3.87.2 \(\int \frac {1}{36} (324 x^3+225 x^4+360 x^6+240 x^7+84 x^9+55 x^{10}+e^8 (52 x^5+35 x^6)+e^6 (-240 x^6-160 x^7)+e^4 (264 x^4+180 x^5+408 x^7+270 x^8)+e^2 (-624 x^5-420 x^6-304 x^8-200 x^9)+(144 x^3+24 e^8 x^5+168 x^6-112 e^6 x^6+40 x^9+e^4 (120 x^4+192 x^7)+e^2 (-288 x^5-144 x^8)) \log (x)) \, dx\)

Optimal. Leaf size=31 \[ \frac {1}{9} x^4 \left (3+\left (e^2-x\right )^2 x\right )^2 \left (2+\frac {5 x}{4}+\log (x)\right ) \]

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Rubi [B]  time = 0.21, antiderivative size = 278, normalized size of antiderivative = 8.97, number of steps used = 16, number of rules used = 4, integrand size = 180, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {12, 6, 2356, 2304} \begin {gather*} \frac {5 x^{11}}{36}-\frac {5 e^2 x^{10}}{9}+\frac {2 x^{10}}{9}+\frac {1}{9} x^{10} \log (x)+\frac {5 e^4 x^9}{6}-\frac {8 e^2 x^9}{9}-\frac {4}{9} e^2 x^9 \log (x)-\frac {5 e^6 x^8}{9}+\frac {4 e^4 x^8}{3}+\frac {5 x^8}{6}+\frac {2}{3} e^4 x^8 \log (x)-\frac {2}{63} \left (3-2 e^6\right ) x^7+\frac {5 e^8 x^7}{36}-\frac {20 e^6 x^7}{21}-\frac {5 e^2 x^7}{3}+\frac {10 x^7}{7}+\frac {2}{9} \left (3-2 e^6\right ) x^7 \log (x)+\frac {1}{54} e^2 \left (12-e^6\right ) x^6+\frac {13 e^8 x^6}{54}+\frac {5 e^4 x^6}{6}-\frac {26 e^2 x^6}{9}-\frac {1}{9} e^2 \left (12-e^6\right ) x^6 \log (x)+\frac {4 e^4 x^5}{3}+\frac {5 x^5}{4}+\frac {2}{3} e^4 x^5 \log (x)+2 x^4+x^4 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(324*x^3 + 225*x^4 + 360*x^6 + 240*x^7 + 84*x^9 + 55*x^10 + E^8*(52*x^5 + 35*x^6) + E^6*(-240*x^6 - 160*x^
7) + E^4*(264*x^4 + 180*x^5 + 408*x^7 + 270*x^8) + E^2*(-624*x^5 - 420*x^6 - 304*x^8 - 200*x^9) + (144*x^3 + 2
4*E^8*x^5 + 168*x^6 - 112*E^6*x^6 + 40*x^9 + E^4*(120*x^4 + 192*x^7) + E^2*(-288*x^5 - 144*x^8))*Log[x])/36,x]

[Out]

2*x^4 + (5*x^5)/4 + (4*E^4*x^5)/3 - (26*E^2*x^6)/9 + (5*E^4*x^6)/6 + (13*E^8*x^6)/54 + (E^2*(12 - E^6)*x^6)/54
+ (10*x^7)/7 - (5*E^2*x^7)/3 - (20*E^6*x^7)/21 + (5*E^8*x^7)/36 - (2*(3 - 2*E^6)*x^7)/63 + (5*x^8)/6 + (4*E^4
*x^8)/3 - (5*E^6*x^8)/9 - (8*E^2*x^9)/9 + (5*E^4*x^9)/6 + (2*x^10)/9 - (5*E^2*x^10)/9 + (5*x^11)/36 + x^4*Log[
x] + (2*E^4*x^5*Log[x])/3 - (E^2*(12 - E^6)*x^6*Log[x])/9 + (2*(3 - 2*E^6)*x^7*Log[x])/9 + (2*E^4*x^8*Log[x])/
3 - (4*E^2*x^9*Log[x])/9 + (x^10*Log[x])/9

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 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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 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} &=\frac {1}{36} \int \left (324 x^3+225 x^4+360 x^6+240 x^7+84 x^9+55 x^{10}+e^8 \left (52 x^5+35 x^6\right )+e^6 \left (-240 x^6-160 x^7\right )+e^4 \left (264 x^4+180 x^5+408 x^7+270 x^8\right )+e^2 \left (-624 x^5-420 x^6-304 x^8-200 x^9\right )+\left (144 x^3+24 e^8 x^5+168 x^6-112 e^6 x^6+40 x^9+e^4 \left (120 x^4+192 x^7\right )+e^2 \left (-288 x^5-144 x^8\right )\right ) \log (x)\right ) \, dx\\ &=\frac {9 x^4}{4}+\frac {5 x^5}{4}+\frac {10 x^7}{7}+\frac {5 x^8}{6}+\frac {7 x^{10}}{30}+\frac {5 x^{11}}{36}+\frac {1}{36} \int \left (144 x^3+24 e^8 x^5+168 x^6-112 e^6 x^6+40 x^9+e^4 \left (120 x^4+192 x^7\right )+e^2 \left (-288 x^5-144 x^8\right )\right ) \log (x) \, dx+\frac {1}{36} e^2 \int \left (-624 x^5-420 x^6-304 x^8-200 x^9\right ) \, dx+\frac {1}{36} e^4 \int \left (264 x^4+180 x^5+408 x^7+270 x^8\right ) \, dx+\frac {1}{36} e^6 \int \left (-240 x^6-160 x^7\right ) \, dx+\frac {1}{36} e^8 \int \left (52 x^5+35 x^6\right ) \, dx\\ &=\frac {9 x^4}{4}+\frac {5 x^5}{4}+\frac {22 e^4 x^5}{15}-\frac {26 e^2 x^6}{9}+\frac {5 e^4 x^6}{6}+\frac {13 e^8 x^6}{54}+\frac {10 x^7}{7}-\frac {5 e^2 x^7}{3}-\frac {20 e^6 x^7}{21}+\frac {5 e^8 x^7}{36}+\frac {5 x^8}{6}+\frac {17 e^4 x^8}{12}-\frac {5 e^6 x^8}{9}-\frac {76 e^2 x^9}{81}+\frac {5 e^4 x^9}{6}+\frac {7 x^{10}}{30}-\frac {5 e^2 x^{10}}{9}+\frac {5 x^{11}}{36}+\frac {1}{36} \int \left (144 x^3+24 e^8 x^5+\left (168-112 e^6\right ) x^6+40 x^9+e^4 \left (120 x^4+192 x^7\right )+e^2 \left (-288 x^5-144 x^8\right )\right ) \log (x) \, dx\\ &=\frac {9 x^4}{4}+\frac {5 x^5}{4}+\frac {22 e^4 x^5}{15}-\frac {26 e^2 x^6}{9}+\frac {5 e^4 x^6}{6}+\frac {13 e^8 x^6}{54}+\frac {10 x^7}{7}-\frac {5 e^2 x^7}{3}-\frac {20 e^6 x^7}{21}+\frac {5 e^8 x^7}{36}+\frac {5 x^8}{6}+\frac {17 e^4 x^8}{12}-\frac {5 e^6 x^8}{9}-\frac {76 e^2 x^9}{81}+\frac {5 e^4 x^9}{6}+\frac {7 x^{10}}{30}-\frac {5 e^2 x^{10}}{9}+\frac {5 x^{11}}{36}+\frac {1}{36} \int \left (144 x^3 \log (x)+120 e^4 x^4 \log (x)+24 e^2 \left (-12+e^6\right ) x^5 \log (x)-56 \left (-3+2 e^6\right ) x^6 \log (x)+192 e^4 x^7 \log (x)-144 e^2 x^8 \log (x)+40 x^9 \log (x)\right ) \, dx\\ &=\frac {9 x^4}{4}+\frac {5 x^5}{4}+\frac {22 e^4 x^5}{15}-\frac {26 e^2 x^6}{9}+\frac {5 e^4 x^6}{6}+\frac {13 e^8 x^6}{54}+\frac {10 x^7}{7}-\frac {5 e^2 x^7}{3}-\frac {20 e^6 x^7}{21}+\frac {5 e^8 x^7}{36}+\frac {5 x^8}{6}+\frac {17 e^4 x^8}{12}-\frac {5 e^6 x^8}{9}-\frac {76 e^2 x^9}{81}+\frac {5 e^4 x^9}{6}+\frac {7 x^{10}}{30}-\frac {5 e^2 x^{10}}{9}+\frac {5 x^{11}}{36}+\frac {10}{9} \int x^9 \log (x) \, dx+4 \int x^3 \log (x) \, dx-\left (4 e^2\right ) \int x^8 \log (x) \, dx+\frac {1}{3} \left (10 e^4\right ) \int x^4 \log (x) \, dx+\frac {1}{3} \left (16 e^4\right ) \int x^7 \log (x) \, dx+\frac {1}{9} \left (14 \left (3-2 e^6\right )\right ) \int x^6 \log (x) \, dx-\frac {1}{3} \left (2 e^2 \left (12-e^6\right )\right ) \int x^5 \log (x) \, dx\\ &=2 x^4+\frac {5 x^5}{4}+\frac {4 e^4 x^5}{3}-\frac {26 e^2 x^6}{9}+\frac {5 e^4 x^6}{6}+\frac {13 e^8 x^6}{54}+\frac {1}{54} e^2 \left (12-e^6\right ) x^6+\frac {10 x^7}{7}-\frac {5 e^2 x^7}{3}-\frac {20 e^6 x^7}{21}+\frac {5 e^8 x^7}{36}-\frac {2}{63} \left (3-2 e^6\right ) x^7+\frac {5 x^8}{6}+\frac {4 e^4 x^8}{3}-\frac {5 e^6 x^8}{9}-\frac {8 e^2 x^9}{9}+\frac {5 e^4 x^9}{6}+\frac {2 x^{10}}{9}-\frac {5 e^2 x^{10}}{9}+\frac {5 x^{11}}{36}+x^4 \log (x)+\frac {2}{3} e^4 x^5 \log (x)-\frac {1}{9} e^2 \left (12-e^6\right ) x^6 \log (x)+\frac {2}{9} \left (3-2 e^6\right ) x^7 \log (x)+\frac {2}{3} e^4 x^8 \log (x)-\frac {4}{9} e^2 x^9 \log (x)+\frac {1}{9} x^{10} \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.05, size = 36, normalized size = 1.16 \begin {gather*} \frac {1}{36} x^4 \left (3+e^4 x-2 e^2 x^2+x^3\right )^2 (8+5 x+4 \log (x)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(324*x^3 + 225*x^4 + 360*x^6 + 240*x^7 + 84*x^9 + 55*x^10 + E^8*(52*x^5 + 35*x^6) + E^6*(-240*x^6 -
160*x^7) + E^4*(264*x^4 + 180*x^5 + 408*x^7 + 270*x^8) + E^2*(-624*x^5 - 420*x^6 - 304*x^8 - 200*x^9) + (144*x
^3 + 24*E^8*x^5 + 168*x^6 - 112*E^6*x^6 + 40*x^9 + E^4*(120*x^4 + 192*x^7) + E^2*(-288*x^5 - 144*x^8))*Log[x])
/36,x]

[Out]

(x^4*(3 + E^4*x - 2*E^2*x^2 + x^3)^2*(8 + 5*x + 4*Log[x]))/36

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fricas [B]  time = 0.58, size = 166, normalized size = 5.35 \begin {gather*} \frac {5}{36} \, x^{11} + \frac {2}{9} \, x^{10} + \frac {5}{6} \, x^{8} + \frac {4}{3} \, x^{7} + \frac {5}{4} \, x^{5} + 2 \, x^{4} + \frac {1}{36} \, {\left (5 \, x^{7} + 8 \, x^{6}\right )} e^{8} - \frac {1}{9} \, {\left (5 \, x^{8} + 8 \, x^{7}\right )} e^{6} + \frac {1}{6} \, {\left (5 \, x^{9} + 8 \, x^{8} + 5 \, x^{6} + 8 \, x^{5}\right )} e^{4} - \frac {1}{9} \, {\left (5 \, x^{10} + 8 \, x^{9} + 15 \, x^{7} + 24 \, x^{6}\right )} e^{2} + \frac {1}{9} \, {\left (x^{10} - 4 \, x^{7} e^{6} + 6 \, x^{7} + x^{6} e^{8} + 9 \, x^{4} + 6 \, {\left (x^{8} + x^{5}\right )} e^{4} - 4 \, {\left (x^{9} + 3 \, x^{6}\right )} e^{2}\right )} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/36*(24*x^5*exp(2)^4-112*x^6*exp(2)^3+(192*x^7+120*x^4)*exp(2)^2+(-144*x^8-288*x^5)*exp(2)+40*x^9+1
68*x^6+144*x^3)*log(x)+1/36*(35*x^6+52*x^5)*exp(2)^4+1/36*(-160*x^7-240*x^6)*exp(2)^3+1/36*(270*x^8+408*x^7+18
0*x^5+264*x^4)*exp(2)^2+1/36*(-200*x^9-304*x^8-420*x^6-624*x^5)*exp(2)+55/36*x^10+7/3*x^9+20/3*x^7+10*x^6+25/4
*x^4+9*x^3,x, algorithm="fricas")

[Out]

5/36*x^11 + 2/9*x^10 + 5/6*x^8 + 4/3*x^7 + 5/4*x^5 + 2*x^4 + 1/36*(5*x^7 + 8*x^6)*e^8 - 1/9*(5*x^8 + 8*x^7)*e^
6 + 1/6*(5*x^9 + 8*x^8 + 5*x^6 + 8*x^5)*e^4 - 1/9*(5*x^10 + 8*x^9 + 15*x^7 + 24*x^6)*e^2 + 1/9*(x^10 - 4*x^7*e
^6 + 6*x^7 + x^6*e^8 + 9*x^4 + 6*(x^8 + x^5)*e^4 - 4*(x^9 + 3*x^6)*e^2)*log(x)

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giac [B]  time = 0.14, size = 227, normalized size = 7.32 \begin {gather*} \frac {5}{36} \, x^{11} + \frac {1}{9} \, x^{10} \log \relax (x) - \frac {4}{9} \, x^{9} e^{2} \log \relax (x) + \frac {2}{9} \, x^{10} + \frac {4}{81} \, x^{9} e^{2} + \frac {2}{3} \, x^{8} e^{4} \log \relax (x) - \frac {1}{12} \, x^{8} e^{4} - \frac {4}{9} \, x^{7} e^{6} \log \relax (x) + \frac {5}{6} \, x^{8} + \frac {4}{63} \, x^{7} e^{6} + \frac {2}{3} \, x^{7} \log \relax (x) + \frac {1}{9} \, x^{6} e^{8} \log \relax (x) - \frac {4}{3} \, x^{6} e^{2} \log \relax (x) + \frac {4}{3} \, x^{7} - \frac {1}{54} \, x^{6} e^{8} + \frac {2}{9} \, x^{6} e^{2} + \frac {2}{3} \, x^{5} e^{4} \log \relax (x) - \frac {2}{15} \, x^{5} e^{4} + \frac {5}{4} \, x^{5} + x^{4} \log \relax (x) + 2 \, x^{4} + \frac {1}{108} \, {\left (15 \, x^{7} + 26 \, x^{6}\right )} e^{8} - \frac {5}{63} \, {\left (7 \, x^{8} + 12 \, x^{7}\right )} e^{6} + \frac {1}{60} \, {\left (50 \, x^{9} + 85 \, x^{8} + 50 \, x^{6} + 88 \, x^{5}\right )} e^{4} - \frac {1}{81} \, {\left (45 \, x^{10} + 76 \, x^{9} + 135 \, x^{7} + 234 \, x^{6}\right )} e^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/36*(24*x^5*exp(2)^4-112*x^6*exp(2)^3+(192*x^7+120*x^4)*exp(2)^2+(-144*x^8-288*x^5)*exp(2)+40*x^9+1
68*x^6+144*x^3)*log(x)+1/36*(35*x^6+52*x^5)*exp(2)^4+1/36*(-160*x^7-240*x^6)*exp(2)^3+1/36*(270*x^8+408*x^7+18
0*x^5+264*x^4)*exp(2)^2+1/36*(-200*x^9-304*x^8-420*x^6-624*x^5)*exp(2)+55/36*x^10+7/3*x^9+20/3*x^7+10*x^6+25/4
*x^4+9*x^3,x, algorithm="giac")

[Out]

5/36*x^11 + 1/9*x^10*log(x) - 4/9*x^9*e^2*log(x) + 2/9*x^10 + 4/81*x^9*e^2 + 2/3*x^8*e^4*log(x) - 1/12*x^8*e^4
- 4/9*x^7*e^6*log(x) + 5/6*x^8 + 4/63*x^7*e^6 + 2/3*x^7*log(x) + 1/9*x^6*e^8*log(x) - 4/3*x^6*e^2*log(x) + 4/
3*x^7 - 1/54*x^6*e^8 + 2/9*x^6*e^2 + 2/3*x^5*e^4*log(x) - 2/15*x^5*e^4 + 5/4*x^5 + x^4*log(x) + 2*x^4 + 1/108*
(15*x^7 + 26*x^6)*e^8 - 5/63*(7*x^8 + 12*x^7)*e^6 + 1/60*(50*x^9 + 85*x^8 + 50*x^6 + 88*x^5)*e^4 - 1/81*(45*x^
10 + 76*x^9 + 135*x^7 + 234*x^6)*e^2

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maple [B]  time = 0.08, size = 178, normalized size = 5.74

method	result	size
risch	\(\frac {\left (4 \,{\mathrm e}^{8} x^{6}-16 \,{\mathrm e}^{6} x^{7}+24 x^{8} {\mathrm e}^{4}-16 \,{\mathrm e}^{2} x^{9}+4 x^{10}+24 x^{5} {\mathrm e}^{4}-48 x^{6} {\mathrm e}^{2}+24 x^{7}+36 x^{4}\right ) \ln \relax (x )}{36}+\frac {2 x^{10}}{9}-\frac {8 \,{\mathrm e}^{2} x^{9}}{9}+\frac {4 x^{8} {\mathrm e}^{4}}{3}-\frac {8 \,{\mathrm e}^{6} x^{7}}{9}+\frac {4 x^{7}}{3}+\frac {2 \,{\mathrm e}^{8} x^{6}}{9}-\frac {8 x^{6} {\mathrm e}^{2}}{3}+\frac {4 x^{5} {\mathrm e}^{4}}{3}+2 x^{4}+\frac {5 \,{\mathrm e}^{8} x^{7}}{36}-\frac {5 \,{\mathrm e}^{6} x^{8}}{9}+\frac {5 x^{9} {\mathrm e}^{4}}{6}+\frac {5 x^{6} {\mathrm e}^{4}}{6}-\frac {5 \,{\mathrm e}^{2} x^{10}}{9}-\frac {5 \,{\mathrm e}^{2} x^{7}}{3}+\frac {5 x^{11}}{36}+\frac {5 x^{8}}{6}+\frac {5 x^{5}}{4}\)	\(178\)
norman	\(x^{4} \ln \relax (x )+\left (\frac {2}{9}-\frac {5 \,{\mathrm e}^{2}}{9}\right ) x^{10}+\left (\frac {4 \,{\mathrm e}^{4}}{3}+\frac {5}{4}\right ) x^{5}+\left (-\frac {8 \,{\mathrm e}^{2}}{9}+\frac {5 \,{\mathrm e}^{4}}{6}\right ) x^{9}+\left (\frac {4 \,{\mathrm e}^{4}}{3}+\frac {5}{6}-\frac {5 \,{\mathrm e}^{6}}{9}\right ) x^{8}+\left (\frac {2 \,{\mathrm e}^{8}}{9}-\frac {8 \,{\mathrm e}^{2}}{3}+\frac {5 \,{\mathrm e}^{4}}{6}\right ) x^{6}+\left (-\frac {8 \,{\mathrm e}^{6}}{9}+\frac {4}{3}-\frac {5 \,{\mathrm e}^{2}}{3}+\frac {5 \,{\mathrm e}^{8}}{36}\right ) x^{7}+\left (-\frac {4 \,{\mathrm e}^{6}}{9}+\frac {2}{3}\right ) x^{7} \ln \relax (x )+\left (\frac {{\mathrm e}^{8}}{9}-\frac {4 \,{\mathrm e}^{2}}{3}\right ) x^{6} \ln \relax (x )+2 x^{4}+\frac {5 x^{11}}{36}+\frac {x^{10} \ln \relax (x )}{9}-\frac {4 \,{\mathrm e}^{2} x^{9} \ln \relax (x )}{9}+\frac {2 \,{\mathrm e}^{4} x^{5} \ln \relax (x )}{3}+\frac {2 \,{\mathrm e}^{4} x^{8} \ln \relax (x )}{3}\)	\(185\)
default	\(\frac {x^{10} \ln \relax (x )}{9}+\frac {5 x^{11}}{36}+\frac {4 x^{7}}{3}+\frac {5 x^{8}}{6}+\frac {2 x^{10}}{9}+\frac {5 x^{5}}{4}+2 x^{4}+\frac {2 x^{6} {\mathrm e}^{2}}{9}+\frac {2 x^{7} \ln \relax (x )}{3}-\frac {x^{8} {\mathrm e}^{4}}{12}+\frac {{\mathrm e}^{6} \left (-20 x^{8}-\frac {240}{7} x^{7}\right )}{36}+\frac {{\mathrm e}^{8} \left (5 x^{7}+\frac {26}{3} x^{6}\right )}{36}+\frac {{\mathrm e}^{4} \left (30 x^{9}+51 x^{8}+30 x^{6}+\frac {264}{5} x^{5}\right )}{36}+x^{4} \ln \relax (x )-\frac {2 x^{5} {\mathrm e}^{4}}{15}+\frac {4 \,{\mathrm e}^{2} x^{9}}{81}-\frac {4 \,{\mathrm e}^{2} \ln \relax (x ) x^{6}}{3}+\frac {{\mathrm e}^{8} \ln \relax (x ) x^{6}}{9}-\frac {4 \,{\mathrm e}^{6} x^{7} \ln \relax (x )}{9}-\frac {4 \,{\mathrm e}^{2} x^{9} \ln \relax (x )}{9}-\frac {{\mathrm e}^{8} x^{6}}{54}+\frac {4 \,{\mathrm e}^{6} x^{7}}{63}+\frac {{\mathrm e}^{2} \left (-20 x^{10}-\frac {304}{9} x^{9}-60 x^{7}-104 x^{6}\right )}{36}+\frac {2 \,{\mathrm e}^{4} x^{5} \ln \relax (x )}{3}+\frac {2 \,{\mathrm e}^{4} x^{8} \ln \relax (x )}{3}\)	\(250\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/36*(24*x^5*exp(2)^4-112*x^6*exp(2)^3+(192*x^7+120*x^4)*exp(2)^2+(-144*x^8-288*x^5)*exp(2)+40*x^9+168*x^6
+144*x^3)*ln(x)+1/36*(35*x^6+52*x^5)*exp(2)^4+1/36*(-160*x^7-240*x^6)*exp(2)^3+1/36*(270*x^8+408*x^7+180*x^5+2
64*x^4)*exp(2)^2+1/36*(-200*x^9-304*x^8-420*x^6-624*x^5)*exp(2)+55/36*x^10+7/3*x^9+20/3*x^7+10*x^6+25/4*x^4+9*
x^3,x,method=_RETURNVERBOSE)

[Out]

1/36*(4*exp(8)*x^6-16*exp(6)*x^7+24*x^8*exp(4)-16*exp(2)*x^9+4*x^10+24*x^5*exp(4)-48*x^6*exp(2)+24*x^7+36*x^4)
*ln(x)+2/9*x^10-8/9*exp(2)*x^9+4/3*x^8*exp(4)-8/9*exp(6)*x^7+4/3*x^7+2/9*exp(8)*x^6-8/3*x^6*exp(2)+4/3*x^5*exp
(4)+2*x^4+5/36*exp(8)*x^7-5/9*exp(6)*x^8+5/6*x^9*exp(4)+5/6*x^6*exp(4)-5/9*exp(2)*x^10-5/3*exp(2)*x^7+5/36*x^1
1+5/6*x^8+5/4*x^5

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maxima [B]  time = 0.35, size = 210, normalized size = 6.77 \begin {gather*} \frac {5}{36} \, x^{11} + \frac {2}{9} \, x^{10} + \frac {4}{81} \, x^{9} e^{2} - \frac {1}{12} \, x^{8} e^{4} + \frac {5}{6} \, x^{8} + \frac {2}{63} \, x^{7} {\left (2 \, e^{6} - 3\right )} + \frac {10}{7} \, x^{7} - \frac {1}{54} \, x^{6} {\left (e^{8} - 12 \, e^{2}\right )} - \frac {2}{15} \, x^{5} e^{4} + \frac {5}{4} \, x^{5} + 2 \, x^{4} + \frac {1}{108} \, {\left (15 \, x^{7} + 26 \, x^{6}\right )} e^{8} - \frac {5}{63} \, {\left (7 \, x^{8} + 12 \, x^{7}\right )} e^{6} + \frac {1}{60} \, {\left (50 \, x^{9} + 85 \, x^{8} + 50 \, x^{6} + 88 \, x^{5}\right )} e^{4} - \frac {1}{81} \, {\left (45 \, x^{10} + 76 \, x^{9} + 135 \, x^{7} + 234 \, x^{6}\right )} e^{2} + \frac {1}{9} \, {\left (x^{10} - 4 \, x^{7} e^{6} + 6 \, x^{7} + x^{6} e^{8} + 9 \, x^{4} + 6 \, {\left (x^{8} + x^{5}\right )} e^{4} - 4 \, {\left (x^{9} + 3 \, x^{6}\right )} e^{2}\right )} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/36*(24*x^5*exp(2)^4-112*x^6*exp(2)^3+(192*x^7+120*x^4)*exp(2)^2+(-144*x^8-288*x^5)*exp(2)+40*x^9+1
68*x^6+144*x^3)*log(x)+1/36*(35*x^6+52*x^5)*exp(2)^4+1/36*(-160*x^7-240*x^6)*exp(2)^3+1/36*(270*x^8+408*x^7+18
0*x^5+264*x^4)*exp(2)^2+1/36*(-200*x^9-304*x^8-420*x^6-624*x^5)*exp(2)+55/36*x^10+7/3*x^9+20/3*x^7+10*x^6+25/4
*x^4+9*x^3,x, algorithm="maxima")

[Out]

5/36*x^11 + 2/9*x^10 + 4/81*x^9*e^2 - 1/12*x^8*e^4 + 5/6*x^8 + 2/63*x^7*(2*e^6 - 3) + 10/7*x^7 - 1/54*x^6*(e^8
- 12*e^2) - 2/15*x^5*e^4 + 5/4*x^5 + 2*x^4 + 1/108*(15*x^7 + 26*x^6)*e^8 - 5/63*(7*x^8 + 12*x^7)*e^6 + 1/60*(
50*x^9 + 85*x^8 + 50*x^6 + 88*x^5)*e^4 - 1/81*(45*x^10 + 76*x^9 + 135*x^7 + 234*x^6)*e^2 + 1/9*(x^10 - 4*x^7*e
^6 + 6*x^7 + x^6*e^8 + 9*x^4 + 6*(x^8 + x^5)*e^4 - 4*(x^9 + 3*x^6)*e^2)*log(x)

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mupad [B]  time = 5.68, size = 32, normalized size = 1.03 \begin {gather*} \frac {x^4\,\left (5\,x+4\,\ln \relax (x)+8\right )\,{\left (x^3-2\,{\mathrm {e}}^2\,x^2+{\mathrm {e}}^4\,x+3\right )}^2}{36} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(8)*(52*x^5 + 35*x^6))/36 - (exp(6)*(240*x^6 + 160*x^7))/36 + (log(x)*(exp(4)*(120*x^4 + 192*x^7) - ex
p(2)*(288*x^5 + 144*x^8) - 112*x^6*exp(6) + 24*x^5*exp(8) + 144*x^3 + 168*x^6 + 40*x^9))/36 + 9*x^3 + (25*x^4)
/4 + 10*x^6 + (20*x^7)/3 + (7*x^9)/3 + (55*x^10)/36 + (exp(4)*(264*x^4 + 180*x^5 + 408*x^7 + 270*x^8))/36 - (e
xp(2)*(624*x^5 + 420*x^6 + 304*x^8 + 200*x^9))/36,x)

[Out]

(x^4*(5*x + 4*log(x) + 8)*(x*exp(4) - 2*x^2*exp(2) + x^3 + 3)^2)/36

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sympy [B]  time = 0.33, size = 204, normalized size = 6.58 \begin {gather*} \frac {5 x^{11}}{36} + x^{10} \left (\frac {2}{9} - \frac {5 e^{2}}{9}\right ) + x^{9} \left (- \frac {8 e^{2}}{9} + \frac {5 e^{4}}{6}\right ) + x^{8} \left (- \frac {5 e^{6}}{9} + \frac {5}{6} + \frac {4 e^{4}}{3}\right ) + x^{7} \left (- \frac {8 e^{6}}{9} - \frac {5 e^{2}}{3} + \frac {4}{3} + \frac {5 e^{8}}{36}\right ) + x^{6} \left (- \frac {8 e^{2}}{3} + \frac {5 e^{4}}{6} + \frac {2 e^{8}}{9}\right ) + x^{5} \left (\frac {5}{4} + \frac {4 e^{4}}{3}\right ) + 2 x^{4} + \left (\frac {x^{10}}{9} - \frac {4 x^{9} e^{2}}{9} + \frac {2 x^{8} e^{4}}{3} - \frac {4 x^{7} e^{6}}{9} + \frac {2 x^{7}}{3} - \frac {4 x^{6} e^{2}}{3} + \frac {x^{6} e^{8}}{9} + \frac {2 x^{5} e^{4}}{3} + x^{4}\right ) \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/36*(24*x**5*exp(2)**4-112*x**6*exp(2)**3+(192*x**7+120*x**4)*exp(2)**2+(-144*x**8-288*x**5)*exp(2)
+40*x**9+168*x**6+144*x**3)*ln(x)+1/36*(35*x**6+52*x**5)*exp(2)**4+1/36*(-160*x**7-240*x**6)*exp(2)**3+1/36*(2
70*x**8+408*x**7+180*x**5+264*x**4)*exp(2)**2+1/36*(-200*x**9-304*x**8-420*x**6-624*x**5)*exp(2)+55/36*x**10+7
/3*x**9+20/3*x**7+10*x**6+25/4*x**4+9*x**3,x)

[Out]

5*x**11/36 + x**10*(2/9 - 5*exp(2)/9) + x**9*(-8*exp(2)/9 + 5*exp(4)/6) + x**8*(-5*exp(6)/9 + 5/6 + 4*exp(4)/3
) + x**7*(-8*exp(6)/9 - 5*exp(2)/3 + 4/3 + 5*exp(8)/36) + x**6*(-8*exp(2)/3 + 5*exp(4)/6 + 2*exp(8)/9) + x**5*
(5/4 + 4*exp(4)/3) + 2*x**4 + (x**10/9 - 4*x**9*exp(2)/9 + 2*x**8*exp(4)/3 - 4*x**7*exp(6)/9 + 2*x**7/3 - 4*x*
*6*exp(2)/3 + x**6*exp(8)/9 + 2*x**5*exp(4)/3 + x**4)*log(x)

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