Integrand size = 210, antiderivative size = 24 \[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx=\frac {x^2}{2 x+(1+x)^2 \left (-4+e^3+x\right )^2} \] Output:
x^2/(2*x+(1+x)^2*(exp(3)+x-4)^2)
Time = 0.05 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.83 \[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx=\frac {x^2}{16+26 x+x^2-6 x^3+x^4+e^6 (1+x)^2+2 e^3 (-4+x) (1+x)^2} \] Input:
Integrate[(32*x + 26*x^2 + 6*x^4 - 2*x^5 + E^6*(2*x + 2*x^2) + E^3*(-16*x - 14*x^2 - 2*x^4))/(256 + 832*x + 708*x^2 - 140*x^3 - 279*x^4 + 40*x^5 + 3 8*x^6 - 12*x^7 + x^8 + E^12*(1 + 4*x + 6*x^2 + 4*x^3 + x^4) + E^9*(-16 - 6 0*x - 80*x^2 - 40*x^3 + 4*x^5) + E^6*(96 + 340*x + 398*x^2 + 124*x^3 - 60* x^4 - 24*x^5 + 6*x^6) + E^3*(-256 - 864*x - 872*x^2 - 76*x^3 + 248*x^4 + 2 4*x^5 - 32*x^6 + 4*x^7)),x]
Output:
x^2/(16 + 26*x + x^2 - 6*x^3 + x^4 + E^6*(1 + x)^2 + 2*E^3*(-4 + x)*(1 + x )^2)
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.
| \(\displaystyle \int \frac {-2 x^5+6 x^4+26 x^2+e^6 \left (2 x^2+2 x\right )+e^3 \left (-2 x^4-14 x^2-16 x\right )+32 x}{x^8-12 x^7+38 x^6+40 x^5-279 x^4-140 x^3+708 x^2+e^9 \left (4 x^5-40 x^3-80 x^2-60 x-16\right )+e^{12} \left (x^4+4 x^3+6 x^2+4 x+1\right )+e^6 \left (6 x^6-24 x^5-60 x^4+124 x^3+398 x^2+340 x+96\right )+e^3 \left (4 x^7-32 x^6+24 x^5+248 x^4-76 x^3-872 x^2-864 x-256\right )+832 x+256} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {2 \left (-x+e^3-3\right )}{x^4-2 \left (3-e^3\right ) x^3+\left (1-4 e^3+e^6\right ) x^2+2 \left (13-7 e^3+e^6\right ) x+\left (e^3-4\right )^2}+\frac {2 \left (-\left (\left (17-8 e^3+e^6\right ) x^3\right )+\left (42-34 e^3+10 e^6-e^9\right ) x^2+2 \left (55-42 e^3+11 e^6-e^9\right ) x+\left (3-e^3\right ) \left (4-e^3\right )^2\right )}{\left (x^4-2 \left (3-e^3\right ) x^3+\left (1-4 e^3+e^6\right ) x^2+2 \left (13-7 e^3+e^6\right ) x+\left (e^3-4\right )^2\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 2 \left (3-e^3\right ) \int \frac {1}{-x^4+2 \left (3-e^3\right ) x^3-\left (1-4 e^3+e^6\right ) x^2-2 \left (13-7 e^3+e^6\right ) x-\left (4-e^3\right )^2}dx+2 \int \frac {x}{-x^4+2 \left (3-e^3\right ) x^3-\left (1-4 e^3+e^6\right ) x^2-2 \left (13-7 e^3+e^6\right ) x-\left (4-e^3\right )^2}dx+\left (317-303 e^3+108 e^6-17 e^9+e^{12}\right ) \int \frac {1}{\left (x^4-2 \left (3-e^3\right ) x^3+\left (1-4 e^3+e^6\right ) x^2+2 \left (13-7 e^3+e^6\right ) x+\left (-4+e^3\right )^2\right )^2}dx+\left (237-244 e^3+94 e^6-16 e^9+e^{12}\right ) \int \frac {x}{\left (x^4-2 \left (3-e^3\right ) x^3+\left (1-4 e^3+e^6\right ) x^2+2 \left (13-7 e^3+e^6\right ) x+\left (-4+e^3\right )^2\right )^2}dx-\left (69-55 e^3+13 e^6-e^9\right ) \int \frac {x^2}{\left (x^4-2 \left (3-e^3\right ) x^3+\left (1-4 e^3+e^6\right ) x^2+2 \left (13-7 e^3+e^6\right ) x+\left (-4+e^3\right )^2\right )^2}dx+\frac {17-8 e^3+e^6}{2 \left (x^4-2 \left (3-e^3\right ) x^3+\left (1-4 e^3+e^6\right ) x^2+2 \left (13-7 e^3+e^6\right ) x+\left (e^3-4\right )^2\right )}\) |
Input:
Int[(32*x + 26*x^2 + 6*x^4 - 2*x^5 + E^6*(2*x + 2*x^2) + E^3*(-16*x - 14*x ^2 - 2*x^4))/(256 + 832*x + 708*x^2 - 140*x^3 - 279*x^4 + 40*x^5 + 38*x^6 - 12*x^7 + x^8 + E^12*(1 + 4*x + 6*x^2 + 4*x^3 + x^4) + E^9*(-16 - 60*x - 80*x^2 - 40*x^3 + 4*x^5) + E^6*(96 + 340*x + 398*x^2 + 124*x^3 - 60*x^4 - 24*x^5 + 6*x^6) + E^3*(-256 - 864*x - 872*x^2 - 76*x^3 + 248*x^4 + 24*x^5 - 32*x^6 + 4*x^7)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(23)=46\).
Time = 0.91 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.46
| method | result | size |
| risch | \(\frac {x^{2}}{x^{2} {\mathrm e}^{6}+2 x^{3} {\mathrm e}^{3}+x^{4}+2 x \,{\mathrm e}^{6}-4 x^{2} {\mathrm e}^{3}-6 x^{3}+{\mathrm e}^{6}-14 x \,{\mathrm e}^{3}+x^{2}-8 \,{\mathrm e}^{3}+26 x +16}\) | \(59\) |
| gosper | \(\frac {x^{2}}{x^{2} {\mathrm e}^{6}+2 x^{3} {\mathrm e}^{3}+x^{4}+2 x \,{\mathrm e}^{6}-4 x^{2} {\mathrm e}^{3}-6 x^{3}+{\mathrm e}^{6}-14 x \,{\mathrm e}^{3}+x^{2}-8 \,{\mathrm e}^{3}+26 x +16}\) | \(65\) |
| norman | \(\frac {x^{2}}{x^{2} {\mathrm e}^{6}+2 x^{3} {\mathrm e}^{3}+x^{4}+2 x \,{\mathrm e}^{6}-4 x^{2} {\mathrm e}^{3}-6 x^{3}+{\mathrm e}^{6}-14 x \,{\mathrm e}^{3}+x^{2}-8 \,{\mathrm e}^{3}+26 x +16}\) | \(65\) |
| parallelrisch | \(\frac {x^{2}}{x^{2} {\mathrm e}^{6}+2 x^{3} {\mathrm e}^{3}+x^{4}+2 x \,{\mathrm e}^{6}-4 x^{2} {\mathrm e}^{3}-6 x^{3}+{\mathrm e}^{6}-14 x \,{\mathrm e}^{3}+x^{2}-8 \,{\mathrm e}^{3}+26 x +16}\) | \(65\) |
| default | \(\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{8}+\left (4 \,{\mathrm e}^{3}-12\right ) \textit {\_Z}^{7}+\left (6 \,{\mathrm e}^{6}-32 \,{\mathrm e}^{3}+38\right ) \textit {\_Z}^{6}+\left (4 \,{\mathrm e}^{9}-24 \,{\mathrm e}^{6}+24 \,{\mathrm e}^{3}+40\right ) \textit {\_Z}^{5}+\left ({\mathrm e}^{12}-60 \,{\mathrm e}^{6}+248 \,{\mathrm e}^{3}-279\right ) \textit {\_Z}^{4}+\left (4 \,{\mathrm e}^{12}-40 \,{\mathrm e}^{9}+124 \,{\mathrm e}^{6}-76 \,{\mathrm e}^{3}-140\right ) \textit {\_Z}^{3}+\left (6 \,{\mathrm e}^{12}-80 \,{\mathrm e}^{9}+398 \,{\mathrm e}^{6}-872 \,{\mathrm e}^{3}+708\right ) \textit {\_Z}^{2}+\left (4 \,{\mathrm e}^{12}-60 \,{\mathrm e}^{9}+340 \,{\mathrm e}^{6}-864 \,{\mathrm e}^{3}+832\right ) \textit {\_Z} +256+{\mathrm e}^{12}+96 \,{\mathrm e}^{6}-16 \,{\mathrm e}^{9}-256 \,{\mathrm e}^{3}\right )}{\sum }\frac {\left (-\textit {\_R}^{5}+\left (-{\mathrm e}^{3}+3\right ) \textit {\_R}^{4}+\left ({\mathrm e}^{6}-7 \,{\mathrm e}^{3}+13\right ) \textit {\_R}^{2}+\left (16+{\mathrm e}^{6}-8 \,{\mathrm e}^{3}\right ) \textit {\_R} \right ) \ln \left (x -\textit {\_R} \right )}{208+354 \textit {\_R} -105 \textit {\_R}^{2}-436 \textit {\_R} \,{\mathrm e}^{3}+{\mathrm e}^{12}+85 \,{\mathrm e}^{6}-15 \,{\mathrm e}^{9}-216 \,{\mathrm e}^{3}+5 \textit {\_R}^{4} {\mathrm e}^{9}-48 \textit {\_R}^{5} {\mathrm e}^{3}+7 \,{\mathrm e}^{3} \textit {\_R}^{6}+30 \textit {\_R}^{4} {\mathrm e}^{3}-30 \textit {\_R}^{4} {\mathrm e}^{6}+9 \,{\mathrm e}^{6} \textit {\_R}^{5}+3 \,{\mathrm e}^{12} \textit {\_R}^{2}+\textit {\_R}^{3} {\mathrm e}^{12}+3 \textit {\_R} \,{\mathrm e}^{12}-30 \,{\mathrm e}^{9} \textit {\_R}^{2}-60 \textit {\_R}^{3} {\mathrm e}^{6}-40 \textit {\_R} \,{\mathrm e}^{9}+93 \textit {\_R}^{2} {\mathrm e}^{6}+248 \textit {\_R}^{3} {\mathrm e}^{3}+199 \textit {\_R} \,{\mathrm e}^{6}-57 \textit {\_R}^{2} {\mathrm e}^{3}-279 \textit {\_R}^{3}+57 \textit {\_R}^{5}+2 \textit {\_R}^{7}-21 \textit {\_R}^{6}+50 \textit {\_R}^{4}}\right )}{2}\) | \(354\) |
Input:
int(((2*x^2+2*x)*exp(3)^2+(-2*x^4-14*x^2-16*x)*exp(3)-2*x^5+6*x^4+26*x^2+3 2*x)/((x^4+4*x^3+6*x^2+4*x+1)*exp(3)^4+(4*x^5-40*x^3-80*x^2-60*x-16)*exp(3 )^3+(6*x^6-24*x^5-60*x^4+124*x^3+398*x^2+340*x+96)*exp(3)^2+(4*x^7-32*x^6+ 24*x^5+248*x^4-76*x^3-872*x^2-864*x-256)*exp(3)+x^8-12*x^7+38*x^6+40*x^5-2 79*x^4-140*x^3+708*x^2+832*x+256),x,method=_RETURNVERBOSE)
Output:
x^2/(x^2*exp(6)+2*x^3*exp(3)+x^4+2*x*exp(6)-4*x^2*exp(3)-6*x^3+exp(6)-14*x *exp(3)+x^2-8*exp(3)+26*x+16)
Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (23) = 46\).
Time = 0.09 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.08 \[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx=\frac {x^{2}}{x^{4} - 6 \, x^{3} + x^{2} + {\left (x^{2} + 2 \, x + 1\right )} e^{6} + 2 \, {\left (x^{3} - 2 \, x^{2} - 7 \, x - 4\right )} e^{3} + 26 \, x + 16} \] Input:
integrate(((2*x^2+2*x)*exp(3)^2+(-2*x^4-14*x^2-16*x)*exp(3)-2*x^5+6*x^4+26 *x^2+32*x)/((x^4+4*x^3+6*x^2+4*x+1)*exp(3)^4+(4*x^5-40*x^3-80*x^2-60*x-16) *exp(3)^3+(6*x^6-24*x^5-60*x^4+124*x^3+398*x^2+340*x+96)*exp(3)^2+(4*x^7-3 2*x^6+24*x^5+248*x^4-76*x^3-872*x^2-864*x-256)*exp(3)+x^8-12*x^7+38*x^6+40 *x^5-279*x^4-140*x^3+708*x^2+832*x+256),x, algorithm="fricas")
Output:
x^2/(x^4 - 6*x^3 + x^2 + (x^2 + 2*x + 1)*e^6 + 2*(x^3 - 2*x^2 - 7*x - 4)*e ^3 + 26*x + 16)
Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (19) = 38\).
Time = 3.63 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.21 \[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx=\frac {x^{2}}{x^{4} + x^{3} \left (-6 + 2 e^{3}\right ) + x^{2} \left (- 4 e^{3} + 1 + e^{6}\right ) + x \left (- 14 e^{3} + 26 + 2 e^{6}\right ) - 8 e^{3} + 16 + e^{6}} \] Input:
integrate(((2*x**2+2*x)*exp(3)**2+(-2*x**4-14*x**2-16*x)*exp(3)-2*x**5+6*x **4+26*x**2+32*x)/((x**4+4*x**3+6*x**2+4*x+1)*exp(3)**4+(4*x**5-40*x**3-80 *x**2-60*x-16)*exp(3)**3+(6*x**6-24*x**5-60*x**4+124*x**3+398*x**2+340*x+9 6)*exp(3)**2+(4*x**7-32*x**6+24*x**5+248*x**4-76*x**3-872*x**2-864*x-256)* exp(3)+x**8-12*x**7+38*x**6+40*x**5-279*x**4-140*x**3+708*x**2+832*x+256), x)
Output:
x**2/(x**4 + x**3*(-6 + 2*exp(3)) + x**2*(-4*exp(3) + 1 + exp(6)) + x*(-14 *exp(3) + 26 + 2*exp(6)) - 8*exp(3) + 16 + exp(6))
Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (23) = 46\).
Time = 0.04 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.04 \[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx=\frac {x^{2}}{x^{4} + 2 \, x^{3} {\left (e^{3} - 3\right )} + x^{2} {\left (e^{6} - 4 \, e^{3} + 1\right )} + 2 \, x {\left (e^{6} - 7 \, e^{3} + 13\right )} + e^{6} - 8 \, e^{3} + 16} \] Input:
integrate(((2*x^2+2*x)*exp(3)^2+(-2*x^4-14*x^2-16*x)*exp(3)-2*x^5+6*x^4+26 *x^2+32*x)/((x^4+4*x^3+6*x^2+4*x+1)*exp(3)^4+(4*x^5-40*x^3-80*x^2-60*x-16) *exp(3)^3+(6*x^6-24*x^5-60*x^4+124*x^3+398*x^2+340*x+96)*exp(3)^2+(4*x^7-3 2*x^6+24*x^5+248*x^4-76*x^3-872*x^2-864*x-256)*exp(3)+x^8-12*x^7+38*x^6+40 *x^5-279*x^4-140*x^3+708*x^2+832*x+256),x, algorithm="maxima")
Output:
x^2/(x^4 + 2*x^3*(e^3 - 3) + x^2*(e^6 - 4*e^3 + 1) + 2*x*(e^6 - 7*e^3 + 13 ) + e^6 - 8*e^3 + 16)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (23) = 46\).
Time = 0.13 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.42 \[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx=\frac {x^{2}}{x^{4} + 2 \, x^{3} e^{3} - 6 \, x^{3} + x^{2} e^{6} - 4 \, x^{2} e^{3} + x^{2} + 2 \, x e^{6} - 14 \, x e^{3} + 26 \, x + e^{6} - 8 \, e^{3} + 16} \] Input:
integrate(((2*x^2+2*x)*exp(3)^2+(-2*x^4-14*x^2-16*x)*exp(3)-2*x^5+6*x^4+26 *x^2+32*x)/((x^4+4*x^3+6*x^2+4*x+1)*exp(3)^4+(4*x^5-40*x^3-80*x^2-60*x-16) *exp(3)^3+(6*x^6-24*x^5-60*x^4+124*x^3+398*x^2+340*x+96)*exp(3)^2+(4*x^7-3 2*x^6+24*x^5+248*x^4-76*x^3-872*x^2-864*x-256)*exp(3)+x^8-12*x^7+38*x^6+40 *x^5-279*x^4-140*x^3+708*x^2+832*x+256),x, algorithm="giac")
Output:
x^2/(x^4 + 2*x^3*e^3 - 6*x^3 + x^2*e^6 - 4*x^2*e^3 + x^2 + 2*x*e^6 - 14*x* e^3 + 26*x + e^6 - 8*e^3 + 16)
Time = 4.46 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12 \[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx=\frac {x^2}{x^4+\left (2\,{\mathrm {e}}^3-6\right )\,x^3+\left ({\mathrm {e}}^6-4\,{\mathrm {e}}^3+1\right )\,x^2+\left (2\,{\mathrm {e}}^6-14\,{\mathrm {e}}^3+26\right )\,x-8\,{\mathrm {e}}^3+{\mathrm {e}}^6+16} \] Input:
int((32*x + exp(6)*(2*x + 2*x^2) - exp(3)*(16*x + 14*x^2 + 2*x^4) + 26*x^2 + 6*x^4 - 2*x^5)/(832*x + exp(6)*(340*x + 398*x^2 + 124*x^3 - 60*x^4 - 24 *x^5 + 6*x^6 + 96) + exp(12)*(4*x + 6*x^2 + 4*x^3 + x^4 + 1) - exp(3)*(864 *x + 872*x^2 + 76*x^3 - 248*x^4 - 24*x^5 + 32*x^6 - 4*x^7 + 256) - exp(9)* (60*x + 80*x^2 + 40*x^3 - 4*x^5 + 16) + 708*x^2 - 140*x^3 - 279*x^4 + 40*x ^5 + 38*x^6 - 12*x^7 + x^8 + 256),x)
Output:
x^2/(exp(6) - 8*exp(3) + x^3*(2*exp(3) - 6) + x*(2*exp(6) - 14*exp(3) + 26 ) + x^2*(exp(6) - 4*exp(3) + 1) + x^4 + 16)
Time = 0.21 (sec) , antiderivative size = 176, normalized size of antiderivative = 7.33 \[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx=\frac {-2 e^{6} x -e^{6}-2 e^{3} x^{3}+14 e^{3} x -x^{4}+8 e^{3}+6 x^{3}-26 x -16}{e^{12} x^{2}+2 e^{12} x +e^{12}+2 e^{9} x^{3}-8 e^{9} x^{2}-22 e^{9} x +e^{6} x^{4}-12 e^{9}-14 e^{6} x^{3}+18 e^{6} x^{2}+84 e^{6} x -4 e^{3} x^{4}+49 e^{6}+26 e^{3} x^{3}-8 e^{3} x^{2}-118 e^{3} x +x^{4}-72 e^{3}-6 x^{3}+x^{2}+26 x +16} \] Input:
int(((2*x^2+2*x)*exp(3)^2+(-2*x^4-14*x^2-16*x)*exp(3)-2*x^5+6*x^4+26*x^2+3 2*x)/((x^4+4*x^3+6*x^2+4*x+1)*exp(3)^4+(4*x^5-40*x^3-80*x^2-60*x-16)*exp(3 )^3+(6*x^6-24*x^5-60*x^4+124*x^3+398*x^2+340*x+96)*exp(3)^2+(4*x^7-32*x^6+ 24*x^5+248*x^4-76*x^3-872*x^2-864*x-256)*exp(3)+x^8-12*x^7+38*x^6+40*x^5-2 79*x^4-140*x^3+708*x^2+832*x+256),x)
Output:
( - 2*e**6*x - e**6 - 2*e**3*x**3 + 14*e**3*x + 8*e**3 - x**4 + 6*x**3 - 2 6*x - 16)/(e**12*x**2 + 2*e**12*x + e**12 + 2*e**9*x**3 - 8*e**9*x**2 - 22 *e**9*x - 12*e**9 + e**6*x**4 - 14*e**6*x**3 + 18*e**6*x**2 + 84*e**6*x + 49*e**6 - 4*e**3*x**4 + 26*e**3*x**3 - 8*e**3*x**2 - 118*e**3*x - 72*e**3 + x**4 - 6*x**3 + x**2 + 26*x + 16)