Integrand size = 115, antiderivative size = 26 \[ \int \frac {1+54 x^4+144 x^5+90 x^6-567 x^8-1296 x^9-729 x^{10}+e^{-4+2 x} \left (1-2 x+54 x^4+36 x^5-567 x^8-162 x^9\right )+e^{-2+x} \left (2-2 x-2 x^2+108 x^4+180 x^5+36 x^6-1134 x^8-1458 x^9-162 x^{10}\right )}{x^2} \, dx=x-\frac {\left (1+e^{-2+x}+x\right )^2 \left (1-9 x^4\right )^2}{x} \] Output:
x-(-9*x^4+1)^2*(exp(-2+x)+x+1)^2/x
Leaf count is larger than twice the leaf count of optimal. \(79\) vs. \(2(26)=52\).
Time = 4.38 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.04 \[ \int \frac {1+54 x^4+144 x^5+90 x^6-567 x^8-1296 x^9-729 x^{10}+e^{-4+2 x} \left (1-2 x+54 x^4+36 x^5-567 x^8-162 x^9\right )+e^{-2+x} \left (2-2 x-2 x^2+108 x^4+180 x^5+36 x^6-1134 x^8-1458 x^9-162 x^{10}\right )}{x^2} \, dx=\frac {-e^{2 x} \left (1-9 x^4\right )^2-2 e^{2+x} (1+x) \left (1-9 x^4\right )^2+e^4 \left (-1+18 x^4+36 x^5+18 x^6-81 x^8-162 x^9-81 x^{10}\right )}{e^4 x} \] Input:
Integrate[(1 + 54*x^4 + 144*x^5 + 90*x^6 - 567*x^8 - 1296*x^9 - 729*x^10 + E^(-4 + 2*x)*(1 - 2*x + 54*x^4 + 36*x^5 - 567*x^8 - 162*x^9) + E^(-2 + x) *(2 - 2*x - 2*x^2 + 108*x^4 + 180*x^5 + 36*x^6 - 1134*x^8 - 1458*x^9 - 162 *x^10))/x^2,x]
Output:
(-(E^(2*x)*(1 - 9*x^4)^2) - 2*E^(2 + x)*(1 + x)*(1 - 9*x^4)^2 + E^4*(-1 + 18*x^4 + 36*x^5 + 18*x^6 - 81*x^8 - 162*x^9 - 81*x^10))/(E^4*x)
Leaf count is larger than twice the leaf count of optimal. \(129\) vs. \(2(26)=52\).
Time = 1.14 (sec) , antiderivative size = 129, normalized size of antiderivative = 4.96, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {2010, 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.
| \(\displaystyle \int \frac {-729 x^{10}-1296 x^9-567 x^8+90 x^6+144 x^5+54 x^4+e^{2 x-4} \left (-162 x^9-567 x^8+36 x^5+54 x^4-2 x+1\right )+e^{x-2} \left (-162 x^{10}-1458 x^9-1134 x^8+36 x^6+180 x^5+108 x^4-2 x^2-2 x+2\right )+1}{x^2} \, dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \int \left (-\frac {2 e^{x-2} \left (3 x^2-1\right ) \left (3 x^2+1\right ) \left (9 x^6+81 x^5+63 x^4-x^2-x+1\right )}{x^2}-\frac {e^{2 x-4} \left (162 x^9+567 x^8-36 x^5-54 x^4+2 x-1\right )}{x^2}+\frac {-729 x^{10}-1296 x^9-567 x^8+90 x^6+144 x^5+54 x^4+1}{x^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -81 x^9-162 e^{x-2} x^8-162 x^8-162 e^{x-2} x^7-81 e^{2 x-4} x^7-81 x^7+18 x^5+36 e^{x-2} x^4+36 x^4+36 e^{x-2} x^3+18 e^{2 x-4} x^3+18 x^3-2 e^{x-2}-\frac {2 e^{x-2}}{x}-\frac {e^{2 x-4}}{x}-\frac {1}{x}\) |
Input:
Int[(1 + 54*x^4 + 144*x^5 + 90*x^6 - 567*x^8 - 1296*x^9 - 729*x^10 + E^(-4 + 2*x)*(1 - 2*x + 54*x^4 + 36*x^5 - 567*x^8 - 162*x^9) + E^(-2 + x)*(2 - 2*x - 2*x^2 + 108*x^4 + 180*x^5 + 36*x^6 - 1134*x^8 - 1458*x^9 - 162*x^10) )/x^2,x]
Output:
-2*E^(-2 + x) - x^(-1) - (2*E^(-2 + x))/x - E^(-4 + 2*x)/x + 18*x^3 + 36*E ^(-2 + x)*x^3 + 18*E^(-4 + 2*x)*x^3 + 36*x^4 + 36*E^(-2 + x)*x^4 + 18*x^5 - 81*x^7 - 162*E^(-2 + x)*x^7 - 81*E^(-4 + 2*x)*x^7 - 162*x^8 - 162*E^(-2 + x)*x^8 - 81*x^9
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Leaf count of result is larger than twice the leaf count of optimal. \(91\) vs. \(2(25)=50\).
Time = 2.87 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.54
| method | result | size |
| risch | \(-81 x^{9}-162 x^{8}-81 x^{7}+18 x^{5}+36 x^{4}+18 x^{3}-\frac {1}{x}-\frac {\left (81 x^{8}-18 x^{4}+1\right ) {\mathrm e}^{2 x -4}}{x}-\frac {2 \left (81 x^{9}+81 x^{8}-18 x^{5}-18 x^{4}+x +1\right ) {\mathrm e}^{-2+x}}{x}\) | \(92\) |
| parallelrisch | \(-\frac {162 \,{\mathrm e}^{-2+x} x^{9}+81 x^{10}+162 \,{\mathrm e}^{-2+x} x^{8}+81 \,{\mathrm e}^{2 x -4} x^{8}+162 x^{9}+81 x^{8}-36 \,{\mathrm e}^{-2+x} x^{5}-18 x^{6}-36 \,{\mathrm e}^{-2+x} x^{4}-18 \,{\mathrm e}^{2 x -4} x^{4}-36 x^{5}-18 x^{4}+2 x \,{\mathrm e}^{-2+x}+2 \,{\mathrm e}^{-2+x}+{\mathrm e}^{2 x -4}+1}{x}\) | \(115\) |
| norman | \(\frac {-1+18 x^{4}+36 x^{5}+18 x^{6}-81 x^{8}-162 x^{9}-81 x^{10}-{\mathrm e}^{2 x -4}-2 x \,{\mathrm e}^{-2+x}+36 \,{\mathrm e}^{-2+x} x^{4}+36 \,{\mathrm e}^{-2+x} x^{5}-162 \,{\mathrm e}^{-2+x} x^{8}-162 \,{\mathrm e}^{-2+x} x^{9}+18 \,{\mathrm e}^{2 x -4} x^{4}-81 \,{\mathrm e}^{2 x -4} x^{8}-2 \,{\mathrm e}^{-2+x}}{x}\) | \(116\) |
| parts | \(-162 x^{8}-81 x^{9}-81 x^{7}-\frac {1}{x}-61346 \,{\mathrm e}^{-2+x}+18 x^{3}+36 x^{4}+18 x^{5}-\frac {2 \,{\mathrm e}^{-2+x}}{x}-398088 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{2}-236880 \,{\mathrm e}^{-2+x} \left (-2+x \right )-162 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{8}-2754 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{7}-20412 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{6}-86184 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{5}-226764 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{4}-380700 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{3}-10224 \,{\mathrm e}^{2 x -4}-81 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{7}-1134 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{6}-6804 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{5}-22680 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{4}-45342 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{3}-54324 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{2}-36072 \,{\mathrm e}^{2 x -4} \left (-2+x \right )-\frac {{\mathrm e}^{2 x -4}}{x}\) | \(246\) |
| derivativedivides | \(771984-385992 x -715572 \left (-2+x \right )^{2}-\frac {1}{x}-61346 \,{\mathrm e}^{-2+x}-81 \left (-2+x \right )^{9}-1620 \left (-2+x \right )^{8}-14337 \left (-2+x \right )^{7}-73710 \left (-2+x \right )^{6}-242658 \left (-2+x \right )^{5}-530496 \left (-2+x \right )^{4}-\frac {2 \,{\mathrm e}^{-2+x}}{x}-398088 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{2}-236880 \,{\mathrm e}^{-2+x} \left (-2+x \right )-162 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{8}-2754 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{7}-20412 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{6}-86184 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{5}-226764 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{4}-380700 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{3}-10224 \,{\mathrm e}^{2 x -4}-81 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{7}-1134 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{6}-6804 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{5}-22680 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{4}-45342 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{3}-54324 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{2}-36072 \,{\mathrm e}^{2 x -4} \left (-2+x \right )-\frac {{\mathrm e}^{2 x -4}}{x}-770094 \left (-2+x \right )^{3}\) | \(276\) |
| default | \(771984-385992 x -715572 \left (-2+x \right )^{2}-\frac {1}{x}-61346 \,{\mathrm e}^{-2+x}-81 \left (-2+x \right )^{9}-1620 \left (-2+x \right )^{8}-14337 \left (-2+x \right )^{7}-73710 \left (-2+x \right )^{6}-242658 \left (-2+x \right )^{5}-530496 \left (-2+x \right )^{4}-\frac {2 \,{\mathrm e}^{-2+x}}{x}-398088 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{2}-236880 \,{\mathrm e}^{-2+x} \left (-2+x \right )-162 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{8}-2754 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{7}-20412 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{6}-86184 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{5}-226764 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{4}-380700 \,{\mathrm e}^{-2+x} \left (-2+x \right )^{3}-10224 \,{\mathrm e}^{2 x -4}-81 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{7}-1134 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{6}-6804 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{5}-22680 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{4}-45342 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{3}-54324 \,{\mathrm e}^{2 x -4} \left (-2+x \right )^{2}-36072 \,{\mathrm e}^{2 x -4} \left (-2+x \right )-\frac {{\mathrm e}^{2 x -4}}{x}-770094 \left (-2+x \right )^{3}\) | \(276\) |
| orering | \(\text {Expression too large to display}\) | \(1674\) |
Input:
int(((-162*x^9-567*x^8+36*x^5+54*x^4-2*x+1)*exp(-2+x)^2+(-162*x^10-1458*x^ 9-1134*x^8+36*x^6+180*x^5+108*x^4-2*x^2-2*x+2)*exp(-2+x)-729*x^10-1296*x^9 -567*x^8+90*x^6+144*x^5+54*x^4+1)/x^2,x,method=_RETURNVERBOSE)
Output:
-81*x^9-162*x^8-81*x^7+18*x^5+36*x^4+18*x^3-1/x-(81*x^8-18*x^4+1)/x*exp(2* x-4)-2*(81*x^9+81*x^8-18*x^5-18*x^4+x+1)/x*exp(-2+x)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (25) = 50\).
Time = 0.08 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.27 \[ \int \frac {1+54 x^4+144 x^5+90 x^6-567 x^8-1296 x^9-729 x^{10}+e^{-4+2 x} \left (1-2 x+54 x^4+36 x^5-567 x^8-162 x^9\right )+e^{-2+x} \left (2-2 x-2 x^2+108 x^4+180 x^5+36 x^6-1134 x^8-1458 x^9-162 x^{10}\right )}{x^2} \, dx=-\frac {81 \, x^{10} + 162 \, x^{9} + 81 \, x^{8} - 18 \, x^{6} - 36 \, x^{5} - 18 \, x^{4} + {\left (81 \, x^{8} - 18 \, x^{4} + 1\right )} e^{\left (2 \, x - 4\right )} + 2 \, {\left (81 \, x^{9} + 81 \, x^{8} - 18 \, x^{5} - 18 \, x^{4} + x + 1\right )} e^{\left (x - 2\right )} + 1}{x} \] Input:
integrate(((-162*x^9-567*x^8+36*x^5+54*x^4-2*x+1)*exp(-2+x)^2+(-162*x^10-1 458*x^9-1134*x^8+36*x^6+180*x^5+108*x^4-2*x^2-2*x+2)*exp(-2+x)-729*x^10-12 96*x^9-567*x^8+90*x^6+144*x^5+54*x^4+1)/x^2,x, algorithm="fricas")
Output:
-(81*x^10 + 162*x^9 + 81*x^8 - 18*x^6 - 36*x^5 - 18*x^4 + (81*x^8 - 18*x^4 + 1)*e^(2*x - 4) + 2*(81*x^9 + 81*x^8 - 18*x^5 - 18*x^4 + x + 1)*e^(x - 2 ) + 1)/x
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (20) = 40\).
Time = 0.11 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.38 \[ \int \frac {1+54 x^4+144 x^5+90 x^6-567 x^8-1296 x^9-729 x^{10}+e^{-4+2 x} \left (1-2 x+54 x^4+36 x^5-567 x^8-162 x^9\right )+e^{-2+x} \left (2-2 x-2 x^2+108 x^4+180 x^5+36 x^6-1134 x^8-1458 x^9-162 x^{10}\right )}{x^2} \, dx=- 81 x^{9} - 162 x^{8} - 81 x^{7} + 18 x^{5} + 36 x^{4} + 18 x^{3} - \frac {1}{x} + \frac {\left (- 81 x^{9} + 18 x^{5} - x\right ) e^{2 x - 4} + \left (- 162 x^{10} - 162 x^{9} + 36 x^{6} + 36 x^{5} - 2 x^{2} - 2 x\right ) e^{x - 2}}{x^{2}} \] Input:
integrate(((-162*x**9-567*x**8+36*x**5+54*x**4-2*x+1)*exp(-2+x)**2+(-162*x **10-1458*x**9-1134*x**8+36*x**6+180*x**5+108*x**4-2*x**2-2*x+2)*exp(-2+x) -729*x**10-1296*x**9-567*x**8+90*x**6+144*x**5+54*x**4+1)/x**2,x)
Output:
-81*x**9 - 162*x**8 - 81*x**7 + 18*x**5 + 36*x**4 + 18*x**3 - 1/x + ((-81* x**9 + 18*x**5 - x)*exp(2*x - 4) + (-162*x**10 - 162*x**9 + 36*x**6 + 36*x **5 - 2*x**2 - 2*x)*exp(x - 2))/x**2
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.09 (sec) , antiderivative size = 370, normalized size of antiderivative = 14.23 \[ \int \frac {1+54 x^4+144 x^5+90 x^6-567 x^8-1296 x^9-729 x^{10}+e^{-4+2 x} \left (1-2 x+54 x^4+36 x^5-567 x^8-162 x^9\right )+e^{-2+x} \left (2-2 x-2 x^2+108 x^4+180 x^5+36 x^6-1134 x^8-1458 x^9-162 x^{10}\right )}{x^2} \, dx=-81 \, x^{9} - 162 \, x^{8} - 81 \, x^{7} + 18 \, x^{5} + 36 \, x^{4} + 18 \, x^{3} - 2 \, {\rm Ei}\left (x\right ) e^{\left (-2\right )} - 2 \, {\rm Ei}\left (2 \, x\right ) e^{\left (-4\right )} - \frac {81}{8} \, {\left (8 \, x^{7} - 28 \, x^{6} + 84 \, x^{5} - 210 \, x^{4} + 420 \, x^{3} - 630 \, x^{2} + 630 \, x - 315\right )} e^{\left (2 \, x - 4\right )} - \frac {567}{8} \, {\left (4 \, x^{6} - 12 \, x^{5} + 30 \, x^{4} - 60 \, x^{3} + 90 \, x^{2} - 90 \, x + 45\right )} e^{\left (2 \, x - 4\right )} + \frac {9}{2} \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x - 4\right )} + \frac {27}{2} \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x - 4\right )} - 162 \, {\left (x^{8} - 8 \, x^{7} + 56 \, x^{6} - 336 \, x^{5} + 1680 \, x^{4} - 6720 \, x^{3} + 20160 \, x^{2} - 40320 \, x + 40320\right )} e^{\left (x - 2\right )} - 1458 \, {\left (x^{7} - 7 \, x^{6} + 42 \, x^{5} - 210 \, x^{4} + 840 \, x^{3} - 2520 \, x^{2} + 5040 \, x - 5040\right )} e^{\left (x - 2\right )} - 1134 \, {\left (x^{6} - 6 \, x^{5} + 30 \, x^{4} - 120 \, x^{3} + 360 \, x^{2} - 720 \, x + 720\right )} e^{\left (x - 2\right )} + 36 \, {\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{\left (x - 2\right )} + 180 \, {\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{\left (x - 2\right )} + 108 \, {\left (x^{2} - 2 \, x + 2\right )} e^{\left (x - 2\right )} + 2 \, e^{\left (-2\right )} \Gamma \left (-1, -x\right ) + 2 \, e^{\left (-4\right )} \Gamma \left (-1, -2 \, x\right ) - \frac {1}{x} - 2 \, e^{\left (x - 2\right )} \] Input:
integrate(((-162*x^9-567*x^8+36*x^5+54*x^4-2*x+1)*exp(-2+x)^2+(-162*x^10-1 458*x^9-1134*x^8+36*x^6+180*x^5+108*x^4-2*x^2-2*x+2)*exp(-2+x)-729*x^10-12 96*x^9-567*x^8+90*x^6+144*x^5+54*x^4+1)/x^2,x, algorithm="maxima")
Output:
-81*x^9 - 162*x^8 - 81*x^7 + 18*x^5 + 36*x^4 + 18*x^3 - 2*Ei(x)*e^(-2) - 2 *Ei(2*x)*e^(-4) - 81/8*(8*x^7 - 28*x^6 + 84*x^5 - 210*x^4 + 420*x^3 - 630* x^2 + 630*x - 315)*e^(2*x - 4) - 567/8*(4*x^6 - 12*x^5 + 30*x^4 - 60*x^3 + 90*x^2 - 90*x + 45)*e^(2*x - 4) + 9/2*(4*x^3 - 6*x^2 + 6*x - 3)*e^(2*x - 4) + 27/2*(2*x^2 - 2*x + 1)*e^(2*x - 4) - 162*(x^8 - 8*x^7 + 56*x^6 - 336* x^5 + 1680*x^4 - 6720*x^3 + 20160*x^2 - 40320*x + 40320)*e^(x - 2) - 1458* (x^7 - 7*x^6 + 42*x^5 - 210*x^4 + 840*x^3 - 2520*x^2 + 5040*x - 5040)*e^(x - 2) - 1134*(x^6 - 6*x^5 + 30*x^4 - 120*x^3 + 360*x^2 - 720*x + 720)*e^(x - 2) + 36*(x^4 - 4*x^3 + 12*x^2 - 24*x + 24)*e^(x - 2) + 180*(x^3 - 3*x^2 + 6*x - 6)*e^(x - 2) + 108*(x^2 - 2*x + 2)*e^(x - 2) + 2*e^(-2)*gamma(-1, -x) + 2*e^(-4)*gamma(-1, -2*x) - 1/x - 2*e^(x - 2)
Leaf count of result is larger than twice the leaf count of optimal. 123 vs. \(2 (25) = 50\).
Time = 0.12 (sec) , antiderivative size = 123, normalized size of antiderivative = 4.73 \[ \int \frac {1+54 x^4+144 x^5+90 x^6-567 x^8-1296 x^9-729 x^{10}+e^{-4+2 x} \left (1-2 x+54 x^4+36 x^5-567 x^8-162 x^9\right )+e^{-2+x} \left (2-2 x-2 x^2+108 x^4+180 x^5+36 x^6-1134 x^8-1458 x^9-162 x^{10}\right )}{x^2} \, dx=-\frac {{\left (81 \, x^{10} e^{4} + 162 \, x^{9} e^{4} + 162 \, x^{9} e^{\left (x + 2\right )} + 81 \, x^{8} e^{4} + 81 \, x^{8} e^{\left (2 \, x\right )} + 162 \, x^{8} e^{\left (x + 2\right )} - 18 \, x^{6} e^{4} - 36 \, x^{5} e^{4} - 36 \, x^{5} e^{\left (x + 2\right )} - 18 \, x^{4} e^{4} - 18 \, x^{4} e^{\left (2 \, x\right )} - 36 \, x^{4} e^{\left (x + 2\right )} + 2 \, x e^{\left (x + 2\right )} + e^{4} + e^{\left (2 \, x\right )} + 2 \, e^{\left (x + 2\right )}\right )} e^{\left (-4\right )}}{x} \] Input:
integrate(((-162*x^9-567*x^8+36*x^5+54*x^4-2*x+1)*exp(-2+x)^2+(-162*x^10-1 458*x^9-1134*x^8+36*x^6+180*x^5+108*x^4-2*x^2-2*x+2)*exp(-2+x)-729*x^10-12 96*x^9-567*x^8+90*x^6+144*x^5+54*x^4+1)/x^2,x, algorithm="giac")
Output:
-(81*x^10*e^4 + 162*x^9*e^4 + 162*x^9*e^(x + 2) + 81*x^8*e^4 + 81*x^8*e^(2 *x) + 162*x^8*e^(x + 2) - 18*x^6*e^4 - 36*x^5*e^4 - 36*x^5*e^(x + 2) - 18* x^4*e^4 - 18*x^4*e^(2*x) - 36*x^4*e^(x + 2) + 2*x*e^(x + 2) + e^4 + e^(2*x ) + 2*e^(x + 2))*e^(-4)/x
Time = 0.15 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.92 \[ \int \frac {1+54 x^4+144 x^5+90 x^6-567 x^8-1296 x^9-729 x^{10}+e^{-4+2 x} \left (1-2 x+54 x^4+36 x^5-567 x^8-162 x^9\right )+e^{-2+x} \left (2-2 x-2 x^2+108 x^4+180 x^5+36 x^6-1134 x^8-1458 x^9-162 x^{10}\right )}{x^2} \, dx=x^3\,\left (36\,{\mathrm {e}}^{x-2}+18\,{\mathrm {e}}^{2\,x-4}+18\right )-2\,{\mathrm {e}}^{x-2}-x^7\,\left (162\,{\mathrm {e}}^{x-2}+81\,{\mathrm {e}}^{2\,x-4}+81\right )+x^4\,\left (36\,{\mathrm {e}}^{x-2}+36\right )-x^8\,\left (162\,{\mathrm {e}}^{x-2}+162\right )-\frac {2\,{\mathrm {e}}^{x-2}+{\mathrm {e}}^{2\,x-4}+1}{x}+18\,x^5-81\,x^9 \] Input:
int(-(exp(2*x - 4)*(2*x - 54*x^4 - 36*x^5 + 567*x^8 + 162*x^9 - 1) + exp(x - 2)*(2*x + 2*x^2 - 108*x^4 - 180*x^5 - 36*x^6 + 1134*x^8 + 1458*x^9 + 16 2*x^10 - 2) - 54*x^4 - 144*x^5 - 90*x^6 + 567*x^8 + 1296*x^9 + 729*x^10 - 1)/x^2,x)
Output:
x^3*(36*exp(x - 2) + 18*exp(2*x - 4) + 18) - 2*exp(x - 2) - x^7*(162*exp(x - 2) + 81*exp(2*x - 4) + 81) + x^4*(36*exp(x - 2) + 36) - x^8*(162*exp(x - 2) + 162) - (2*exp(x - 2) + exp(2*x - 4) + 1)/x + 18*x^5 - 81*x^9
Time = 0.25 (sec) , antiderivative size = 149, normalized size of antiderivative = 5.73 \[ \int \frac {1+54 x^4+144 x^5+90 x^6-567 x^8-1296 x^9-729 x^{10}+e^{-4+2 x} \left (1-2 x+54 x^4+36 x^5-567 x^8-162 x^9\right )+e^{-2+x} \left (2-2 x-2 x^2+108 x^4+180 x^5+36 x^6-1134 x^8-1458 x^9-162 x^{10}\right )}{x^2} \, dx=\frac {-81 e^{2 x} x^{8}+18 e^{2 x} x^{4}-e^{2 x}-162 e^{x} e^{2} x^{9}-162 e^{x} e^{2} x^{8}+36 e^{x} e^{2} x^{5}+36 e^{x} e^{2} x^{4}-2 e^{x} e^{2} x -2 e^{x} e^{2}-81 e^{4} x^{10}-162 e^{4} x^{9}-81 e^{4} x^{8}+18 e^{4} x^{6}+36 e^{4} x^{5}+18 e^{4} x^{4}-e^{4}}{e^{4} x} \] Input:
int(((-162*x^9-567*x^8+36*x^5+54*x^4-2*x+1)*exp(-2+x)^2+(-162*x^10-1458*x^ 9-1134*x^8+36*x^6+180*x^5+108*x^4-2*x^2-2*x+2)*exp(-2+x)-729*x^10-1296*x^9 -567*x^8+90*x^6+144*x^5+54*x^4+1)/x^2,x)
Output:
( - 81*e**(2*x)*x**8 + 18*e**(2*x)*x**4 - e**(2*x) - 162*e**x*e**2*x**9 - 162*e**x*e**2*x**8 + 36*e**x*e**2*x**5 + 36*e**x*e**2*x**4 - 2*e**x*e**2*x - 2*e**x*e**2 - 81*e**4*x**10 - 162*e**4*x**9 - 81*e**4*x**8 + 18*e**4*x* *6 + 36*e**4*x**5 + 18*e**4*x**4 - e**4)/(e**4*x)