Integrand size = 130, antiderivative size = 28 \begin {dmath*} \int \frac {e^{-2 x} \left (e^{2 x} \left (-2000-400 x-3000 x^3+449700 x^4+135000 x^5+13500 x^6+450 x^7\right )+e^x \left (30000 x+39000 x^2-443400 x^3+315300 x^4+121500 x^5+13050 x^6+450 x^7\right ) \log (4)+\left (-450000 x^3-135000 x^4-13500 x^5-450 x^6\right ) \log ^2(4)\right )}{1000 x^3+300 x^4+30 x^5+x^6} \, dx=25 \left (\frac {2}{x (10+x)}+3 \left (x-e^{-x} \log (4)\right )\right )^2 \end {dmath*}
Time = 0.08 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.50 \begin {dmath*} \int \frac {e^{-2 x} \left (e^{2 x} \left (-2000-400 x-3000 x^3+449700 x^4+135000 x^5+13500 x^6+450 x^7\right )+e^x \left (30000 x+39000 x^2-443400 x^3+315300 x^4+121500 x^5+13050 x^6+450 x^7\right ) \log (4)+\left (-450000 x^3-135000 x^4-13500 x^5-450 x^6\right ) \log ^2(4)\right )}{1000 x^3+300 x^4+30 x^5+x^6} \, dx=\frac {25 e^{-2 x} \left (e^x \left (2+30 x^2+3 x^3\right )-3 x (10+x) \log (4)\right )^2}{x^2 (10+x)^2} \end {dmath*}
Integrate[(E^(2*x)*(-2000 - 400*x - 3000*x^3 + 449700*x^4 + 135000*x^5 + 1 3500*x^6 + 450*x^7) + E^x*(30000*x + 39000*x^2 - 443400*x^3 + 315300*x^4 + 121500*x^5 + 13050*x^6 + 450*x^7)*Log[4] + (-450000*x^3 - 135000*x^4 - 13 500*x^5 - 450*x^6)*Log[4]^2)/(E^(2*x)*(1000*x^3 + 300*x^4 + 30*x^5 + x^6)) ,x]
Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(28)=56\).
Time = 1.62 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.75, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {2026, 2007, 7293, 2009}
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.
| \(\displaystyle \int \frac {e^{-2 x} \left (\left (-450 x^6-13500 x^5-135000 x^4-450000 x^3\right ) \log ^2(4)+e^{2 x} \left (450 x^7+13500 x^6+135000 x^5+449700 x^4-3000 x^3-400 x-2000\right )+e^x \left (450 x^7+13050 x^6+121500 x^5+315300 x^4-443400 x^3+39000 x^2+30000 x\right ) \log (4)\right )}{x^6+30 x^5+300 x^4+1000 x^3} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {e^{-2 x} \left (\left (-450 x^6-13500 x^5-135000 x^4-450000 x^3\right ) \log ^2(4)+e^{2 x} \left (450 x^7+13500 x^6+135000 x^5+449700 x^4-3000 x^3-400 x-2000\right )+e^x \left (450 x^7+13050 x^6+121500 x^5+315300 x^4-443400 x^3+39000 x^2+30000 x\right ) \log (4)\right )}{x^3 \left (x^3+30 x^2+300 x+1000\right )}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {e^{-2 x} \left (\left (-450 x^6-13500 x^5-135000 x^4-450000 x^3\right ) \log ^2(4)+e^{2 x} \left (450 x^7+13500 x^6+135000 x^5+449700 x^4-3000 x^3-400 x-2000\right )+e^x \left (450 x^7+13050 x^6+121500 x^5+315300 x^4-443400 x^3+39000 x^2+30000 x\right ) \log (4)\right )}{x^3 (x+10)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {50 \left (3 x^3+30 x^2+2\right ) \left (3 x^4+60 x^3+300 x^2-4 x-20\right )}{x^3 (x+10)^3}+\frac {150 e^{-x} \left (3 x^5+57 x^4+240 x^3-298 x^2+24 x+20\right ) \log (4)}{x^2 (x+10)^2}-450 e^{-2 x} \log ^2(4)\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 225 x^2+\frac {1}{x^2}+\frac {1501}{5 (x+10)}+\frac {1}{(x+10)^2}-\frac {1}{5 x}+225 e^{-2 x} \log ^2(4)-450 e^{-x} x \log (4)+\frac {30 e^{-x} \log (4)}{x+10}-\frac {30 e^{-x} \log (4)}{x}\) |
Int[(E^(2*x)*(-2000 - 400*x - 3000*x^3 + 449700*x^4 + 135000*x^5 + 13500*x ^6 + 450*x^7) + E^x*(30000*x + 39000*x^2 - 443400*x^3 + 315300*x^4 + 12150 0*x^5 + 13050*x^6 + 450*x^7)*Log[4] + (-450000*x^3 - 135000*x^4 - 13500*x^ 5 - 450*x^6)*Log[4]^2)/(E^(2*x)*(1000*x^3 + 300*x^4 + 30*x^5 + x^6)),x]
x^(-2) - 1/(5*x) + 225*x^2 + (10 + x)^(-2) + 1501/(5*(10 + x)) - (30*Log[4 ])/(E^x*x) - (450*x*Log[4])/E^x + (30*Log[4])/(E^x*(10 + x)) + (225*Log[4] ^2)/E^(2*x)
3.3.64.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Time = 0.87 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.21
| method | result | size |
| parts | \(900 \ln \left (2\right )^{2} {\mathrm e}^{-2 x}+\frac {1}{\left (x +10\right )^{2}}+\frac {1501}{5 \left (x +10\right )}+\frac {1}{x^{2}}-\frac {1}{5 x}+225 x^{2}-\frac {600 \ln \left (2\right ) {\mathrm e}^{-x}}{\left (x +10\right ) x}-900 \ln \left (2\right ) {\mathrm e}^{-x} x\) | \(62\) |
| risch | \(225 x^{2}+\frac {300 x^{3}+3000 x^{2}+100}{x^{2} \left (x^{2}+20 x +100\right )}-\frac {300 \ln \left (2\right ) \left (3 x^{3}+30 x^{2}+2\right ) {\mathrm e}^{-x}}{x \left (x +10\right )}+900 \ln \left (2\right )^{2} {\mathrm e}^{-2 x}\) | \(71\) |
| norman | \(\frac {\left (-2247000 \,{\mathrm e}^{2 x} x^{2}-449700 \,{\mathrm e}^{2 x} x^{3}+100 \,{\mathrm e}^{2 x}+90000 x^{2} \ln \left (2\right )^{2}+18000 x^{3} \ln \left (2\right )^{2}+900 x^{4} \ln \left (2\right )^{2}+4500 x^{5} {\mathrm e}^{2 x}+225 \,{\mathrm e}^{2 x} x^{6}-6000 x \ln \left (2\right ) {\mathrm e}^{x}-600 x^{2} \ln \left (2\right ) {\mathrm e}^{x}-90000 x^{3} \ln \left (2\right ) {\mathrm e}^{x}-18000 \,{\mathrm e}^{x} \ln \left (2\right ) x^{4}-900 \,{\mathrm e}^{x} \ln \left (2\right ) x^{5}\right ) {\mathrm e}^{-2 x}}{x^{2} \left (x +10\right )^{2}}\) | \(127\) |
| parallelrisch | \(\frac {\left (-2247000 \,{\mathrm e}^{2 x} x^{2}-449700 \,{\mathrm e}^{2 x} x^{3}+100 \,{\mathrm e}^{2 x}+90000 x^{2} \ln \left (2\right )^{2}+18000 x^{3} \ln \left (2\right )^{2}+900 x^{4} \ln \left (2\right )^{2}+4500 x^{5} {\mathrm e}^{2 x}+225 \,{\mathrm e}^{2 x} x^{6}-6000 x \ln \left (2\right ) {\mathrm e}^{x}-600 x^{2} \ln \left (2\right ) {\mathrm e}^{x}-90000 x^{3} \ln \left (2\right ) {\mathrm e}^{x}-18000 \,{\mathrm e}^{x} \ln \left (2\right ) x^{4}-900 \,{\mathrm e}^{x} \ln \left (2\right ) x^{5}\right ) {\mathrm e}^{-2 x}}{x^{2} \left (x^{2}+20 x +100\right )}\) | \(132\) |
| default | \(\frac {1}{\left (x +10\right )^{2}}+\frac {1501}{5 \left (x +10\right )}+\frac {1}{x^{2}}-\frac {1}{5 x}+225 x^{2}-1800000 \ln \left (2\right )^{2} \left (\frac {{\mathrm e}^{-2 x} \left (2 x +19\right )}{2 x^{2}+40 x +200}-2 \,{\mathrm e}^{20} \operatorname {Ei}_{1}\left (2 x +20\right )\right )-540000 \ln \left (2\right )^{2} \left (-\frac {{\mathrm e}^{-2 x} \left (11 x +105\right )}{x^{2}+20 x +100}+22 \,{\mathrm e}^{20} \operatorname {Ei}_{1}\left (2 x +20\right )\right )-54000 \ln \left (2\right )^{2} \left (\frac {10 \,{\mathrm e}^{-2 x} \left (12 x +115\right )}{x^{2}+20 x +100}-241 \,{\mathrm e}^{20} \operatorname {Ei}_{1}\left (2 x +20\right )\right )-1800 \ln \left (2\right )^{2} \left (-\frac {{\mathrm e}^{-2 x}}{2}-\frac {100 \,{\mathrm e}^{-2 x} \left (13 x +125\right )}{x^{2}+20 x +100}+2630 \,{\mathrm e}^{20} \operatorname {Ei}_{1}\left (2 x +20\right )\right )+60000 \ln \left (2\right ) \left (\frac {{\mathrm e}^{-x} \left (2 x^{2}+5 x -100\right )}{1000 x \left (x^{2}+20 x +100\right )}-\frac {33 \,{\mathrm e}^{10} \operatorname {Ei}_{1}\left (x +10\right )}{10000}+\frac {13 \,\operatorname {Ei}_{1}\left (x \right )}{10000}\right )+78000 \ln \left (2\right ) \left (-\frac {{\mathrm e}^{-x} \left (4 x +35\right )}{100 \left (x^{2}+20 x +100\right )}+\frac {41 \,{\mathrm e}^{10} \operatorname {Ei}_{1}\left (x +10\right )}{1000}-\frac {\operatorname {Ei}_{1}\left (x \right )}{1000}\right )-886800 \ln \left (2\right ) \left (\frac {{\mathrm e}^{-x} \left (x +9\right )}{2 x^{2}+40 x +200}-\frac {{\mathrm e}^{10} \operatorname {Ei}_{1}\left (x +10\right )}{2}\right )+630600 \ln \left (2\right ) \left (-\frac {{\mathrm e}^{-x} \left (6 x +55\right )}{x^{2}+20 x +100}+6 \,{\mathrm e}^{10} \operatorname {Ei}_{1}\left (x +10\right )\right )+243000 \ln \left (2\right ) \left (\frac {10 \,{\mathrm e}^{-x} \left (7 x +65\right )}{x^{2}+20 x +100}-71 \,{\mathrm e}^{10} \operatorname {Ei}_{1}\left (x +10\right )\right )+26100 \ln \left (2\right ) \left (-{\mathrm e}^{-x}-\frac {100 \,{\mathrm e}^{-x} \left (8 x +75\right )}{x^{2}+20 x +100}+830 \,{\mathrm e}^{10} \operatorname {Ei}_{1}\left (x +10\right )\right )+900 \ln \left (2\right ) \left (-\left (x -29\right ) {\mathrm e}^{-x}+\frac {1000 \,{\mathrm e}^{-x} \left (9 x +85\right )}{x^{2}+20 x +100}-9600 \,{\mathrm e}^{10} \operatorname {Ei}_{1}\left (x +10\right )\right )\) | \(465\) |
int(((450*x^7+13500*x^6+135000*x^5+449700*x^4-3000*x^3-400*x-2000)*exp(x)^ 2+2*(450*x^7+13050*x^6+121500*x^5+315300*x^4-443400*x^3+39000*x^2+30000*x) *ln(2)*exp(x)+4*(-450*x^6-13500*x^5-135000*x^4-450000*x^3)*ln(2)^2)/(x^6+3 0*x^5+300*x^4+1000*x^3)/exp(x)^2,x,method=_RETURNVERBOSE)
900*ln(2)^2/exp(x)^2+1/(x+10)^2+1501/5/(x+10)+1/x^2-1/5/x+225*x^2-600*ln(2 )*exp(-x)/(x+10)/x-900*ln(2)*exp(-x)*x
Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (26) = 52\).
Time = 0.27 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.79 \begin {dmath*} \int \frac {e^{-2 x} \left (e^{2 x} \left (-2000-400 x-3000 x^3+449700 x^4+135000 x^5+13500 x^6+450 x^7\right )+e^x \left (30000 x+39000 x^2-443400 x^3+315300 x^4+121500 x^5+13050 x^6+450 x^7\right ) \log (4)+\left (-450000 x^3-135000 x^4-13500 x^5-450 x^6\right ) \log ^2(4)\right )}{1000 x^3+300 x^4+30 x^5+x^6} \, dx=-\frac {25 \, {\left (12 \, {\left (3 \, x^{5} + 60 \, x^{4} + 300 \, x^{3} + 2 \, x^{2} + 20 \, x\right )} e^{x} \log \left (2\right ) - 36 \, {\left (x^{4} + 20 \, x^{3} + 100 \, x^{2}\right )} \log \left (2\right )^{2} - {\left (9 \, x^{6} + 180 \, x^{5} + 900 \, x^{4} + 12 \, x^{3} + 120 \, x^{2} + 4\right )} e^{\left (2 \, x\right )}\right )} e^{\left (-2 \, x\right )}}{x^{4} + 20 \, x^{3} + 100 \, x^{2}} \end {dmath*}
integrate(((450*x^7+13500*x^6+135000*x^5+449700*x^4-3000*x^3-400*x-2000)*e xp(x)^2+2*(450*x^7+13050*x^6+121500*x^5+315300*x^4-443400*x^3+39000*x^2+30 000*x)*log(2)*exp(x)+4*(-450*x^6-13500*x^5-135000*x^4-450000*x^3)*log(2)^2 )/(x^6+30*x^5+300*x^4+1000*x^3)/exp(x)^2,x, algorithm=\
-25*(12*(3*x^5 + 60*x^4 + 300*x^3 + 2*x^2 + 20*x)*e^x*log(2) - 36*(x^4 + 2 0*x^3 + 100*x^2)*log(2)^2 - (9*x^6 + 180*x^5 + 900*x^4 + 12*x^3 + 120*x^2 + 4)*e^(2*x))*e^(-2*x)/(x^4 + 20*x^3 + 100*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (19) = 38\).
Time = 0.15 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.11 \begin {dmath*} \int \frac {e^{-2 x} \left (e^{2 x} \left (-2000-400 x-3000 x^3+449700 x^4+135000 x^5+13500 x^6+450 x^7\right )+e^x \left (30000 x+39000 x^2-443400 x^3+315300 x^4+121500 x^5+13050 x^6+450 x^7\right ) \log (4)+\left (-450000 x^3-135000 x^4-13500 x^5-450 x^6\right ) \log ^2(4)\right )}{1000 x^3+300 x^4+30 x^5+x^6} \, dx=225 x^{2} + \frac {300 x^{3} + 3000 x^{2} + 100}{x^{4} + 20 x^{3} + 100 x^{2}} + \frac {\left (900 x^{2} \log {\left (2 \right )}^{2} + 9000 x \log {\left (2 \right )}^{2}\right ) e^{- 2 x} + \left (- 900 x^{3} \log {\left (2 \right )} - 9000 x^{2} \log {\left (2 \right )} - 600 \log {\left (2 \right )}\right ) e^{- x}}{x^{2} + 10 x} \end {dmath*}
integrate(((450*x**7+13500*x**6+135000*x**5+449700*x**4-3000*x**3-400*x-20 00)*exp(x)**2+2*(450*x**7+13050*x**6+121500*x**5+315300*x**4-443400*x**3+3 9000*x**2+30000*x)*ln(2)*exp(x)+4*(-450*x**6-13500*x**5-135000*x**4-450000 *x**3)*ln(2)**2)/(x**6+30*x**5+300*x**4+1000*x**3)/exp(x)**2,x)
225*x**2 + (300*x**3 + 3000*x**2 + 100)/(x**4 + 20*x**3 + 100*x**2) + ((90 0*x**2*log(2)**2 + 9000*x*log(2)**2)*exp(-2*x) + (-900*x**3*log(2) - 9000* x**2*log(2) - 600*log(2))*exp(-x))/(x**2 + 10*x)
\begin {dmath*} \int \frac {e^{-2 x} \left (e^{2 x} \left (-2000-400 x-3000 x^3+449700 x^4+135000 x^5+13500 x^6+450 x^7\right )+e^x \left (30000 x+39000 x^2-443400 x^3+315300 x^4+121500 x^5+13050 x^6+450 x^7\right ) \log (4)+\left (-450000 x^3-135000 x^4-13500 x^5-450 x^6\right ) \log ^2(4)\right )}{1000 x^3+300 x^4+30 x^5+x^6} \, dx=\int { \frac {50 \, {\left (6 \, {\left (3 \, x^{7} + 87 \, x^{6} + 810 \, x^{5} + 2102 \, x^{4} - 2956 \, x^{3} + 260 \, x^{2} + 200 \, x\right )} e^{x} \log \left (2\right ) - 36 \, {\left (x^{6} + 30 \, x^{5} + 300 \, x^{4} + 1000 \, x^{3}\right )} \log \left (2\right )^{2} + {\left (9 \, x^{7} + 270 \, x^{6} + 2700 \, x^{5} + 8994 \, x^{4} - 60 \, x^{3} - 8 \, x - 40\right )} e^{\left (2 \, x\right )}\right )} e^{\left (-2 \, x\right )}}{x^{6} + 30 \, x^{5} + 300 \, x^{4} + 1000 \, x^{3}} \,d x } \end {dmath*}
integrate(((450*x^7+13500*x^6+135000*x^5+449700*x^4-3000*x^3-400*x-2000)*e xp(x)^2+2*(450*x^7+13050*x^6+121500*x^5+315300*x^4-443400*x^3+39000*x^2+30 000*x)*log(2)*exp(x)+4*(-450*x^6-13500*x^5-135000*x^4-450000*x^3)*log(2)^2 )/(x^6+30*x^5+300*x^4+1000*x^3)/exp(x)^2,x, algorithm=\
-2700000*integrate(e^(-2*x)/(x^4 + 40*x^3 + 600*x^2 + 4000*x + 10000), x)* log(2)^2 + 1800000*e^20*exp_integral_e(3, 2*x + 20)*log(2)^2/(x + 10)^2 + 25*(9*x^7 + 270*x^6 + 2700*x^5 + 9012*x^4 + 240*x^3 + 1200*x^2 - 12*(3*x^6 *log(2) + 90*x^5*log(2) + 900*x^4*log(2) + 3002*x^3*log(2) + 40*x^2*log(2) + 200*x*log(2))*e^(-x) + 36*(x^5*log(2)^2 + 30*x^4*log(2)^2 + 300*x^3*log (2)^2)*e^(-2*x) + 4*x + 40)/(x^5 + 30*x^4 + 300*x^3 + 1000*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 137 vs. \(2 (26) = 52\).
Time = 0.27 (sec) , antiderivative size = 137, normalized size of antiderivative = 4.89 \begin {dmath*} \int \frac {e^{-2 x} \left (e^{2 x} \left (-2000-400 x-3000 x^3+449700 x^4+135000 x^5+13500 x^6+450 x^7\right )+e^x \left (30000 x+39000 x^2-443400 x^3+315300 x^4+121500 x^5+13050 x^6+450 x^7\right ) \log (4)+\left (-450000 x^3-135000 x^4-13500 x^5-450 x^6\right ) \log ^2(4)\right )}{1000 x^3+300 x^4+30 x^5+x^6} \, dx=-\frac {25 \, {\left (36 \, x^{5} e^{\left (-x\right )} \log \left (2\right ) - 36 \, x^{4} e^{\left (-2 \, x\right )} \log \left (2\right )^{2} - 9 \, x^{6} + 720 \, x^{4} e^{\left (-x\right )} \log \left (2\right ) - 720 \, x^{3} e^{\left (-2 \, x\right )} \log \left (2\right )^{2} - 180 \, x^{5} + 3600 \, x^{3} e^{\left (-x\right )} \log \left (2\right ) - 3600 \, x^{2} e^{\left (-2 \, x\right )} \log \left (2\right )^{2} - 900 \, x^{4} + 24 \, x^{2} e^{\left (-x\right )} \log \left (2\right ) - 12 \, x^{3} + 240 \, x e^{\left (-x\right )} \log \left (2\right ) - 120 \, x^{2} - 4\right )}}{x^{4} + 20 \, x^{3} + 100 \, x^{2}} \end {dmath*}
integrate(((450*x^7+13500*x^6+135000*x^5+449700*x^4-3000*x^3-400*x-2000)*e xp(x)^2+2*(450*x^7+13050*x^6+121500*x^5+315300*x^4-443400*x^3+39000*x^2+30 000*x)*log(2)*exp(x)+4*(-450*x^6-13500*x^5-135000*x^4-450000*x^3)*log(2)^2 )/(x^6+30*x^5+300*x^4+1000*x^3)/exp(x)^2,x, algorithm=\
-25*(36*x^5*e^(-x)*log(2) - 36*x^4*e^(-2*x)*log(2)^2 - 9*x^6 + 720*x^4*e^( -x)*log(2) - 720*x^3*e^(-2*x)*log(2)^2 - 180*x^5 + 3600*x^3*e^(-x)*log(2) - 3600*x^2*e^(-2*x)*log(2)^2 - 900*x^4 + 24*x^2*e^(-x)*log(2) - 12*x^3 + 2 40*x*e^(-x)*log(2) - 120*x^2 - 4)/(x^4 + 20*x^3 + 100*x^2)
Time = 14.40 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.82 \begin {dmath*} \int \frac {e^{-2 x} \left (e^{2 x} \left (-2000-400 x-3000 x^3+449700 x^4+135000 x^5+13500 x^6+450 x^7\right )+e^x \left (30000 x+39000 x^2-443400 x^3+315300 x^4+121500 x^5+13050 x^6+450 x^7\right ) \log (4)+\left (-450000 x^3-135000 x^4-13500 x^5-450 x^6\right ) \log ^2(4)\right )}{1000 x^3+300 x^4+30 x^5+x^6} \, dx=\frac {300\,x^3+3000\,x^2+100}{x^4+20\,x^3+100\,x^2}+900\,{\mathrm {e}}^{-2\,x}\,{\ln \left (2\right )}^2+225\,x^2-\frac {{\mathrm {e}}^{-x}\,\left (900\,\ln \left (2\right )\,x^3+9000\,\ln \left (2\right )\,x^2+600\,\ln \left (2\right )\right )}{x^2+10\,x} \end {dmath*}
int((exp(-2*x)*(exp(2*x)*(449700*x^4 - 3000*x^3 - 400*x + 135000*x^5 + 135 00*x^6 + 450*x^7 - 2000) - 4*log(2)^2*(450000*x^3 + 135000*x^4 + 13500*x^5 + 450*x^6) + 2*exp(x)*log(2)*(30000*x + 39000*x^2 - 443400*x^3 + 315300*x ^4 + 121500*x^5 + 13050*x^6 + 450*x^7)))/(1000*x^3 + 300*x^4 + 30*x^5 + x^ 6),x)