Integrand size = 279, antiderivative size = 30 \[ \int \frac {\left (-5632-12288 x-6144 x^2\right ) \log ^2(4)+e^{2 x} \left (-384 x^2-256 x^3\right ) \log ^2(4)+e^x \left (3072 x+4608 x^2+1024 x^3\right ) \log ^2(4)}{64000+211200 x+462720 x^2+668864 x^3+724224 x^4+581376 x^5+344064 x^6+144384 x^7+36864 x^8+4096 x^9+e^{6 x} x^9+e^x \left (-57600 x^2-165120 x^3-292416 x^4-336768 x^5-265728 x^6-144384 x^7-46080 x^8-6144 x^9\right )+e^{3 x} \left (-2880 x^5-6816 x^6-9024 x^7-5760 x^8-1280 x^9\right )+e^{5 x} \left (-36 x^8-24 x^9\right )+e^{4 x} \left (120 x^6+564 x^7+720 x^8+240 x^9\right )+e^{2 x} \left (4800 x^3+27840 x^4+59376 x^5+70272 x^6+54144 x^7+23040 x^8+3840 x^9\right )} \, dx=\frac {\log ^2(4)}{\left (5+x+\frac {1}{2} x \left (3+2 x-\frac {e^x x}{2}\right )^2\right )^2} \]
Time = 0.22 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.13 \[ \int \frac {\left (-5632-12288 x-6144 x^2\right ) \log ^2(4)+e^{2 x} \left (-384 x^2-256 x^3\right ) \log ^2(4)+e^x \left (3072 x+4608 x^2+1024 x^3\right ) \log ^2(4)}{64000+211200 x+462720 x^2+668864 x^3+724224 x^4+581376 x^5+344064 x^6+144384 x^7+36864 x^8+4096 x^9+e^{6 x} x^9+e^x \left (-57600 x^2-165120 x^3-292416 x^4-336768 x^5-265728 x^6-144384 x^7-46080 x^8-6144 x^9\right )+e^{3 x} \left (-2880 x^5-6816 x^6-9024 x^7-5760 x^8-1280 x^9\right )+e^{5 x} \left (-36 x^8-24 x^9\right )+e^{4 x} \left (120 x^6+564 x^7+720 x^8+240 x^9\right )+e^{2 x} \left (4800 x^3+27840 x^4+59376 x^5+70272 x^6+54144 x^7+23040 x^8+3840 x^9\right )} \, dx=\frac {64 \log ^2(4)}{\left (40+44 x-12 \left (-4+e^x\right ) x^2+\left (-4+e^x\right )^2 x^3\right )^2} \]
Integrate[((-5632 - 12288*x - 6144*x^2)*Log[4]^2 + E^(2*x)*(-384*x^2 - 256 *x^3)*Log[4]^2 + E^x*(3072*x + 4608*x^2 + 1024*x^3)*Log[4]^2)/(64000 + 211 200*x + 462720*x^2 + 668864*x^3 + 724224*x^4 + 581376*x^5 + 344064*x^6 + 1 44384*x^7 + 36864*x^8 + 4096*x^9 + E^(6*x)*x^9 + E^x*(-57600*x^2 - 165120* x^3 - 292416*x^4 - 336768*x^5 - 265728*x^6 - 144384*x^7 - 46080*x^8 - 6144 *x^9) + E^(3*x)*(-2880*x^5 - 6816*x^6 - 9024*x^7 - 5760*x^8 - 1280*x^9) + E^(5*x)*(-36*x^8 - 24*x^9) + E^(4*x)*(120*x^6 + 564*x^7 + 720*x^8 + 240*x^ 9) + E^(2*x)*(4800*x^3 + 27840*x^4 + 59376*x^5 + 70272*x^6 + 54144*x^7 + 2 3040*x^8 + 3840*x^9)),x]
Time = 1.46 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.27, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {7239, 27, 25, 7237}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (-6144 x^2-12288 x-5632\right ) \log ^2(4)+e^{2 x} \left (-256 x^3-384 x^2\right ) \log ^2(4)+e^x \left (1024 x^3+4608 x^2+3072 x\right ) \log ^2(4)}{e^{6 x} x^9+4096 x^9+36864 x^8+144384 x^7+344064 x^6+581376 x^5+724224 x^4+668864 x^3+462720 x^2+e^{5 x} \left (-24 x^9-36 x^8\right )+e^{4 x} \left (240 x^9+720 x^8+564 x^7+120 x^6\right )+e^{3 x} \left (-1280 x^9-5760 x^8-9024 x^7-6816 x^6-2880 x^5\right )+e^{2 x} \left (3840 x^9+23040 x^8+54144 x^7+70272 x^6+59376 x^5+27840 x^4+4800 x^3\right )+e^x \left (-6144 x^9-46080 x^8-144384 x^7-265728 x^6-336768 x^5-292416 x^4-165120 x^3-57600 x^2\right )+211200 x+64000} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {128 \left (-2 e^x \left (e^x-4\right ) x^3-3 \left (-12 e^x+e^{2 x}+16\right ) x^2+24 \left (e^x-4\right ) x-44\right ) \log ^2(4)}{\left (\left (e^x-4\right )^2 x^3-12 \left (e^x-4\right ) x^2+44 x+40\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 128 \log ^2(4) \int -\frac {-2 e^x \left (4-e^x\right ) x^3+3 \left (16-12 e^x+e^{2 x}\right ) x^2+24 \left (4-e^x\right ) x+44}{\left (\left (4-e^x\right )^2 x^3+12 \left (4-e^x\right ) x^2+44 x+40\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -128 \log ^2(4) \int \frac {-2 e^x \left (4-e^x\right ) x^3+3 \left (16-12 e^x+e^{2 x}\right ) x^2+24 \left (4-e^x\right ) x+44}{\left (\left (4-e^x\right )^2 x^3+12 \left (4-e^x\right ) x^2+44 x+40\right )^3}dx\) |
| \(\Big \downarrow \) 7237 |
| \(\displaystyle \frac {64 \log ^2(4)}{\left (\left (4-e^x\right )^2 x^3+12 \left (4-e^x\right ) x^2+44 x+40\right )^2}\) |
Int[((-5632 - 12288*x - 6144*x^2)*Log[4]^2 + E^(2*x)*(-384*x^2 - 256*x^3)* Log[4]^2 + E^x*(3072*x + 4608*x^2 + 1024*x^3)*Log[4]^2)/(64000 + 211200*x + 462720*x^2 + 668864*x^3 + 724224*x^4 + 581376*x^5 + 344064*x^6 + 144384* x^7 + 36864*x^8 + 4096*x^9 + E^(6*x)*x^9 + E^x*(-57600*x^2 - 165120*x^3 - 292416*x^4 - 336768*x^5 - 265728*x^6 - 144384*x^7 - 46080*x^8 - 6144*x^9) + E^(3*x)*(-2880*x^5 - 6816*x^6 - 9024*x^7 - 5760*x^8 - 1280*x^9) + E^(5*x )*(-36*x^8 - 24*x^9) + E^(4*x)*(120*x^6 + 564*x^7 + 720*x^8 + 240*x^9) + E ^(2*x)*(4800*x^3 + 27840*x^4 + 59376*x^5 + 70272*x^6 + 54144*x^7 + 23040*x ^8 + 3840*x^9)),x]
3.2.14.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Si mp[q*(y^(m + 1)/(m + 1)), x] /; !FalseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 0.98 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.53
| method | result | size |
| risch | \(\frac {256 \ln \left (2\right )^{2}}{\left ({\mathrm e}^{2 x} x^{3}-8 \,{\mathrm e}^{x} x^{3}-12 \,{\mathrm e}^{x} x^{2}+16 x^{3}+48 x^{2}+44 x +40\right )^{2}}\) | \(46\) |
| parallelrisch | \(\frac {256 \ln \left (2\right )^{2}}{{\mathrm e}^{4 x} x^{6}-16 \,{\mathrm e}^{3 x} x^{6}+96 \,{\mathrm e}^{2 x} x^{6}-24 \,{\mathrm e}^{3 x} x^{5}-256 x^{6} {\mathrm e}^{x}+288 x^{5} {\mathrm e}^{2 x}+256 x^{6}-1152 x^{5} {\mathrm e}^{x}+232 \,{\mathrm e}^{2 x} x^{4}+1536 x^{5}-1856 \,{\mathrm e}^{x} x^{4}+80 \,{\mathrm e}^{2 x} x^{3}+3712 x^{4}-1696 \,{\mathrm e}^{x} x^{3}+5504 x^{3}-960 \,{\mathrm e}^{x} x^{2}+5776 x^{2}+3520 x +1600}\) | \(136\) |
int((4*(-256*x^3-384*x^2)*ln(2)^2*exp(x)^2+4*(1024*x^3+4608*x^2+3072*x)*ln (2)^2*exp(x)+4*(-6144*x^2-12288*x-5632)*ln(2)^2)/(x^9*exp(x)^6+(-24*x^9-36 *x^8)*exp(x)^5+(240*x^9+720*x^8+564*x^7+120*x^6)*exp(x)^4+(-1280*x^9-5760* x^8-9024*x^7-6816*x^6-2880*x^5)*exp(x)^3+(3840*x^9+23040*x^8+54144*x^7+702 72*x^6+59376*x^5+27840*x^4+4800*x^3)*exp(x)^2+(-6144*x^9-46080*x^8-144384* x^7-265728*x^6-336768*x^5-292416*x^4-165120*x^3-57600*x^2)*exp(x)+4096*x^9 +36864*x^8+144384*x^7+344064*x^6+581376*x^5+724224*x^4+668864*x^3+462720*x ^2+211200*x+64000),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 120 vs. \(2 (26) = 52\).
Time = 0.26 (sec) , antiderivative size = 120, normalized size of antiderivative = 4.00 \[ \int \frac {\left (-5632-12288 x-6144 x^2\right ) \log ^2(4)+e^{2 x} \left (-384 x^2-256 x^3\right ) \log ^2(4)+e^x \left (3072 x+4608 x^2+1024 x^3\right ) \log ^2(4)}{64000+211200 x+462720 x^2+668864 x^3+724224 x^4+581376 x^5+344064 x^6+144384 x^7+36864 x^8+4096 x^9+e^{6 x} x^9+e^x \left (-57600 x^2-165120 x^3-292416 x^4-336768 x^5-265728 x^6-144384 x^7-46080 x^8-6144 x^9\right )+e^{3 x} \left (-2880 x^5-6816 x^6-9024 x^7-5760 x^8-1280 x^9\right )+e^{5 x} \left (-36 x^8-24 x^9\right )+e^{4 x} \left (120 x^6+564 x^7+720 x^8+240 x^9\right )+e^{2 x} \left (4800 x^3+27840 x^4+59376 x^5+70272 x^6+54144 x^7+23040 x^8+3840 x^9\right )} \, dx=\frac {256 \, \log \left (2\right )^{2}}{x^{6} e^{\left (4 \, x\right )} + 256 \, x^{6} + 1536 \, x^{5} + 3712 \, x^{4} + 5504 \, x^{3} + 5776 \, x^{2} - 8 \, {\left (2 \, x^{6} + 3 \, x^{5}\right )} e^{\left (3 \, x\right )} + 8 \, {\left (12 \, x^{6} + 36 \, x^{5} + 29 \, x^{4} + 10 \, x^{3}\right )} e^{\left (2 \, x\right )} - 32 \, {\left (8 \, x^{6} + 36 \, x^{5} + 58 \, x^{4} + 53 \, x^{3} + 30 \, x^{2}\right )} e^{x} + 3520 \, x + 1600} \]
integrate((4*(-256*x^3-384*x^2)*log(2)^2*exp(x)^2+4*(1024*x^3+4608*x^2+307 2*x)*log(2)^2*exp(x)+4*(-6144*x^2-12288*x-5632)*log(2)^2)/(x^9*exp(x)^6+(- 24*x^9-36*x^8)*exp(x)^5+(240*x^9+720*x^8+564*x^7+120*x^6)*exp(x)^4+(-1280* x^9-5760*x^8-9024*x^7-6816*x^6-2880*x^5)*exp(x)^3+(3840*x^9+23040*x^8+5414 4*x^7+70272*x^6+59376*x^5+27840*x^4+4800*x^3)*exp(x)^2+(-6144*x^9-46080*x^ 8-144384*x^7-265728*x^6-336768*x^5-292416*x^4-165120*x^3-57600*x^2)*exp(x) +4096*x^9+36864*x^8+144384*x^7+344064*x^6+581376*x^5+724224*x^4+668864*x^3 +462720*x^2+211200*x+64000),x, algorithm=\
256*log(2)^2/(x^6*e^(4*x) + 256*x^6 + 1536*x^5 + 3712*x^4 + 5504*x^3 + 577 6*x^2 - 8*(2*x^6 + 3*x^5)*e^(3*x) + 8*(12*x^6 + 36*x^5 + 29*x^4 + 10*x^3)* e^(2*x) - 32*(8*x^6 + 36*x^5 + 58*x^4 + 53*x^3 + 30*x^2)*e^x + 3520*x + 16 00)
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (27) = 54\).
Time = 0.30 (sec) , antiderivative size = 117, normalized size of antiderivative = 3.90 \[ \int \frac {\left (-5632-12288 x-6144 x^2\right ) \log ^2(4)+e^{2 x} \left (-384 x^2-256 x^3\right ) \log ^2(4)+e^x \left (3072 x+4608 x^2+1024 x^3\right ) \log ^2(4)}{64000+211200 x+462720 x^2+668864 x^3+724224 x^4+581376 x^5+344064 x^6+144384 x^7+36864 x^8+4096 x^9+e^{6 x} x^9+e^x \left (-57600 x^2-165120 x^3-292416 x^4-336768 x^5-265728 x^6-144384 x^7-46080 x^8-6144 x^9\right )+e^{3 x} \left (-2880 x^5-6816 x^6-9024 x^7-5760 x^8-1280 x^9\right )+e^{5 x} \left (-36 x^8-24 x^9\right )+e^{4 x} \left (120 x^6+564 x^7+720 x^8+240 x^9\right )+e^{2 x} \left (4800 x^3+27840 x^4+59376 x^5+70272 x^6+54144 x^7+23040 x^8+3840 x^9\right )} \, dx=\frac {256 \log {\left (2 \right )}^{2}}{x^{6} e^{4 x} + 256 x^{6} + 1536 x^{5} + 3712 x^{4} + 5504 x^{3} + 5776 x^{2} + 3520 x + \left (- 16 x^{6} - 24 x^{5}\right ) e^{3 x} + \left (96 x^{6} + 288 x^{5} + 232 x^{4} + 80 x^{3}\right ) e^{2 x} + \left (- 256 x^{6} - 1152 x^{5} - 1856 x^{4} - 1696 x^{3} - 960 x^{2}\right ) e^{x} + 1600} \]
integrate((4*(-256*x**3-384*x**2)*ln(2)**2*exp(x)**2+4*(1024*x**3+4608*x** 2+3072*x)*ln(2)**2*exp(x)+4*(-6144*x**2-12288*x-5632)*ln(2)**2)/(x**9*exp( x)**6+(-24*x**9-36*x**8)*exp(x)**5+(240*x**9+720*x**8+564*x**7+120*x**6)*e xp(x)**4+(-1280*x**9-5760*x**8-9024*x**7-6816*x**6-2880*x**5)*exp(x)**3+(3 840*x**9+23040*x**8+54144*x**7+70272*x**6+59376*x**5+27840*x**4+4800*x**3) *exp(x)**2+(-6144*x**9-46080*x**8-144384*x**7-265728*x**6-336768*x**5-2924 16*x**4-165120*x**3-57600*x**2)*exp(x)+4096*x**9+36864*x**8+144384*x**7+34 4064*x**6+581376*x**5+724224*x**4+668864*x**3+462720*x**2+211200*x+64000), x)
256*log(2)**2/(x**6*exp(4*x) + 256*x**6 + 1536*x**5 + 3712*x**4 + 5504*x** 3 + 5776*x**2 + 3520*x + (-16*x**6 - 24*x**5)*exp(3*x) + (96*x**6 + 288*x* *5 + 232*x**4 + 80*x**3)*exp(2*x) + (-256*x**6 - 1152*x**5 - 1856*x**4 - 1 696*x**3 - 960*x**2)*exp(x) + 1600)
Leaf count of result is larger than twice the leaf count of optimal. 120 vs. \(2 (26) = 52\).
Time = 0.61 (sec) , antiderivative size = 120, normalized size of antiderivative = 4.00 \[ \int \frac {\left (-5632-12288 x-6144 x^2\right ) \log ^2(4)+e^{2 x} \left (-384 x^2-256 x^3\right ) \log ^2(4)+e^x \left (3072 x+4608 x^2+1024 x^3\right ) \log ^2(4)}{64000+211200 x+462720 x^2+668864 x^3+724224 x^4+581376 x^5+344064 x^6+144384 x^7+36864 x^8+4096 x^9+e^{6 x} x^9+e^x \left (-57600 x^2-165120 x^3-292416 x^4-336768 x^5-265728 x^6-144384 x^7-46080 x^8-6144 x^9\right )+e^{3 x} \left (-2880 x^5-6816 x^6-9024 x^7-5760 x^8-1280 x^9\right )+e^{5 x} \left (-36 x^8-24 x^9\right )+e^{4 x} \left (120 x^6+564 x^7+720 x^8+240 x^9\right )+e^{2 x} \left (4800 x^3+27840 x^4+59376 x^5+70272 x^6+54144 x^7+23040 x^8+3840 x^9\right )} \, dx=\frac {256 \, \log \left (2\right )^{2}}{x^{6} e^{\left (4 \, x\right )} + 256 \, x^{6} + 1536 \, x^{5} + 3712 \, x^{4} + 5504 \, x^{3} + 5776 \, x^{2} - 8 \, {\left (2 \, x^{6} + 3 \, x^{5}\right )} e^{\left (3 \, x\right )} + 8 \, {\left (12 \, x^{6} + 36 \, x^{5} + 29 \, x^{4} + 10 \, x^{3}\right )} e^{\left (2 \, x\right )} - 32 \, {\left (8 \, x^{6} + 36 \, x^{5} + 58 \, x^{4} + 53 \, x^{3} + 30 \, x^{2}\right )} e^{x} + 3520 \, x + 1600} \]
integrate((4*(-256*x^3-384*x^2)*log(2)^2*exp(x)^2+4*(1024*x^3+4608*x^2+307 2*x)*log(2)^2*exp(x)+4*(-6144*x^2-12288*x-5632)*log(2)^2)/(x^9*exp(x)^6+(- 24*x^9-36*x^8)*exp(x)^5+(240*x^9+720*x^8+564*x^7+120*x^6)*exp(x)^4+(-1280* x^9-5760*x^8-9024*x^7-6816*x^6-2880*x^5)*exp(x)^3+(3840*x^9+23040*x^8+5414 4*x^7+70272*x^6+59376*x^5+27840*x^4+4800*x^3)*exp(x)^2+(-6144*x^9-46080*x^ 8-144384*x^7-265728*x^6-336768*x^5-292416*x^4-165120*x^3-57600*x^2)*exp(x) +4096*x^9+36864*x^8+144384*x^7+344064*x^6+581376*x^5+724224*x^4+668864*x^3 +462720*x^2+211200*x+64000),x, algorithm=\
256*log(2)^2/(x^6*e^(4*x) + 256*x^6 + 1536*x^5 + 3712*x^4 + 5504*x^3 + 577 6*x^2 - 8*(2*x^6 + 3*x^5)*e^(3*x) + 8*(12*x^6 + 36*x^5 + 29*x^4 + 10*x^3)* e^(2*x) - 32*(8*x^6 + 36*x^5 + 58*x^4 + 53*x^3 + 30*x^2)*e^x + 3520*x + 16 00)
Leaf count of result is larger than twice the leaf count of optimal. 135 vs. \(2 (26) = 52\).
Time = 0.67 (sec) , antiderivative size = 135, normalized size of antiderivative = 4.50 \[ \int \frac {\left (-5632-12288 x-6144 x^2\right ) \log ^2(4)+e^{2 x} \left (-384 x^2-256 x^3\right ) \log ^2(4)+e^x \left (3072 x+4608 x^2+1024 x^3\right ) \log ^2(4)}{64000+211200 x+462720 x^2+668864 x^3+724224 x^4+581376 x^5+344064 x^6+144384 x^7+36864 x^8+4096 x^9+e^{6 x} x^9+e^x \left (-57600 x^2-165120 x^3-292416 x^4-336768 x^5-265728 x^6-144384 x^7-46080 x^8-6144 x^9\right )+e^{3 x} \left (-2880 x^5-6816 x^6-9024 x^7-5760 x^8-1280 x^9\right )+e^{5 x} \left (-36 x^8-24 x^9\right )+e^{4 x} \left (120 x^6+564 x^7+720 x^8+240 x^9\right )+e^{2 x} \left (4800 x^3+27840 x^4+59376 x^5+70272 x^6+54144 x^7+23040 x^8+3840 x^9\right )} \, dx=\frac {512 \, \log \left (2\right )^{2}}{x^{6} e^{\left (4 \, x\right )} - 16 \, x^{6} e^{\left (3 \, x\right )} + 96 \, x^{6} e^{\left (2 \, x\right )} - 256 \, x^{6} e^{x} + 256 \, x^{6} - 24 \, x^{5} e^{\left (3 \, x\right )} + 288 \, x^{5} e^{\left (2 \, x\right )} - 1152 \, x^{5} e^{x} + 1536 \, x^{5} + 232 \, x^{4} e^{\left (2 \, x\right )} - 1856 \, x^{4} e^{x} + 3712 \, x^{4} + 80 \, x^{3} e^{\left (2 \, x\right )} - 1696 \, x^{3} e^{x} + 5504 \, x^{3} - 960 \, x^{2} e^{x} + 5776 \, x^{2} + 3520 \, x + 1600} \]
integrate((4*(-256*x^3-384*x^2)*log(2)^2*exp(x)^2+4*(1024*x^3+4608*x^2+307 2*x)*log(2)^2*exp(x)+4*(-6144*x^2-12288*x-5632)*log(2)^2)/(x^9*exp(x)^6+(- 24*x^9-36*x^8)*exp(x)^5+(240*x^9+720*x^8+564*x^7+120*x^6)*exp(x)^4+(-1280* x^9-5760*x^8-9024*x^7-6816*x^6-2880*x^5)*exp(x)^3+(3840*x^9+23040*x^8+5414 4*x^7+70272*x^6+59376*x^5+27840*x^4+4800*x^3)*exp(x)^2+(-6144*x^9-46080*x^ 8-144384*x^7-265728*x^6-336768*x^5-292416*x^4-165120*x^3-57600*x^2)*exp(x) +4096*x^9+36864*x^8+144384*x^7+344064*x^6+581376*x^5+724224*x^4+668864*x^3 +462720*x^2+211200*x+64000),x, algorithm=\
512*log(2)^2/(x^6*e^(4*x) - 16*x^6*e^(3*x) + 96*x^6*e^(2*x) - 256*x^6*e^x + 256*x^6 - 24*x^5*e^(3*x) + 288*x^5*e^(2*x) - 1152*x^5*e^x + 1536*x^5 + 2 32*x^4*e^(2*x) - 1856*x^4*e^x + 3712*x^4 + 80*x^3*e^(2*x) - 1696*x^3*e^x + 5504*x^3 - 960*x^2*e^x + 5776*x^2 + 3520*x + 1600)
Timed out. \[ \int \frac {\left (-5632-12288 x-6144 x^2\right ) \log ^2(4)+e^{2 x} \left (-384 x^2-256 x^3\right ) \log ^2(4)+e^x \left (3072 x+4608 x^2+1024 x^3\right ) \log ^2(4)}{64000+211200 x+462720 x^2+668864 x^3+724224 x^4+581376 x^5+344064 x^6+144384 x^7+36864 x^8+4096 x^9+e^{6 x} x^9+e^x \left (-57600 x^2-165120 x^3-292416 x^4-336768 x^5-265728 x^6-144384 x^7-46080 x^8-6144 x^9\right )+e^{3 x} \left (-2880 x^5-6816 x^6-9024 x^7-5760 x^8-1280 x^9\right )+e^{5 x} \left (-36 x^8-24 x^9\right )+e^{4 x} \left (120 x^6+564 x^7+720 x^8+240 x^9\right )+e^{2 x} \left (4800 x^3+27840 x^4+59376 x^5+70272 x^6+54144 x^7+23040 x^8+3840 x^9\right )} \, dx=\text {Hanged} \]
int(-(4*log(2)^2*(12288*x + 6144*x^2 + 5632) + 4*exp(2*x)*log(2)^2*(384*x^ 2 + 256*x^3) - 4*exp(x)*log(2)^2*(3072*x + 4608*x^2 + 1024*x^3))/(211200*x - exp(3*x)*(2880*x^5 + 6816*x^6 + 9024*x^7 + 5760*x^8 + 1280*x^9) - exp(x )*(57600*x^2 + 165120*x^3 + 292416*x^4 + 336768*x^5 + 265728*x^6 + 144384* x^7 + 46080*x^8 + 6144*x^9) - exp(5*x)*(36*x^8 + 24*x^9) + x^9*exp(6*x) + exp(2*x)*(4800*x^3 + 27840*x^4 + 59376*x^5 + 70272*x^6 + 54144*x^7 + 23040 *x^8 + 3840*x^9) + exp(4*x)*(120*x^6 + 564*x^7 + 720*x^8 + 240*x^9) + 4627 20*x^2 + 668864*x^3 + 724224*x^4 + 581376*x^5 + 344064*x^6 + 144384*x^7 + 36864*x^8 + 4096*x^9 + 64000),x)