3.99.44 \(\int \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+200 x^9-2 e^4 x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10})+e^8 (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 (-10 x^9-2 x^{10}))+(16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 (10 x^9+2 x^{10})) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx\)

Optimal. Leaf size=29 \[ \left (e^8+\frac {16}{x^4}-x+\frac {e^2+x}{5+x}-\log (x)\right )^2 \]

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Rubi [B]  time = 2.23, antiderivative size = 518, normalized size of antiderivative = 17.86, number of steps used = 22, number of rules used = 11, integrand size = 259, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {6, 6688, 12, 6742, 1620, 2357, 2295, 2304, 2301, 2314, 31} \begin {gather*} \frac {256}{x^8}+\frac {32 e^2 \left (1+5 e^6\right )}{5 x^4}-\frac {32 \log (x)}{x^4}-\frac {128 \left (4-e^8\right )}{15 x^3}-\frac {128 e^2 \left (1+5 e^6\right )}{75 x^3}+\frac {32 \left (1811+125 e^2\right )}{9375 x^3}+\frac {22048}{9375 x^3}+x^2+\frac {64 \left (4-e^8\right )}{25 x^2}+\frac {64 e^2 \left (1+5 e^6\right )}{125 x^2}+\frac {16 \left (1811+125 e^2\right )}{15625 x^2}-\frac {48 \left (187+125 e^2\right )}{15625 x^2}-\frac {64}{5 x^2}+2 \left (4-e^8\right ) x-10 x+\frac {2 \left (5-e^2\right ) \left (2-e^4\right ) \left (2+e^4\right )}{x+5}-\frac {12532 \left (5-e^2\right )}{625 (x+5)}-\frac {e^2 \left (5-e^2\right ) \left (1+5 e^6\right )}{(x+5)^2}-\frac {5 \left (5-e^2\right ) \left (2-e^4\right ) \left (2+e^4\right )}{(x+5)^2}+\frac {25 \left (5-e^2\right )}{(x+5)^2}-\frac {128 \left (4-e^8\right )}{125 x}-\frac {128 e^2 \left (1+5 e^6\right )}{625 x}-\frac {96 \left (187+125 e^2\right )}{78125 x}-\frac {192 \left (219-125 e^2\right )}{78125 x}+\frac {128}{25 x}+\log ^2(x)-\frac {2 \left (5-e^2\right ) x \log (x)}{5 (x+5)}+2 x \log (x)-\frac {128}{625} \left (4-e^8\right ) \log (x)-\frac {1378 e^2 \left (1+5 e^6\right ) \log (x)}{3125}+\frac {192 \left (219-125 e^2\right ) \log (x)}{390625}-\frac {64 \left (1907-625 e^2\right ) \log (x)}{390625}+\frac {128 \log (x)}{125}-\frac {4872}{625} \left (4-e^8\right ) \log (x+5)-\frac {4872 e^2 \left (1+5 e^6\right ) \log (x+5)}{3125}+\frac {2}{125} \left (1811+125 e^2\right ) \log (x+5)+\frac {2}{5} \left (5-e^2\right ) \log (x+5)-\frac {192 \left (219-125 e^2\right ) \log (x+5)}{390625}+\frac {64 \left (1907-625 e^2\right ) \log (x+5)}{390625} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-256000 - 153600*x - 30720*x^2 - 2048*x^3 - 4000*x^4 + 7200*x^5 + 5600*x^6 + 1280*x^7 + 96*x^8 + 200*x^9
- 2*E^4*x^9 + 290*x^10 + 148*x^11 + 30*x^12 + 2*x^13 + E^2*(-3200*x^4 - 1440*x^5 - 160*x^6 - 50*x^8 - 60*x^9 -
14*x^10) + E^8*(-16000*x^4 - 9600*x^5 - 1920*x^6 - 128*x^7 - 250*x^8 - 350*x^9 - 170*x^10 - 32*x^11 - 2*x^12
+ E^2*(-10*x^9 - 2*x^10)) + (16000*x^4 + 9600*x^5 + 1920*x^6 + 128*x^7 + 250*x^8 + 350*x^9 + 170*x^10 + 32*x^1
1 + 2*x^12 + E^2*(10*x^9 + 2*x^10))*Log[x])/(125*x^9 + 75*x^10 + 15*x^11 + x^12),x]

[Out]

256/x^8 + (32*E^2*(1 + 5*E^6))/(5*x^4) + 22048/(9375*x^3) + (32*(1811 + 125*E^2))/(9375*x^3) - (128*E^2*(1 + 5
*E^6))/(75*x^3) - (128*(4 - E^8))/(15*x^3) - 64/(5*x^2) - (48*(187 + 125*E^2))/(15625*x^2) + (16*(1811 + 125*E
^2))/(15625*x^2) + (64*E^2*(1 + 5*E^6))/(125*x^2) + (64*(4 - E^8))/(25*x^2) + 128/(25*x) - (192*(219 - 125*E^2
))/(78125*x) - (96*(187 + 125*E^2))/(78125*x) - (128*E^2*(1 + 5*E^6))/(625*x) - (128*(4 - E^8))/(125*x) - 10*x
+ 2*(4 - E^8)*x + x^2 + (25*(5 - E^2))/(5 + x)^2 - (5*(5 - E^2)*(2 - E^4)*(2 + E^4))/(5 + x)^2 - (E^2*(5 - E^
2)*(1 + 5*E^6))/(5 + x)^2 - (12532*(5 - E^2))/(625*(5 + x)) + (2*(5 - E^2)*(2 - E^4)*(2 + E^4))/(5 + x) + (128
*Log[x])/125 - (64*(1907 - 625*E^2)*Log[x])/390625 + (192*(219 - 125*E^2)*Log[x])/390625 - (1378*E^2*(1 + 5*E^
6)*Log[x])/3125 - (128*(4 - E^8)*Log[x])/625 - (32*Log[x])/x^4 + 2*x*Log[x] - (2*(5 - E^2)*x*Log[x])/(5*(5 + x
)) + Log[x]^2 + (64*(1907 - 625*E^2)*Log[5 + x])/390625 - (192*(219 - 125*E^2)*Log[5 + x])/390625 + (2*(5 - E^
2)*Log[5 + x])/5 + (2*(1811 + 125*E^2)*Log[5 + x])/125 - (4872*E^2*(1 + 5*E^6)*Log[5 + x])/3125 - (4872*(4 - E
^8)*Log[5 + x])/625

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 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 1620

Int[(Px_)*((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[Px*(a + b*x)
^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && PolyQ[Px, x] && (IntegersQ[m, n] || IGtQ[m, -2]) &&
GtQ[Expon[Px, x], 2]

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 2301

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, 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 2314

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_) + (e_.)*(x_)^(r_.))^(q_), x_Symbol] :> Simp[(x*(d + e*x^r)^(q
+ 1)*(a + b*Log[c*x^n]))/d, x] - Dist[(b*n)/d, Int[(d + e*x^r)^(q + 1), x], x] /; FreeQ[{a, b, c, d, e, n, q,
r}, x] && EqQ[r*(q + 1) + 1, 0]

Rule 2357

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]

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 \frac {-256000-153600 x-30720 x^2-2048 x^3-4000 x^4+7200 x^5+5600 x^6+1280 x^7+96 x^8+\left (200-2 e^4\right ) x^9+290 x^{10}+148 x^{11}+30 x^{12}+2 x^{13}+e^2 \left (-3200 x^4-1440 x^5-160 x^6-50 x^8-60 x^9-14 x^{10}\right )+e^8 \left (-16000 x^4-9600 x^5-1920 x^6-128 x^7-250 x^8-350 x^9-170 x^{10}-32 x^{11}-2 x^{12}+e^2 \left (-10 x^9-2 x^{10}\right )\right )+\left (16000 x^4+9600 x^5+1920 x^6+128 x^7+250 x^8+350 x^9+170 x^{10}+32 x^{11}+2 x^{12}+e^2 \left (10 x^9+2 x^{10}\right )\right ) \log (x)}{125 x^9+75 x^{10}+15 x^{11}+x^{12}} \, dx\\ &=\int \frac {2 \left (1600+640 x+64 x^2+25 x^4+\left (30+e^2\right ) x^5+11 x^6+x^7\right ) \left (-80-16 x-\left (e^2+5 e^8\right ) x^4-\left (-4+e^8\right ) x^5+x^6+x^4 (5+x) \log (x)\right )}{x^9 (5+x)^3} \, dx\\ &=2 \int \frac {\left (1600+640 x+64 x^2+25 x^4+\left (30+e^2\right ) x^5+11 x^6+x^7\right ) \left (-80-16 x-\left (e^2+5 e^8\right ) x^4-\left (-4+e^8\right ) x^5+x^6+x^4 (5+x) \log (x)\right )}{x^9 (5+x)^3} \, dx\\ &=2 \int \left (\frac {80 \left (-1600-640 x-64 x^2-25 x^4-30 \left (1+\frac {e^2}{30}\right ) x^5-11 x^6-x^7\right )}{x^9 (5+x)^3}+\frac {16 \left (-1600-640 x-64 x^2-25 x^4-30 \left (1+\frac {e^2}{30}\right ) x^5-11 x^6-x^7\right )}{x^8 (5+x)^3}+\frac {e^2 \left (1+5 e^6\right ) \left (-1600-640 x-64 x^2-25 x^4-30 \left (1+\frac {e^2}{30}\right ) x^5-11 x^6-x^7\right )}{x^5 (5+x)^3}+\frac {\left (2-e^4\right ) \left (2+e^4\right ) \left (1600+640 x+64 x^2+25 x^4+30 \left (1+\frac {e^2}{30}\right ) x^5+11 x^6+x^7\right )}{x^4 (5+x)^3}+\frac {1600+640 x+64 x^2+25 x^4+30 \left (1+\frac {e^2}{30}\right ) x^5+11 x^6+x^7}{x^3 (5+x)^3}+\frac {\left (1600+640 x+64 x^2+25 x^4+30 \left (1+\frac {e^2}{30}\right ) x^5+11 x^6+x^7\right ) \log (x)}{x^5 (5+x)^2}\right ) \, dx\\ &=2 \int \frac {1600+640 x+64 x^2+25 x^4+30 \left (1+\frac {e^2}{30}\right ) x^5+11 x^6+x^7}{x^3 (5+x)^3} \, dx+2 \int \frac {\left (1600+640 x+64 x^2+25 x^4+30 \left (1+\frac {e^2}{30}\right ) x^5+11 x^6+x^7\right ) \log (x)}{x^5 (5+x)^2} \, dx+32 \int \frac {-1600-640 x-64 x^2-25 x^4-30 \left (1+\frac {e^2}{30}\right ) x^5-11 x^6-x^7}{x^8 (5+x)^3} \, dx+160 \int \frac {-1600-640 x-64 x^2-25 x^4-30 \left (1+\frac {e^2}{30}\right ) x^5-11 x^6-x^7}{x^9 (5+x)^3} \, dx+\left (2 e^2 \left (1+5 e^6\right )\right ) \int \frac {-1600-640 x-64 x^2-25 x^4-30 \left (1+\frac {e^2}{30}\right ) x^5-11 x^6-x^7}{x^5 (5+x)^3} \, dx+\left (2 \left (4-e^8\right )\right ) \int \frac {1600+640 x+64 x^2+25 x^4+30 \left (1+\frac {e^2}{30}\right ) x^5+11 x^6+x^7}{x^4 (5+x)^3} \, dx\\ &=2 \int \left (-4+\frac {64}{5 x^3}-\frac {64}{25 x^2}+\frac {64}{125 x}+x+\frac {25 \left (-5+e^2\right )}{(5+x)^3}-\frac {10 \left (-5+e^2\right )}{(5+x)^2}+\frac {1811+125 e^2}{125 (5+x)}\right ) \, dx+2 \int \left (\log (x)+\frac {64 \log (x)}{x^5}+\frac {\log (x)}{x}+\frac {\left (-5+e^2\right ) \log (x)}{(5+x)^2}\right ) \, dx+32 \int \left (-\frac {64}{5 x^8}+\frac {64}{25 x^7}-\frac {64}{125 x^6}+\frac {64}{625 x^5}-\frac {689}{3125 x^4}+\frac {-1811-125 e^2}{15625 x^3}+\frac {3 \left (187+125 e^2\right )}{78125 x^2}-\frac {6 \left (-219+125 e^2\right )}{390625 x}+\frac {-5+e^2}{125 (5+x)^3}+\frac {3 \left (-5+e^2\right )}{625 (5+x)^2}+\frac {6 \left (-219+125 e^2\right )}{390625 (5+x)}\right ) \, dx+160 \int \left (-\frac {64}{5 x^9}+\frac {64}{25 x^8}-\frac {64}{125 x^7}+\frac {64}{625 x^6}-\frac {689}{3125 x^5}+\frac {-1811-125 e^2}{15625 x^4}+\frac {3 \left (187+125 e^2\right )}{78125 x^3}-\frac {6 \left (-219+125 e^2\right )}{390625 x^2}+\frac {2 \left (-1907+625 e^2\right )}{1953125 x}+\frac {5-e^2}{625 (5+x)^3}-\frac {4 \left (-5+e^2\right )}{3125 (5+x)^2}-\frac {2 \left (-1907+625 e^2\right )}{1953125 (5+x)}\right ) \, dx+\left (2 e^2 \left (1+5 e^6\right )\right ) \int \left (-\frac {64}{5 x^5}+\frac {64}{25 x^4}-\frac {64}{125 x^3}+\frac {64}{625 x^2}-\frac {689}{3125 x}+\frac {5-e^2}{(5+x)^3}-\frac {2436}{3125 (5+x)}\right ) \, dx+\left (2 \left (4-e^8\right )\right ) \int \left (1+\frac {64}{5 x^4}-\frac {64}{25 x^3}+\frac {64}{125 x^2}-\frac {64}{625 x}-\frac {5 \left (-5+e^2\right )}{(5+x)^3}+\frac {-5+e^2}{(5+x)^2}-\frac {2436}{625 (5+x)}\right ) \, dx\\ &=\frac {256}{x^8}+\frac {8}{x^4}+\frac {32 e^2 \left (1+5 e^6\right )}{5 x^4}+\frac {22048}{9375 x^3}+\frac {32 \left (1811+125 e^2\right )}{9375 x^3}-\frac {128 e^2 \left (1+5 e^6\right )}{75 x^3}-\frac {128 \left (4-e^8\right )}{15 x^3}-\frac {64}{5 x^2}-\frac {48 \left (187+125 e^2\right )}{15625 x^2}+\frac {16 \left (1811+125 e^2\right )}{15625 x^2}+\frac {64 e^2 \left (1+5 e^6\right )}{125 x^2}+\frac {64 \left (4-e^8\right )}{25 x^2}+\frac {128}{25 x}-\frac {192 \left (219-125 e^2\right )}{78125 x}-\frac {96 \left (187+125 e^2\right )}{78125 x}-\frac {128 e^2 \left (1+5 e^6\right )}{625 x}-\frac {128 \left (4-e^8\right )}{125 x}-8 x+2 \left (4-e^8\right ) x+x^2+\frac {25 \left (5-e^2\right )}{(5+x)^2}-\frac {e^2 \left (5-e^2\right ) \left (1+5 e^6\right )}{(5+x)^2}-\frac {5 \left (5-e^2\right ) \left (4-e^8\right )}{(5+x)^2}-\frac {12532 \left (5-e^2\right )}{625 (5+x)}+\frac {2 \left (5-e^2\right ) \left (4-e^8\right )}{5+x}+\frac {128 \log (x)}{125}-\frac {64 \left (1907-625 e^2\right ) \log (x)}{390625}+\frac {192 \left (219-125 e^2\right ) \log (x)}{390625}-\frac {1378 e^2 \left (1+5 e^6\right ) \log (x)}{3125}-\frac {128}{625} \left (4-e^8\right ) \log (x)+\frac {64 \left (1907-625 e^2\right ) \log (5+x)}{390625}-\frac {192 \left (219-125 e^2\right ) \log (5+x)}{390625}+\frac {2}{125} \left (1811+125 e^2\right ) \log (5+x)-\frac {4872 e^2 \left (1+5 e^6\right ) \log (5+x)}{3125}-\frac {4872}{625} \left (4-e^8\right ) \log (5+x)+2 \int \log (x) \, dx+2 \int \frac {\log (x)}{x} \, dx+128 \int \frac {\log (x)}{x^5} \, dx-\left (2 \left (5-e^2\right )\right ) \int \frac {\log (x)}{(5+x)^2} \, dx\\ &=\frac {256}{x^8}+\frac {32 e^2 \left (1+5 e^6\right )}{5 x^4}+\frac {22048}{9375 x^3}+\frac {32 \left (1811+125 e^2\right )}{9375 x^3}-\frac {128 e^2 \left (1+5 e^6\right )}{75 x^3}-\frac {128 \left (4-e^8\right )}{15 x^3}-\frac {64}{5 x^2}-\frac {48 \left (187+125 e^2\right )}{15625 x^2}+\frac {16 \left (1811+125 e^2\right )}{15625 x^2}+\frac {64 e^2 \left (1+5 e^6\right )}{125 x^2}+\frac {64 \left (4-e^8\right )}{25 x^2}+\frac {128}{25 x}-\frac {192 \left (219-125 e^2\right )}{78125 x}-\frac {96 \left (187+125 e^2\right )}{78125 x}-\frac {128 e^2 \left (1+5 e^6\right )}{625 x}-\frac {128 \left (4-e^8\right )}{125 x}-10 x+2 \left (4-e^8\right ) x+x^2+\frac {25 \left (5-e^2\right )}{(5+x)^2}-\frac {e^2 \left (5-e^2\right ) \left (1+5 e^6\right )}{(5+x)^2}-\frac {5 \left (5-e^2\right ) \left (4-e^8\right )}{(5+x)^2}-\frac {12532 \left (5-e^2\right )}{625 (5+x)}+\frac {2 \left (5-e^2\right ) \left (4-e^8\right )}{5+x}+\frac {128 \log (x)}{125}-\frac {64 \left (1907-625 e^2\right ) \log (x)}{390625}+\frac {192 \left (219-125 e^2\right ) \log (x)}{390625}-\frac {1378 e^2 \left (1+5 e^6\right ) \log (x)}{3125}-\frac {128}{625} \left (4-e^8\right ) \log (x)-\frac {32 \log (x)}{x^4}+2 x \log (x)-\frac {2 \left (5-e^2\right ) x \log (x)}{5 (5+x)}+\log ^2(x)+\frac {64 \left (1907-625 e^2\right ) \log (5+x)}{390625}-\frac {192 \left (219-125 e^2\right ) \log (5+x)}{390625}+\frac {2}{125} \left (1811+125 e^2\right ) \log (5+x)-\frac {4872 e^2 \left (1+5 e^6\right ) \log (5+x)}{3125}-\frac {4872}{625} \left (4-e^8\right ) \log (5+x)+\frac {1}{5} \left (2 \left (5-e^2\right )\right ) \int \frac {1}{5+x} \, dx\\ &=\frac {256}{x^8}+\frac {32 e^2 \left (1+5 e^6\right )}{5 x^4}+\frac {22048}{9375 x^3}+\frac {32 \left (1811+125 e^2\right )}{9375 x^3}-\frac {128 e^2 \left (1+5 e^6\right )}{75 x^3}-\frac {128 \left (4-e^8\right )}{15 x^3}-\frac {64}{5 x^2}-\frac {48 \left (187+125 e^2\right )}{15625 x^2}+\frac {16 \left (1811+125 e^2\right )}{15625 x^2}+\frac {64 e^2 \left (1+5 e^6\right )}{125 x^2}+\frac {64 \left (4-e^8\right )}{25 x^2}+\frac {128}{25 x}-\frac {192 \left (219-125 e^2\right )}{78125 x}-\frac {96 \left (187+125 e^2\right )}{78125 x}-\frac {128 e^2 \left (1+5 e^6\right )}{625 x}-\frac {128 \left (4-e^8\right )}{125 x}-10 x+2 \left (4-e^8\right ) x+x^2+\frac {25 \left (5-e^2\right )}{(5+x)^2}-\frac {e^2 \left (5-e^2\right ) \left (1+5 e^6\right )}{(5+x)^2}-\frac {5 \left (5-e^2\right ) \left (4-e^8\right )}{(5+x)^2}-\frac {12532 \left (5-e^2\right )}{625 (5+x)}+\frac {2 \left (5-e^2\right ) \left (4-e^8\right )}{5+x}+\frac {128 \log (x)}{125}-\frac {64 \left (1907-625 e^2\right ) \log (x)}{390625}+\frac {192 \left (219-125 e^2\right ) \log (x)}{390625}-\frac {1378 e^2 \left (1+5 e^6\right ) \log (x)}{3125}-\frac {128}{625} \left (4-e^8\right ) \log (x)-\frac {32 \log (x)}{x^4}+2 x \log (x)-\frac {2 \left (5-e^2\right ) x \log (x)}{5 (5+x)}+\log ^2(x)+\frac {64 \left (1907-625 e^2\right ) \log (5+x)}{390625}-\frac {192 \left (219-125 e^2\right ) \log (5+x)}{390625}+\frac {2}{5} \left (5-e^2\right ) \log (5+x)+\frac {2}{125} \left (1811+125 e^2\right ) \log (5+x)-\frac {4872 e^2 \left (1+5 e^6\right ) \log (5+x)}{3125}-\frac {4872}{625} \left (4-e^8\right ) \log (5+x)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.15, size = 169, normalized size = 5.83 \begin {gather*} 2 \left (\frac {128}{x^8}+\frac {16 e^2 \left (1+5 e^6\right )}{5 x^4}-\frac {16 \left (20+e^2\right )}{25 x^3}+\frac {16 \left (-5+e^2\right )}{125 x^2}-\frac {16 \left (-5+e^2\right )}{625 x}-\left (1+e^8\right ) x+\frac {x^2}{2}+\frac {\left (-5+e^2\right )^2}{2 (5+x)^2}+\frac {-18830+3766 e^2-3125 e^8+625 e^{10}}{625 (5+x)}-\left (1+e^8\right ) \log (x)+\frac {\left (-80-16 x-\left (-5+e^2\right ) x^4+5 x^5+x^6\right ) \log (x)}{x^4 (5+x)}+\frac {\log ^2(x)}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-256000 - 153600*x - 30720*x^2 - 2048*x^3 - 4000*x^4 + 7200*x^5 + 5600*x^6 + 1280*x^7 + 96*x^8 + 20
0*x^9 - 2*E^4*x^9 + 290*x^10 + 148*x^11 + 30*x^12 + 2*x^13 + E^2*(-3200*x^4 - 1440*x^5 - 160*x^6 - 50*x^8 - 60
*x^9 - 14*x^10) + E^8*(-16000*x^4 - 9600*x^5 - 1920*x^6 - 128*x^7 - 250*x^8 - 350*x^9 - 170*x^10 - 32*x^11 - 2
*x^12 + E^2*(-10*x^9 - 2*x^10)) + (16000*x^4 + 9600*x^5 + 1920*x^6 + 128*x^7 + 250*x^8 + 350*x^9 + 170*x^10 +
32*x^11 + 2*x^12 + E^2*(10*x^9 + 2*x^10))*Log[x])/(125*x^9 + 75*x^10 + 15*x^11 + x^12),x]

[Out]

2*(128/x^8 + (16*E^2*(1 + 5*E^6))/(5*x^4) - (16*(20 + E^2))/(25*x^3) + (16*(-5 + E^2))/(125*x^2) - (16*(-5 + E
^2))/(625*x) - (1 + E^8)*x + x^2/2 + (-5 + E^2)^2/(2*(5 + x)^2) + (-18830 + 3766*E^2 - 3125*E^8 + 625*E^10)/(6
25*(5 + x)) - (1 + E^8)*Log[x] + ((-80 - 16*x - (-5 + E^2)*x^4 + 5*x^5 + x^6)*Log[x])/(x^4*(5 + x)) + Log[x]^2
/2)

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fricas [B]  time = 0.95, size = 230, normalized size = 7.93 \begin {gather*} \frac {x^{12} + 8 \, x^{11} + 5 \, x^{10} - 110 \, x^{9} + x^{8} e^{4} - 275 \, x^{8} - 32 \, x^{7} - 288 \, x^{6} - 640 \, x^{5} + {\left (x^{10} + 10 \, x^{9} + 25 \, x^{8}\right )} \log \relax (x)^{2} + 256 \, x^{2} + 2 \, {\left (x^{9} + 5 \, x^{8}\right )} e^{10} - 2 \, {\left (x^{11} + 10 \, x^{10} + 30 \, x^{9} + 25 \, x^{8} - 16 \, x^{6} - 160 \, x^{5} - 400 \, x^{4}\right )} e^{8} + 2 \, {\left (6 \, x^{9} + 25 \, x^{8} + 16 \, x^{5} + 80 \, x^{4}\right )} e^{2} + 2 \, {\left (x^{11} + 9 \, x^{10} + 20 \, x^{9} - 16 \, x^{6} - 160 \, x^{5} - 400 \, x^{4} - {\left (x^{10} + 10 \, x^{9} + 25 \, x^{8}\right )} e^{8} - {\left (x^{9} + 5 \, x^{8}\right )} e^{2}\right )} \log \relax (x) + 2560 \, x + 6400}{x^{10} + 10 \, x^{9} + 25 \, x^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8+128*x^7+1920*x^6+9600*x^5+16000*x^4
)*log(x)+((-2*x^10-10*x^9)*exp(2)-2*x^12-32*x^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)
*exp(4)^2-2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)*exp(2)+2*x^13+30*x^12+148*x^11+290
*x^10+200*x^9+96*x^8+1280*x^7+5600*x^6+7200*x^5-4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*
x^10+125*x^9),x, algorithm="fricas")

[Out]

(x^12 + 8*x^11 + 5*x^10 - 110*x^9 + x^8*e^4 - 275*x^8 - 32*x^7 - 288*x^6 - 640*x^5 + (x^10 + 10*x^9 + 25*x^8)*
log(x)^2 + 256*x^2 + 2*(x^9 + 5*x^8)*e^10 - 2*(x^11 + 10*x^10 + 30*x^9 + 25*x^8 - 16*x^6 - 160*x^5 - 400*x^4)*
e^8 + 2*(6*x^9 + 25*x^8 + 16*x^5 + 80*x^4)*e^2 + 2*(x^11 + 9*x^10 + 20*x^9 - 16*x^6 - 160*x^5 - 400*x^4 - (x^1
0 + 10*x^9 + 25*x^8)*e^8 - (x^9 + 5*x^8)*e^2)*log(x) + 2560*x + 6400)/(x^10 + 10*x^9 + 25*x^8)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (x^{13} + 15 \, x^{12} + 74 \, x^{11} + 145 \, x^{10} - x^{9} e^{4} + 100 \, x^{9} + 48 \, x^{8} + 640 \, x^{7} + 2800 \, x^{6} + 3600 \, x^{5} - 2000 \, x^{4} - 1024 \, x^{3} - 15360 \, x^{2} - {\left (x^{12} + 16 \, x^{11} + 85 \, x^{10} + 175 \, x^{9} + 125 \, x^{8} + 64 \, x^{7} + 960 \, x^{6} + 4800 \, x^{5} + 8000 \, x^{4} + {\left (x^{10} + 5 \, x^{9}\right )} e^{2}\right )} e^{8} - {\left (7 \, x^{10} + 30 \, x^{9} + 25 \, x^{8} + 80 \, x^{6} + 720 \, x^{5} + 1600 \, x^{4}\right )} e^{2} + {\left (x^{12} + 16 \, x^{11} + 85 \, x^{10} + 175 \, x^{9} + 125 \, x^{8} + 64 \, x^{7} + 960 \, x^{6} + 4800 \, x^{5} + 8000 \, x^{4} + {\left (x^{10} + 5 \, x^{9}\right )} e^{2}\right )} \log \relax (x) - 76800 \, x - 128000\right )}}{x^{12} + 15 \, x^{11} + 75 \, x^{10} + 125 \, x^{9}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8+128*x^7+1920*x^6+9600*x^5+16000*x^4
)*log(x)+((-2*x^10-10*x^9)*exp(2)-2*x^12-32*x^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)
*exp(4)^2-2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)*exp(2)+2*x^13+30*x^12+148*x^11+290
*x^10+200*x^9+96*x^8+1280*x^7+5600*x^6+7200*x^5-4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*
x^10+125*x^9),x, algorithm="giac")

[Out]

integrate(2*(x^13 + 15*x^12 + 74*x^11 + 145*x^10 - x^9*e^4 + 100*x^9 + 48*x^8 + 640*x^7 + 2800*x^6 + 3600*x^5
- 2000*x^4 - 1024*x^3 - 15360*x^2 - (x^12 + 16*x^11 + 85*x^10 + 175*x^9 + 125*x^8 + 64*x^7 + 960*x^6 + 4800*x^
5 + 8000*x^4 + (x^10 + 5*x^9)*e^2)*e^8 - (7*x^10 + 30*x^9 + 25*x^8 + 80*x^6 + 720*x^5 + 1600*x^4)*e^2 + (x^12
+ 16*x^11 + 85*x^10 + 175*x^9 + 125*x^8 + 64*x^7 + 960*x^6 + 4800*x^5 + 8000*x^4 + (x^10 + 5*x^9)*e^2)*log(x)
- 76800*x - 128000)/(x^12 + 15*x^11 + 75*x^10 + 125*x^9), x)

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maple [B]  time = 0.15, size = 176, normalized size = 6.07

method	result	size
default	\(-2 x -\frac {32 \,{\mathrm e}^{2}}{25 x^{3}}-2 x \,{\mathrm e}^{8}-\frac {32 \,{\mathrm e}^{2}}{625 x}+\ln \relax (x )^{2}+x^{2}-\frac {2 \,{\mathrm e}^{2} \ln \relax (x )}{5}+\frac {32 \,{\mathrm e}^{2}}{125 x^{2}}+2 x \ln \relax (x )-\frac {32}{25 x^{2}}+\frac {32}{125 x}+\frac {2 \,{\mathrm e}^{2} \ln \relax (x ) x}{5 \left (5+x \right )}-\frac {7532}{125 \left (5+x \right )}+\frac {256}{x^{8}}-\frac {128}{5 x^{3}}-\frac {32 \ln \relax (x )}{x^{4}}-2 \ln \relax (x ) {\mathrm e}^{8}+\frac {32 \,{\mathrm e}^{2}}{5 x^{4}}+\frac {32 \,{\mathrm e}^{8}}{x^{4}}+\frac {{\mathrm e}^{4}}{\left (5+x \right )^{2}}-\frac {10 \,{\mathrm e}^{2}}{\left (5+x \right )^{2}}+\frac {7532 \,{\mathrm e}^{2}}{625 \left (5+x \right )}-\frac {10 \,{\mathrm e}^{8}}{5+x}+\frac {2 \,{\mathrm e}^{10}}{5+x}+\frac {25}{\left (5+x \right )^{2}}-\frac {2 \ln \relax (x ) x}{5+x}\)	\(176\)
risch	\(\ln \relax (x )^{2}-\frac {2 \left (-x^{6}+x^{4} {\mathrm e}^{2}-5 x^{5}-5 x^{4}+16 x +80\right ) \ln \relax (x )}{\left (5+x \right ) x^{4}}+\frac {6400+2560 x -2 x^{10} \ln \relax (x )+32 \,{\mathrm e}^{2} x^{5}-20 x^{9} \ln \relax (x )+8 x^{11}+x^{12}-32 x^{7}-275 x^{8}+5 x^{10}-110 x^{9}-288 x^{6}-640 x^{5}+256 x^{2}+50 x^{8} {\mathrm e}^{2}+x^{8} {\mathrm e}^{4}-50 x^{8} \ln \relax (x )+160 x^{4} {\mathrm e}^{2}+12 \,{\mathrm e}^{2} x^{9}+320 x^{5} {\mathrm e}^{8}-2 \,{\mathrm e}^{8} \ln \relax (x ) x^{10}-20 \,{\mathrm e}^{8} \ln \relax (x ) x^{9}-50 \,{\mathrm e}^{8} \ln \relax (x ) x^{8}-60 \,{\mathrm e}^{8} x^{9}-50 \,{\mathrm e}^{8} x^{8}+32 \,{\mathrm e}^{8} x^{6}+10 \,{\mathrm e}^{10} x^{8}+800 x^{4} {\mathrm e}^{8}-2 \,{\mathrm e}^{8} x^{11}+2 \,{\mathrm e}^{10} x^{9}-20 \,{\mathrm e}^{8} x^{10}}{\left (5+x \right )^{2} x^{8}}\)	\(246\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8+128*x^7+1920*x^6+9600*x^5+16000*x^4)*ln(x
)+((-2*x^10-10*x^9)*exp(2)-2*x^12-32*x^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)*exp(4)
^2-2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)*exp(2)+2*x^13+30*x^12+148*x^11+290*x^10+2
00*x^9+96*x^8+1280*x^7+5600*x^6+7200*x^5-4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*x^10+12
5*x^9),x,method=_RETURNVERBOSE)

[Out]

-2*x-32/25*exp(2)/x^3-2*x*exp(8)-32/625*exp(2)/x+ln(x)^2+x^2-2/5*exp(2)*ln(x)+32/125*exp(2)/x^2+2*x*ln(x)-32/2
5/x^2+32/125/x+2/5*exp(2)*ln(x)*x/(5+x)-7532/125/(5+x)+256/x^8-128/5/x^3-32/x^4*ln(x)-2*ln(x)*exp(8)+32/5/x^4*
exp(2)+32/x^4*exp(8)+1/(5+x)^2*exp(4)-10/(5+x)^2*exp(2)+7532/625/(5+x)*exp(2)-10/(5+x)*exp(8)+2/(5+x)*exp(10)+
25/(5+x)^2-2*ln(x)*x/(5+x)

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maxima [B]  time = 0.44, size = 1137, normalized size = 39.21 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^10+10*x^9)*exp(2)+2*x^12+32*x^11+170*x^10+350*x^9+250*x^8+128*x^7+1920*x^6+9600*x^5+16000*x^4
)*log(x)+((-2*x^10-10*x^9)*exp(2)-2*x^12-32*x^11-170*x^10-350*x^9-250*x^8-128*x^7-1920*x^6-9600*x^5-16000*x^4)
*exp(4)^2-2*x^9*exp(2)^2+(-14*x^10-60*x^9-50*x^8-160*x^6-1440*x^5-3200*x^4)*exp(2)+2*x^13+30*x^12+148*x^11+290
*x^10+200*x^9+96*x^8+1280*x^7+5600*x^6+7200*x^5-4000*x^4-2048*x^3-30720*x^2-153600*x-256000)/(x^12+15*x^11+75*
x^10+125*x^9),x, algorithm="maxima")

[Out]

x^2 - (2*x - 25*(6*x + 25)/(x^2 + 10*x + 25) - 30*log(x + 5))*e^8 - 32/125*(5*(12*x^5 + 90*x^4 + 100*x^3 - 125
*x^2 + 250*x - 625)/(x^6 + 10*x^5 + 25*x^4) - 12*log(x + 5) + 12*log(x))*e^8 + 64/125*(5*(12*x^4 + 90*x^3 + 10
0*x^2 - 125*x + 250)/(x^5 + 10*x^4 + 25*x^3) - 12*log(x + 5) + 12*log(x))*e^8 - 192/625*(5*(12*x^3 + 90*x^2 +
100*x - 125)/(x^4 + 10*x^3 + 25*x^2) - 12*log(x + 5) + 12*log(x))*e^8 + 64/625*(5*(6*x^2 + 45*x + 50)/(x^3 + 1
0*x^2 + 25*x) - 6*log(x + 5) + 6*log(x))*e^8 - 16*(5*(4*x + 15)/(x^2 + 10*x + 25) + 2*log(x + 5))*e^8 - (5*(2*
x + 15)/(x^2 + 10*x + 25) - 2*log(x + 5) + 2*log(x))*e^8 - 32/625*(5*(12*x^5 + 90*x^4 + 100*x^3 - 125*x^2 + 25
0*x - 625)/(x^6 + 10*x^5 + 25*x^4) - 12*log(x + 5) + 12*log(x))*e^2 + 48/625*(5*(12*x^4 + 90*x^3 + 100*x^2 - 1
25*x + 250)/(x^5 + 10*x^4 + 25*x^3) - 12*log(x + 5) + 12*log(x))*e^2 - 16/625*(5*(12*x^3 + 90*x^2 + 100*x - 12
5)/(x^4 + 10*x^3 + 25*x^2) - 12*log(x + 5) + 12*log(x))*e^2 - 1/5*(5*(2*x + 15)/(x^2 + 10*x + 25) - 2*log(x +
5) + 2*log(x))*e^2 - 2/5*(e^2 - 5)*log(x + 5) + (2*x + 5)*e^10/(x^2 + 10*x + 25) + 85*(2*x + 5)*e^8/(x^2 + 10*
x + 25) + 7*(2*x + 5)*e^2/(x^2 + 10*x + 25) - 256/109375*(504*x^9 + 3780*x^8 + 4200*x^7 - 5250*x^6 + 10500*x^5
- 26250*x^4 + 75000*x^3 - 234375*x^2 + 781250*x - 2734375)/(x^10 + 10*x^9 + 25*x^8) + 3072/546875*(504*x^8 +
3780*x^7 + 4200*x^6 - 5250*x^5 + 10500*x^4 - 26250*x^3 + 75000*x^2 - 234375*x + 781250)/(x^9 + 10*x^8 + 25*x^7
) - 1024/78125*(168*x^7 + 1260*x^6 + 1400*x^5 - 1750*x^4 + 3500*x^3 - 8750*x^2 + 25000*x - 78125)/(x^8 + 10*x^
7 + 25*x^6) + 512/78125*(84*x^6 + 630*x^5 + 700*x^4 - 875*x^3 + 1750*x^2 - 4375*x + 12500)/(x^7 + 10*x^6 + 25*
x^5) - 8/25*(12*x^5 + 90*x^4 + 100*x^3 - 125*x^2 + 250*x - 625)/(x^6 + 10*x^5 + 25*x^4) - 1/5*(10*x^6 + 50*x^5
- 5*(x^5 + 5*x^4)*log(x)^2 - 2*(5*x^6 + x^5*(e^2 + 20) - 80*x - 400)*log(x) + 40*x + 200)/(x^5 + 5*x^4) - 48/
25*(12*x^4 + 90*x^3 + 100*x^2 - 125*x + 250)/(x^5 + 10*x^4 + 25*x^3) + 112/25*(12*x^3 + 90*x^2 + 100*x - 125)/
(x^4 + 10*x^3 + 25*x^2) - 128/25*(6*x^2 + 45*x + 50)/(x^3 + 10*x^2 + 25*x) + 125*(8*x + 35)/(x^2 + 10*x + 25)
- 375*(6*x + 25)/(x^2 + 10*x + 25) + 370*(4*x + 15)/(x^2 + 10*x + 25) + 48/25*(2*x + 15)/(x^2 + 10*x + 25) - 1
45*(2*x + 5)/(x^2 + 10*x + 25) + 5*e^10/(x^2 + 10*x + 25) + 175*e^8/(x^2 + 10*x + 25) + e^4/(x^2 + 10*x + 25)
+ 30*e^2/(x^2 + 10*x + 25) - 100/(x^2 + 10*x + 25) - 2*log(x + 5)

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mupad [B]  time = 6.52, size = 178, normalized size = 6.14 \begin {gather*} {\ln \relax (x)}^2-\ln \relax (x)\,\left (2\,{\mathrm {e}}^8-\frac {5}{3}\right )+\frac {\left (36\,{\mathrm {e}}^2-30\,{\mathrm {e}}^8+6\,{\mathrm {e}}^{10}-180\right )\,x^9+\left (150\,{\mathrm {e}}^2+3\,{\mathrm {e}}^4-150\,{\mathrm {e}}^8+30\,{\mathrm {e}}^{10}-825\right )\,x^8-96\,x^7+\left (96\,{\mathrm {e}}^8-864\right )\,x^6+\left (96\,{\mathrm {e}}^2+960\,{\mathrm {e}}^8-1920\right )\,x^5+\left (480\,{\mathrm {e}}^2+2400\,{\mathrm {e}}^8\right )\,x^4+768\,x^2+7680\,x+19200}{3\,x^{10}+30\,x^9+75\,x^8}+x^2-x\,\left (2\,{\mathrm {e}}^8+2\right )-\frac {\ln \relax (x)\,\left (-2\,x^6-\frac {19\,x^5}{3}+\left (2\,{\mathrm {e}}^2+\frac {25}{3}\right )\,x^4+32\,x+160\right )}{x^5+5\,x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(exp(2)*(10*x^9 + 2*x^10) + 16000*x^4 + 9600*x^5 + 1920*x^6 + 128*x^7 + 250*x^8 + 350*x^9 + 170*x^
10 + 32*x^11 + 2*x^12) - 153600*x - exp(2)*(3200*x^4 + 1440*x^5 + 160*x^6 + 50*x^8 + 60*x^9 + 14*x^10) - 2*x^9
*exp(4) - exp(8)*(exp(2)*(10*x^9 + 2*x^10) + 16000*x^4 + 9600*x^5 + 1920*x^6 + 128*x^7 + 250*x^8 + 350*x^9 + 1
70*x^10 + 32*x^11 + 2*x^12) - 30720*x^2 - 2048*x^3 - 4000*x^4 + 7200*x^5 + 5600*x^6 + 1280*x^7 + 96*x^8 + 200*
x^9 + 290*x^10 + 148*x^11 + 30*x^12 + 2*x^13 - 256000)/(125*x^9 + 75*x^10 + 15*x^11 + x^12),x)

[Out]

log(x)^2 - log(x)*(2*exp(8) - 5/3) + (7680*x + x^4*(480*exp(2) + 2400*exp(8)) + x^5*(96*exp(2) + 960*exp(8) -
1920) + x^6*(96*exp(8) - 864) + x^8*(150*exp(2) + 3*exp(4) - 150*exp(8) + 30*exp(10) - 825) + 768*x^2 - 96*x^7
+ x^9*(36*exp(2) - 30*exp(8) + 6*exp(10) - 180) + 19200)/(75*x^8 + 30*x^9 + 3*x^10) + x^2 - x*(2*exp(8) + 2)
- (log(x)*(32*x + x^4*(2*exp(2) + 25/3) - (19*x^5)/3 - 2*x^6 + 160))/(5*x^4 + x^5)

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sympy [B]  time = 45.62, size = 180, normalized size = 6.21 \begin {gather*} x^{2} + x \left (- 2 e^{8} - 2\right ) + \log {\relax (x )}^{2} - 2 \left (1 + e^{8}\right ) \log {\relax (x )} + \frac {x^{9} \left (- 10 e^{8} - 60 + 12 e^{2} + 2 e^{10}\right ) + x^{8} \left (- 50 e^{8} - 275 + e^{4} + 50 e^{2} + 10 e^{10}\right ) - 32 x^{7} + x^{6} \left (-288 + 32 e^{8}\right ) + x^{5} \left (-640 + 32 e^{2} + 320 e^{8}\right ) + x^{4} \left (160 e^{2} + 800 e^{8}\right ) + 256 x^{2} + 2560 x + 6400}{x^{10} + 10 x^{9} + 25 x^{8}} + \frac {\left (2 x^{6} + 10 x^{5} - 2 x^{4} e^{2} + 10 x^{4} - 32 x - 160\right ) \log {\relax (x )}}{x^{5} + 5 x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**10+10*x**9)*exp(2)+2*x**12+32*x**11+170*x**10+350*x**9+250*x**8+128*x**7+1920*x**6+9600*x**5
+16000*x**4)*ln(x)+((-2*x**10-10*x**9)*exp(2)-2*x**12-32*x**11-170*x**10-350*x**9-250*x**8-128*x**7-1920*x**6-
9600*x**5-16000*x**4)*exp(4)**2-2*x**9*exp(2)**2+(-14*x**10-60*x**9-50*x**8-160*x**6-1440*x**5-3200*x**4)*exp(
2)+2*x**13+30*x**12+148*x**11+290*x**10+200*x**9+96*x**8+1280*x**7+5600*x**6+7200*x**5-4000*x**4-2048*x**3-307
20*x**2-153600*x-256000)/(x**12+15*x**11+75*x**10+125*x**9),x)

[Out]

x**2 + x*(-2*exp(8) - 2) + log(x)**2 - 2*(1 + exp(8))*log(x) + (x**9*(-10*exp(8) - 60 + 12*exp(2) + 2*exp(10))
+ x**8*(-50*exp(8) - 275 + exp(4) + 50*exp(2) + 10*exp(10)) - 32*x**7 + x**6*(-288 + 32*exp(8)) + x**5*(-640
+ 32*exp(2) + 320*exp(8)) + x**4*(160*exp(2) + 800*exp(8)) + 256*x**2 + 2560*x + 6400)/(x**10 + 10*x**9 + 25*x
**8) + (2*x**6 + 10*x**5 - 2*x**4*exp(2) + 10*x**4 - 32*x - 160)*log(x)/(x**5 + 5*x**4)

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