2+(28*x^6+272*x^5+716*x^4+664*x^3+1312*x^2+1632*x+832)*exp
(2)+8*x^7+114*x^6+526*x^5+934*x^4+1130*x^3+2032*x^2+1800*x+1152,x, algorithm="maxima")

[Out]

x^8 + 1/18*(18*log(x)^2 - 6*log(x) + 1)*x^6 + 16*x^7 - 1/18*x^6*(24*e^2 + 103) + 2/25*(25*(2*e^2 + 9)*log(x)^2
- 10*(2*e^2 + 9)*log(x) + 4*e^2 + 18)*x^5 + 263/3*x^6 - 2/25*x^5*(30*e^4 + 244*e^2 + 503) + 1/8*(8*(6*e^4 + 5
2*e^2 + 113)*log(x)^2 - 4*(6*e^4 + 52*e^2 + 113)*log(x) + 6*e^4 + 52*e^2 + 113)*x^4 + 934/5*x^5 - 1/8*x^4*(16*
e^6 + 182*e^4 + 708*e^2 + 957) + 2/9*(9*(2*e^6 + 25*e^4 + 104*e^2 + 144)*log(x)^2 - 6*(2*e^6 + 25*e^4 + 104*e^
2 + 144)*log(x) + 4*e^6 + 50*e^4 + 208*e^2 + 288)*x^3 + 565/2*x^4 - 2/9*x^3*(3*e^8 + 40*e^6 + 224*e^4 + 664*e^
2 + 870) + 1/2*(2*(e^8 + 16*e^6 + 96*e^4 + 256*e^2 + 256)*log(x)^2 - 2*(e^8 + 16*e^6 + 96*e^4 + 256*e^2 + 256)
*log(x) + e^8 + 16*e^6 + 96*e^4 + 256*e^2 + 256)*x^2 + 2032/3*x^3 + 1/2*x^2*(e^8 - 104*e^4 - 576*e^2 - 896) +
900*x^2 - 4*x*(e^8 + 16*e^6 + 96*e^4 + 256*e^2 + 256) + 1/3*(3*x^4 - 4*x^3 + 12*x^2)*e^8 + 2*(2*x^5 + 5*x^4 -
2*x^3 + 28*x^2 + 8*x)*e^6 + 2/15*(45*x^6 + 303*x^5 + 360*x^4 + 545*x^3 + 2310*x^2 + 1500*x)*e^4 + 2/15*(30*x^7
+ 340*x^6 + 1074*x^5 + 1245*x^4 + 3280*x^3 + 6120*x^2 + 6240*x)*e^2 + 1/30*(60*x^7 + 1030*x^6 + 6036*x^5 + 14
355*x^4 + 17400*x^3 + 26880*x^2 + 30*(2*x^3 - x^2 + 4*x)*e^8 + 80*(3*x^4 + 10*x^3 + 24*x)*e^6 + 10*(36*x^5 + 2
73*x^4 + 448*x^3 + 312*x^2 + 1152*x)*e^4 + 4*(60*x^6 + 732*x^5 + 2655*x^4 + 3320*x^3 + 4320*x^2 + 7680*x)*e^2
+ 30720*x)*log(x) + 1152*x

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mupad [B]  time = 2.64, size = 309, normalized size = 10.66 \begin {gather*} x^8+2\,x^7\,\ln \relax (x)+\left (4\,{\mathrm {e}}^2+16\right )\,x^7+x^6\,{\ln \relax (x)}^2+\left (8\,{\mathrm {e}}^2+34\right )\,x^6\,\ln \relax (x)+\left (44\,{\mathrm {e}}^2+6\,{\mathrm {e}}^4+82\right )\,x^6+\left (4\,{\mathrm {e}}^2+18\right )\,x^5\,{\ln \relax (x)}^2+\left (96\,{\mathrm {e}}^2+12\,{\mathrm {e}}^4+194\right )\,x^5\,\ln \relax (x)+\left (124\,{\mathrm {e}}^2+38\,{\mathrm {e}}^4+4\,{\mathrm {e}}^6+148\right )\,x^5+\left (52\,{\mathrm {e}}^2+6\,{\mathrm {e}}^4+113\right )\,x^4\,{\ln \relax (x)}^2+\left (328\,{\mathrm {e}}^2+88\,{\mathrm {e}}^4+8\,{\mathrm {e}}^6+422\right )\,x^4\,\ln \relax (x)+\left (84\,{\mathrm {e}}^2+26\,{\mathrm {e}}^4+8\,{\mathrm {e}}^6+{\mathrm {e}}^8+177\right )\,x^4+2\,\left (2\,{\mathrm {e}}^2+9\right )\,{\left ({\mathrm {e}}^2+4\right )}^2\,x^3\,{\ln \relax (x)}^2+\left (304\,{\mathrm {e}}^2+116\,{\mathrm {e}}^4+24\,{\mathrm {e}}^6+2\,{\mathrm {e}}^8+388\right )\,x^3\,\ln \relax (x)+\left (336\,{\mathrm {e}}^2+34\,{\mathrm {e}}^4-12\,{\mathrm {e}}^6-2\,{\mathrm {e}}^8+548\right )\,x^3+{\left ({\mathrm {e}}^2+4\right )}^4\,x^2\,{\ln \relax (x)}^2-2\,{\left ({\mathrm {e}}^2+4\right )}^2\,\left ({\mathrm {e}}^4-20\right )\,x^2\,\ln \relax (x)+\left (656\,{\mathrm {e}}^2+304\,{\mathrm {e}}^4+64\,{\mathrm {e}}^6+5\,{\mathrm {e}}^8+580\right )\,x^2+4\,{\left ({\mathrm {e}}^2+4\right )}^4\,x\,\ln \relax (x)-4\,{\left ({\mathrm {e}}^2+4\right )}^2\,\left (4\,{\mathrm {e}}^2+{\mathrm {e}}^4-2\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1800*x + exp(2)*(1632*x + 1312*x^2 + 664*x^3 + 716*x^4 + 272*x^5 + 28*x^6 + 832) + log(x)^2*(512*x + exp(6
)*(32*x + 12*x^2) + 2*x*exp(8) + exp(4)*(192*x + 150*x^2 + 24*x^3) + exp(2)*(512*x + 624*x^2 + 208*x^3 + 20*x^
4) + 864*x^2 + 452*x^3 + 90*x^4 + 6*x^5) + exp(8)*(8*x - 4*x^2 + 4*x^3) + exp(6)*(112*x - 12*x^2 + 40*x^3 + 20
*x^4 + 16) + log(x)*(1792*x + exp(8)*(6*x^2 - 2*x + 4) + exp(6)*(80*x^2 + 32*x^3 + 64) + exp(4)*(208*x + 448*x
^2 + 364*x^3 + 60*x^4 + 384) + exp(2)*(1152*x + 1328*x^2 + 1416*x^3 + 488*x^4 + 48*x^5 + 1024) + 1740*x^2 + 19
14*x^3 + 1006*x^4 + 206*x^5 + 14*x^6 + 1024) + exp(4)*(616*x + 218*x^2 + 192*x^3 + 202*x^4 + 36*x^5 + 200) + 2
032*x^2 + 1130*x^3 + 934*x^4 + 526*x^5 + 114*x^6 + 8*x^7 + 1152,x)

[Out]

2*x^7*log(x) + x^6*(44*exp(2) + 6*exp(4) + 82) + x^4*(84*exp(2) + 26*exp(4) + 8*exp(6) + exp(8) + 177) + x^7*(
4*exp(2) + 16) + x^6*log(x)^2 + x^3*(336*exp(2) + 34*exp(4) - 12*exp(6) - 2*exp(8) + 548) + x^2*(656*exp(2) +
304*exp(4) + 64*exp(6) + 5*exp(8) + 580) + x^8 + x^5*(124*exp(2) + 38*exp(4) + 4*exp(6) + 148) + x^5*log(x)*(9
6*exp(2) + 12*exp(4) + 194) + x^6*log(x)*(8*exp(2) + 34) + x^4*log(x)^2*(52*exp(2) + 6*exp(4) + 113) - 4*x*(ex
p(2) + 4)^2*(4*exp(2) + exp(4) - 2) + x^3*log(x)*(304*exp(2) + 116*exp(4) + 24*exp(6) + 2*exp(8) + 388) + x^5*
log(x)^2*(4*exp(2) + 18) + x^2*log(x)^2*(exp(2) + 4)^4 + x^4*log(x)*(328*exp(2) + 88*exp(4) + 8*exp(6) + 422)
+ 4*x*log(x)*(exp(2) + 4)^4 - 2*x^2*log(x)*(exp(2) + 4)^2*(exp(4) - 20) + 2*x^3*log(x)^2*(2*exp(2) + 9)*(exp(2
) + 4)^2

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sympy [B]  time = 0.64, size = 442, normalized size = 15.24 \begin {gather*} x^{8} + x^{7} \left (16 + 4 e^{2}\right ) + x^{6} \left (82 + 44 e^{2} + 6 e^{4}\right ) + x^{5} \left (148 + 124 e^{2} + 4 e^{6} + 38 e^{4}\right ) + x^{4} \left (177 + 84 e^{2} + 26 e^{4} + e^{8} + 8 e^{6}\right ) + x^{3} \left (- 2 e^{8} - 12 e^{6} + 548 + 34 e^{4} + 336 e^{2}\right ) + x^{2} \left (580 + 656 e^{2} + 5 e^{8} + 304 e^{4} + 64 e^{6}\right ) + x \left (- 48 e^{6} - 4 e^{8} - 184 e^{4} - 192 e^{2} + 128\right ) + \left (x^{6} + 18 x^{5} + 4 x^{5} e^{2} + 113 x^{4} + 6 x^{4} e^{4} + 52 x^{4} e^{2} + 288 x^{3} + 208 x^{3} e^{2} + 4 x^{3} e^{6} + 50 x^{3} e^{4} + 256 x^{2} + 256 x^{2} e^{2} + x^{2} e^{8} + 96 x^{2} e^{4} + 16 x^{2} e^{6}\right ) \log {\relax (x )}^{2} + \left (2 x^{7} + 34 x^{6} + 8 x^{6} e^{2} + 194 x^{5} + 12 x^{5} e^{4} + 96 x^{5} e^{2} + 422 x^{4} + 328 x^{4} e^{2} + 8 x^{4} e^{6} + 88 x^{4} e^{4} + 388 x^{3} + 304 x^{3} e^{2} + 2 x^{3} e^{8} + 116 x^{3} e^{4} + 24 x^{3} e^{6} - 16 x^{2} e^{6} - 2 x^{2} e^{8} + 8 x^{2} e^{4} + 640 x^{2} + 320 x^{2} e^{2} + 1024 x + 1024 x e^{2} + 4 x e^{8} + 384 x e^{4} + 64 x e^{6}\right ) \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*exp(2)**4+(12*x**2+32*x)*exp(2)**3+(24*x**3+150*x**2+192*x)*exp(2)**2+(20*x**4+208*x**3+624*x**
2+512*x)*exp(2)+6*x**5+90*x**4+452*x**3+864*x**2+512*x)*ln(x)**2+((6*x**2-2*x+4)*exp(2)**4+(32*x**3+80*x**2+64
)*exp(2)**3+(60*x**4+364*x**3+448*x**2+208*x+384)*exp(2)**2+(48*x**5+488*x**4+1416*x**3+1328*x**2+1152*x+1024)
*exp(2)+14*x**6+206*x**5+1006*x**4+1914*x**3+1740*x**2+1792*x+1024)*ln(x)+(4*x**3-4*x**2+8*x)*exp(2)**4+(20*x*
*4+40*x**3-12*x**2+112*x+16)*exp(2)**3+(36*x**5+202*x**4+192*x**3+218*x**2+616*x+200)*exp(2)**2+(28*x**6+272*x
**5+716*x**4+664*x**3+1312*x**2+1632*x+832)*exp(2)+8*x**7+114*x**6+526*x**5+934*x**4+1130*x**3+2032*x**2+1800*
x+1152,x)

[Out]

x**8 + x**7*(16 + 4*exp(2)) + x**6*(82 + 44*exp(2) + 6*exp(4)) + x**5*(148 + 124*exp(2) + 4*exp(6) + 38*exp(4)
) + x**4*(177 + 84*exp(2) + 26*exp(4) + exp(8) + 8*exp(6)) + x**3*(-2*exp(8) - 12*exp(6) + 548 + 34*exp(4) + 3
36*exp(2)) + x**2*(580 + 656*exp(2) + 5*exp(8) + 304*exp(4) + 64*exp(6)) + x*(-48*exp(6) - 4*exp(8) - 184*exp(
4) - 192*exp(2) + 128) + (x**6 + 18*x**5 + 4*x**5*exp(2) + 113*x**4 + 6*x**4*exp(4) + 52*x**4*exp(2) + 288*x**
3 + 208*x**3*exp(2) + 4*x**3*exp(6) + 50*x**3*exp(4) + 256*x**2 + 256*x**2*exp(2) + x**2*exp(8) + 96*x**2*exp(
4) + 16*x**2*exp(6))*log(x)**2 + (2*x**7 + 34*x**6 + 8*x**6*exp(2) + 194*x**5 + 12*x**5*exp(4) + 96*x**5*exp(2
) + 422*x**4 + 328*x**4*exp(2) + 8*x**4*exp(6) + 88*x**4*exp(4) + 388*x**3 + 304*x**3*exp(2) + 2*x**3*exp(8) +
116*x**3*exp(4) + 24*x**3*exp(6) - 16*x**2*exp(6) - 2*x**2*exp(8) + 8*x**2*exp(4) + 640*x**2 + 320*x**2*exp(2
) + 1024*x + 1024*x*exp(2) + 4*x*exp(8) + 384*x*exp(4) + 64*x*exp(6))*log(x)

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