Integrand size = 245, antiderivative size = 36 \[ \int \frac {-48-160 x-144 x^2-80 x^3-264 x^4-320 x^5-220 x^6-120 x^7-36 x^8+e^{2 x} \left (-32 x^2-96 x^3-88 x^4-48 x^5-36 x^6\right )+e^x \left (32+128 x+80 x^2+208 x^3+368 x^4+272 x^5+168 x^6+72 x^7\right )}{36 x^2+120 x^3+148 x^4+20 x^5-120 x^6-100 x^7+x^8+30 x^9+9 x^{10}+e^{2 x} \left (16 x^2+48 x^3+20 x^4-48 x^5-32 x^6+12 x^7+9 x^8\right )+e^x \left (-48 x^2-152 x^3-128 x^4+68 x^5+160 x^6+40 x^7-42 x^8-18 x^9\right )} \, dx=\frac {4}{x-\frac {2 x}{x^2-\frac {1}{\left (1-e^x+x\right ) \left (1+\frac {3 x}{2}\right )}}} \] Output:
4/(x-2*x/(x^2-1/(1+3/2*x)/(1-exp(x)+x)))
Time = 9.39 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.69 \[ \int \frac {-48-160 x-144 x^2-80 x^3-264 x^4-320 x^5-220 x^6-120 x^7-36 x^8+e^{2 x} \left (-32 x^2-96 x^3-88 x^4-48 x^5-36 x^6\right )+e^x \left (32+128 x+80 x^2+208 x^3+368 x^4+272 x^5+168 x^6+72 x^7\right )}{36 x^2+120 x^3+148 x^4+20 x^5-120 x^6-100 x^7+x^8+30 x^9+9 x^{10}+e^{2 x} \left (16 x^2+48 x^3+20 x^4-48 x^5-32 x^6+12 x^7+9 x^8\right )+e^x \left (-48 x^2-152 x^3-128 x^4+68 x^5+160 x^6+40 x^7-42 x^8-18 x^9\right )} \, dx=-\frac {4 \left (-x^2+\frac {4}{6+10 x+4 x^2-5 x^3-3 x^4+e^x \left (-4-6 x+2 x^2+3 x^3\right )}\right )}{x \left (-2+x^2\right )} \] Input:
Integrate[(-48 - 160*x - 144*x^2 - 80*x^3 - 264*x^4 - 320*x^5 - 220*x^6 - 120*x^7 - 36*x^8 + E^(2*x)*(-32*x^2 - 96*x^3 - 88*x^4 - 48*x^5 - 36*x^6) + E^x*(32 + 128*x + 80*x^2 + 208*x^3 + 368*x^4 + 272*x^5 + 168*x^6 + 72*x^7 ))/(36*x^2 + 120*x^3 + 148*x^4 + 20*x^5 - 120*x^6 - 100*x^7 + x^8 + 30*x^9 + 9*x^10 + E^(2*x)*(16*x^2 + 48*x^3 + 20*x^4 - 48*x^5 - 32*x^6 + 12*x^7 + 9*x^8) + E^x*(-48*x^2 - 152*x^3 - 128*x^4 + 68*x^5 + 160*x^6 + 40*x^7 - 4 2*x^8 - 18*x^9)),x]
Output:
(-4*(-x^2 + 4/(6 + 10*x + 4*x^2 - 5*x^3 - 3*x^4 + E^x*(-4 - 6*x + 2*x^2 + 3*x^3))))/(x*(-2 + 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.
| \(\displaystyle \int \frac {-36 x^8-120 x^7-220 x^6-320 x^5-264 x^4-80 x^3-144 x^2+e^{2 x} \left (-36 x^6-48 x^5-88 x^4-96 x^3-32 x^2\right )+e^x \left (72 x^7+168 x^6+272 x^5+368 x^4+208 x^3+80 x^2+128 x+32\right )-160 x-48}{9 x^{10}+30 x^9+x^8-100 x^7-120 x^6+20 x^5+148 x^4+120 x^3+36 x^2+e^{2 x} \left (9 x^8+12 x^7-32 x^6-48 x^5+20 x^4+48 x^3+16 x^2\right )+e^x \left (-18 x^9-42 x^8+40 x^7+160 x^6+68 x^5-128 x^4-152 x^3-48 x^2\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-36 x^8-120 x^7-220 x^6-320 x^5-264 x^4-80 x^3-144 x^2+e^{2 x} \left (-36 x^6-48 x^5-88 x^4-96 x^3-32 x^2\right )+e^x \left (72 x^7+168 x^6+272 x^5+368 x^4+208 x^3+80 x^2+128 x+32\right )-160 x-48}{x^2 \left (-3 x^4+3 e^x x^3-5 x^3+2 e^x x^2+4 x^2-6 e^x x+10 x-4 e^x+6\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {4 \left (x^2+2\right )}{\left (x^2-2\right )^2}-\frac {16 \left (3 x^4+20 x^3+4 x^2-16 x-4\right )}{x^2 (3 x+2) \left (x^2-2\right )^2 \left (3 x^4-3 e^x x^3+5 x^3-2 e^x x^2-4 x^2+6 e^x x-10 x+4 e^x-6\right )}+\frac {16 \left (9 x^7+12 x^6-32 x^5-48 x^4+14 x^3+26 x^2+20 x+20\right )}{x (3 x+2) \left (x^2-2\right )^2 \left (3 x^4-3 e^x x^3+5 x^3-2 e^x x^2-4 x^2+6 e^x x-10 x+4 e^x-6\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (-\frac {4 \left (x^2+2\right )}{\left (x^2-2\right )^2}-\frac {16 \left (3 x^4+20 x^3+4 x^2-16 x-4\right )}{x^2 (3 x+2) \left (x^2-2\right )^2 \left (3 x^4-3 e^x x^3+5 x^3-2 e^x x^2-4 x^2+6 e^x x-10 x+4 e^x-6\right )}+\frac {16 \left (9 x^7+12 x^6-32 x^5-48 x^4+14 x^3+26 x^2+20 x+20\right )}{x (3 x+2) \left (x^2-2\right )^2 \left (3 x^4-3 e^x x^3+5 x^3-2 e^x x^2-4 x^2+6 e^x x-10 x+4 e^x-6\right )^2}\right )dx\) |
Input:
Int[(-48 - 160*x - 144*x^2 - 80*x^3 - 264*x^4 - 320*x^5 - 220*x^6 - 120*x^ 7 - 36*x^8 + E^(2*x)*(-32*x^2 - 96*x^3 - 88*x^4 - 48*x^5 - 36*x^6) + E^x*( 32 + 128*x + 80*x^2 + 208*x^3 + 368*x^4 + 272*x^5 + 168*x^6 + 72*x^7))/(36 *x^2 + 120*x^3 + 148*x^4 + 20*x^5 - 120*x^6 - 100*x^7 + x^8 + 30*x^9 + 9*x ^10 + E^(2*x)*(16*x^2 + 48*x^3 + 20*x^4 - 48*x^5 - 32*x^6 + 12*x^7 + 9*x^8 ) + E^x*(-48*x^2 - 152*x^3 - 128*x^4 + 68*x^5 + 160*x^6 + 40*x^7 - 42*x^8 - 18*x^9)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(68\) vs. \(2(33)=66\).
Time = 1.25 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.92
| method | result | size |
| risch | \(\frac {4 x}{x^{2}-2}+\frac {16}{\left (x^{2}-2\right ) x \left (3 x^{4}-3 \,{\mathrm e}^{x} x^{3}+5 x^{3}-2 \,{\mathrm e}^{x} x^{2}-4 x^{2}+6 \,{\mathrm e}^{x} x -10 x +4 \,{\mathrm e}^{x}-6\right )}\) | \(69\) |
| norman | \(\frac {-8+8 x^{2}+12 x^{4}+20 x^{3}-12 \,{\mathrm e}^{x} x^{3}-8 \,{\mathrm e}^{x} x^{2}}{x \left (3 x^{4}-3 \,{\mathrm e}^{x} x^{3}+5 x^{3}-2 \,{\mathrm e}^{x} x^{2}-4 x^{2}+6 \,{\mathrm e}^{x} x -10 x +4 \,{\mathrm e}^{x}-6\right )}\) | \(81\) |
| parallelrisch | \(-\frac {24-36 x^{4}+36 \,{\mathrm e}^{x} x^{3}-60 x^{3}+24 \,{\mathrm e}^{x} x^{2}-24 x^{2}}{3 x \left (3 x^{4}-3 \,{\mathrm e}^{x} x^{3}+5 x^{3}-2 \,{\mathrm e}^{x} x^{2}-4 x^{2}+6 \,{\mathrm e}^{x} x -10 x +4 \,{\mathrm e}^{x}-6\right )}\) | \(82\) |
Input:
int(((-36*x^6-48*x^5-88*x^4-96*x^3-32*x^2)*exp(x)^2+(72*x^7+168*x^6+272*x^ 5+368*x^4+208*x^3+80*x^2+128*x+32)*exp(x)-36*x^8-120*x^7-220*x^6-320*x^5-2 64*x^4-80*x^3-144*x^2-160*x-48)/((9*x^8+12*x^7-32*x^6-48*x^5+20*x^4+48*x^3 +16*x^2)*exp(x)^2+(-18*x^9-42*x^8+40*x^7+160*x^6+68*x^5-128*x^4-152*x^3-48 *x^2)*exp(x)+9*x^10+30*x^9+x^8-100*x^7-120*x^6+20*x^5+148*x^4+120*x^3+36*x ^2),x,method=_RETURNVERBOSE)
Output:
4*x/(x^2-2)+16/(x^2-2)/x/(3*x^4-3*exp(x)*x^3+5*x^3-2*exp(x)*x^2-4*x^2+6*ex p(x)*x-10*x+4*exp(x)-6)
Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (33) = 66\).
Time = 0.09 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.31 \[ \int \frac {-48-160 x-144 x^2-80 x^3-264 x^4-320 x^5-220 x^6-120 x^7-36 x^8+e^{2 x} \left (-32 x^2-96 x^3-88 x^4-48 x^5-36 x^6\right )+e^x \left (32+128 x+80 x^2+208 x^3+368 x^4+272 x^5+168 x^6+72 x^7\right )}{36 x^2+120 x^3+148 x^4+20 x^5-120 x^6-100 x^7+x^8+30 x^9+9 x^{10}+e^{2 x} \left (16 x^2+48 x^3+20 x^4-48 x^5-32 x^6+12 x^7+9 x^8\right )+e^x \left (-48 x^2-152 x^3-128 x^4+68 x^5+160 x^6+40 x^7-42 x^8-18 x^9\right )} \, dx=\frac {4 \, {\left (3 \, x^{4} + 5 \, x^{3} + 2 \, x^{2} - {\left (3 \, x^{3} + 2 \, x^{2}\right )} e^{x} - 2\right )}}{3 \, x^{5} + 5 \, x^{4} - 4 \, x^{3} - 10 \, x^{2} - {\left (3 \, x^{4} + 2 \, x^{3} - 6 \, x^{2} - 4 \, x\right )} e^{x} - 6 \, x} \] Input:
integrate(((-36*x^6-48*x^5-88*x^4-96*x^3-32*x^2)*exp(x)^2+(72*x^7+168*x^6+ 272*x^5+368*x^4+208*x^3+80*x^2+128*x+32)*exp(x)-36*x^8-120*x^7-220*x^6-320 *x^5-264*x^4-80*x^3-144*x^2-160*x-48)/((9*x^8+12*x^7-32*x^6-48*x^5+20*x^4+ 48*x^3+16*x^2)*exp(x)^2+(-18*x^9-42*x^8+40*x^7+160*x^6+68*x^5-128*x^4-152* x^3-48*x^2)*exp(x)+9*x^10+30*x^9+x^8-100*x^7-120*x^6+20*x^5+148*x^4+120*x^ 3+36*x^2),x, algorithm="fricas")
Output:
4*(3*x^4 + 5*x^3 + 2*x^2 - (3*x^3 + 2*x^2)*e^x - 2)/(3*x^5 + 5*x^4 - 4*x^3 - 10*x^2 - (3*x^4 + 2*x^3 - 6*x^2 - 4*x)*e^x - 6*x)
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (24) = 48\).
Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.08 \[ \int \frac {-48-160 x-144 x^2-80 x^3-264 x^4-320 x^5-220 x^6-120 x^7-36 x^8+e^{2 x} \left (-32 x^2-96 x^3-88 x^4-48 x^5-36 x^6\right )+e^x \left (32+128 x+80 x^2+208 x^3+368 x^4+272 x^5+168 x^6+72 x^7\right )}{36 x^2+120 x^3+148 x^4+20 x^5-120 x^6-100 x^7+x^8+30 x^9+9 x^{10}+e^{2 x} \left (16 x^2+48 x^3+20 x^4-48 x^5-32 x^6+12 x^7+9 x^8\right )+e^x \left (-48 x^2-152 x^3-128 x^4+68 x^5+160 x^6+40 x^7-42 x^8-18 x^9\right )} \, dx=\frac {4 x}{x^{2} - 2} - \frac {16}{- 3 x^{7} - 5 x^{6} + 10 x^{5} + 20 x^{4} - 2 x^{3} - 20 x^{2} - 12 x + \left (3 x^{6} + 2 x^{5} - 12 x^{4} - 8 x^{3} + 12 x^{2} + 8 x\right ) e^{x}} \] Input:
integrate(((-36*x**6-48*x**5-88*x**4-96*x**3-32*x**2)*exp(x)**2+(72*x**7+1 68*x**6+272*x**5+368*x**4+208*x**3+80*x**2+128*x+32)*exp(x)-36*x**8-120*x* *7-220*x**6-320*x**5-264*x**4-80*x**3-144*x**2-160*x-48)/((9*x**8+12*x**7- 32*x**6-48*x**5+20*x**4+48*x**3+16*x**2)*exp(x)**2+(-18*x**9-42*x**8+40*x* *7+160*x**6+68*x**5-128*x**4-152*x**3-48*x**2)*exp(x)+9*x**10+30*x**9+x**8 -100*x**7-120*x**6+20*x**5+148*x**4+120*x**3+36*x**2),x)
Output:
4*x/(x**2 - 2) - 16/(-3*x**7 - 5*x**6 + 10*x**5 + 20*x**4 - 2*x**3 - 20*x* *2 - 12*x + (3*x**6 + 2*x**5 - 12*x**4 - 8*x**3 + 12*x**2 + 8*x)*exp(x))
Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (33) = 66\).
Time = 0.17 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.31 \[ \int \frac {-48-160 x-144 x^2-80 x^3-264 x^4-320 x^5-220 x^6-120 x^7-36 x^8+e^{2 x} \left (-32 x^2-96 x^3-88 x^4-48 x^5-36 x^6\right )+e^x \left (32+128 x+80 x^2+208 x^3+368 x^4+272 x^5+168 x^6+72 x^7\right )}{36 x^2+120 x^3+148 x^4+20 x^5-120 x^6-100 x^7+x^8+30 x^9+9 x^{10}+e^{2 x} \left (16 x^2+48 x^3+20 x^4-48 x^5-32 x^6+12 x^7+9 x^8\right )+e^x \left (-48 x^2-152 x^3-128 x^4+68 x^5+160 x^6+40 x^7-42 x^8-18 x^9\right )} \, dx=\frac {4 \, {\left (3 \, x^{4} + 5 \, x^{3} + 2 \, x^{2} - {\left (3 \, x^{3} + 2 \, x^{2}\right )} e^{x} - 2\right )}}{3 \, x^{5} + 5 \, x^{4} - 4 \, x^{3} - 10 \, x^{2} - {\left (3 \, x^{4} + 2 \, x^{3} - 6 \, x^{2} - 4 \, x\right )} e^{x} - 6 \, x} \] Input:
integrate(((-36*x^6-48*x^5-88*x^4-96*x^3-32*x^2)*exp(x)^2+(72*x^7+168*x^6+ 272*x^5+368*x^4+208*x^3+80*x^2+128*x+32)*exp(x)-36*x^8-120*x^7-220*x^6-320 *x^5-264*x^4-80*x^3-144*x^2-160*x-48)/((9*x^8+12*x^7-32*x^6-48*x^5+20*x^4+ 48*x^3+16*x^2)*exp(x)^2+(-18*x^9-42*x^8+40*x^7+160*x^6+68*x^5-128*x^4-152* x^3-48*x^2)*exp(x)+9*x^10+30*x^9+x^8-100*x^7-120*x^6+20*x^5+148*x^4+120*x^ 3+36*x^2),x, algorithm="maxima")
Output:
4*(3*x^4 + 5*x^3 + 2*x^2 - (3*x^3 + 2*x^2)*e^x - 2)/(3*x^5 + 5*x^4 - 4*x^3 - 10*x^2 - (3*x^4 + 2*x^3 - 6*x^2 - 4*x)*e^x - 6*x)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (33) = 66\).
Time = 0.16 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.36 \[ \int \frac {-48-160 x-144 x^2-80 x^3-264 x^4-320 x^5-220 x^6-120 x^7-36 x^8+e^{2 x} \left (-32 x^2-96 x^3-88 x^4-48 x^5-36 x^6\right )+e^x \left (32+128 x+80 x^2+208 x^3+368 x^4+272 x^5+168 x^6+72 x^7\right )}{36 x^2+120 x^3+148 x^4+20 x^5-120 x^6-100 x^7+x^8+30 x^9+9 x^{10}+e^{2 x} \left (16 x^2+48 x^3+20 x^4-48 x^5-32 x^6+12 x^7+9 x^8\right )+e^x \left (-48 x^2-152 x^3-128 x^4+68 x^5+160 x^6+40 x^7-42 x^8-18 x^9\right )} \, dx=\frac {4 \, {\left (3 \, x^{4} - 3 \, x^{3} e^{x} + 5 \, x^{3} - 2 \, x^{2} e^{x} + 2 \, x^{2} - 2\right )}}{3 \, x^{5} - 3 \, x^{4} e^{x} + 5 \, x^{4} - 2 \, x^{3} e^{x} - 4 \, x^{3} + 6 \, x^{2} e^{x} - 10 \, x^{2} + 4 \, x e^{x} - 6 \, x} \] Input:
integrate(((-36*x^6-48*x^5-88*x^4-96*x^3-32*x^2)*exp(x)^2+(72*x^7+168*x^6+ 272*x^5+368*x^4+208*x^3+80*x^2+128*x+32)*exp(x)-36*x^8-120*x^7-220*x^6-320 *x^5-264*x^4-80*x^3-144*x^2-160*x-48)/((9*x^8+12*x^7-32*x^6-48*x^5+20*x^4+ 48*x^3+16*x^2)*exp(x)^2+(-18*x^9-42*x^8+40*x^7+160*x^6+68*x^5-128*x^4-152* x^3-48*x^2)*exp(x)+9*x^10+30*x^9+x^8-100*x^7-120*x^6+20*x^5+148*x^4+120*x^ 3+36*x^2),x, algorithm="giac")
Output:
4*(3*x^4 - 3*x^3*e^x + 5*x^3 - 2*x^2*e^x + 2*x^2 - 2)/(3*x^5 - 3*x^4*e^x + 5*x^4 - 2*x^3*e^x - 4*x^3 + 6*x^2*e^x - 10*x^2 + 4*x*e^x - 6*x)
Time = 3.24 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.11 \[ \int \frac {-48-160 x-144 x^2-80 x^3-264 x^4-320 x^5-220 x^6-120 x^7-36 x^8+e^{2 x} \left (-32 x^2-96 x^3-88 x^4-48 x^5-36 x^6\right )+e^x \left (32+128 x+80 x^2+208 x^3+368 x^4+272 x^5+168 x^6+72 x^7\right )}{36 x^2+120 x^3+148 x^4+20 x^5-120 x^6-100 x^7+x^8+30 x^9+9 x^{10}+e^{2 x} \left (16 x^2+48 x^3+20 x^4-48 x^5-32 x^6+12 x^7+9 x^8\right )+e^x \left (-48 x^2-152 x^3-128 x^4+68 x^5+160 x^6+40 x^7-42 x^8-18 x^9\right )} \, dx=\frac {x^2\,\left (8\,{\mathrm {e}}^x-8\right )+x^3\,\left (12\,{\mathrm {e}}^x-20\right )-12\,x^4+8}{x\,\left (10\,x-4\,{\mathrm {e}}^x+2\,x^2\,{\mathrm {e}}^x+3\,x^3\,{\mathrm {e}}^x-6\,x\,{\mathrm {e}}^x+4\,x^2-5\,x^3-3\,x^4+6\right )} \] Input:
int(-(160*x + exp(2*x)*(32*x^2 + 96*x^3 + 88*x^4 + 48*x^5 + 36*x^6) - exp( x)*(128*x + 80*x^2 + 208*x^3 + 368*x^4 + 272*x^5 + 168*x^6 + 72*x^7 + 32) + 144*x^2 + 80*x^3 + 264*x^4 + 320*x^5 + 220*x^6 + 120*x^7 + 36*x^8 + 48)/ (exp(2*x)*(16*x^2 + 48*x^3 + 20*x^4 - 48*x^5 - 32*x^6 + 12*x^7 + 9*x^8) - exp(x)*(48*x^2 + 152*x^3 + 128*x^4 - 68*x^5 - 160*x^6 - 40*x^7 + 42*x^8 + 18*x^9) + 36*x^2 + 120*x^3 + 148*x^4 + 20*x^5 - 120*x^6 - 100*x^7 + x^8 + 30*x^9 + 9*x^10),x)
Output:
(x^2*(8*exp(x) - 8) + x^3*(12*exp(x) - 20) - 12*x^4 + 8)/(x*(10*x - 4*exp( x) + 2*x^2*exp(x) + 3*x^3*exp(x) - 6*x*exp(x) + 4*x^2 - 5*x^3 - 3*x^4 + 6) )
Time = 0.17 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.42 \[ \int \frac {-48-160 x-144 x^2-80 x^3-264 x^4-320 x^5-220 x^6-120 x^7-36 x^8+e^{2 x} \left (-32 x^2-96 x^3-88 x^4-48 x^5-36 x^6\right )+e^x \left (32+128 x+80 x^2+208 x^3+368 x^4+272 x^5+168 x^6+72 x^7\right )}{36 x^2+120 x^3+148 x^4+20 x^5-120 x^6-100 x^7+x^8+30 x^9+9 x^{10}+e^{2 x} \left (16 x^2+48 x^3+20 x^4-48 x^5-32 x^6+12 x^7+9 x^8\right )+e^x \left (-48 x^2-152 x^3-128 x^4+68 x^5+160 x^6+40 x^7-42 x^8-18 x^9\right )} \, dx=\frac {12 e^{x} x^{3}+8 e^{x} x^{2}-12 x^{4}-20 x^{3}-8 x^{2}+8}{x \left (3 e^{x} x^{3}+2 e^{x} x^{2}-6 e^{x} x -4 e^{x}-3 x^{4}-5 x^{3}+4 x^{2}+10 x +6\right )} \] Input:
int(((-36*x^6-48*x^5-88*x^4-96*x^3-32*x^2)*exp(x)^2+(72*x^7+168*x^6+272*x^ 5+368*x^4+208*x^3+80*x^2+128*x+32)*exp(x)-36*x^8-120*x^7-220*x^6-320*x^5-2 64*x^4-80*x^3-144*x^2-160*x-48)/((9*x^8+12*x^7-32*x^6-48*x^5+20*x^4+48*x^3 +16*x^2)*exp(x)^2+(-18*x^9-42*x^8+40*x^7+160*x^6+68*x^5-128*x^4-152*x^3-48 *x^2)*exp(x)+9*x^10+30*x^9+x^8-100*x^7-120*x^6+20*x^5+148*x^4+120*x^3+36*x ^2),x)
Output:
(4*(3*e**x*x**3 + 2*e**x*x**2 - 3*x**4 - 5*x**3 - 2*x**2 + 2))/(x*(3*e**x* x**3 + 2*e**x*x**2 - 6*e**x*x - 4*e**x - 3*x**4 - 5*x**3 + 4*x**2 + 10*x + 6))