Integrand size = 197, antiderivative size = 37 \[ \int \frac {-78 x^3+36 x^4-3 x^5+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (-45 x+30 x^2-3 x^3\right )+e^{\frac {5+3 x^2}{3 x}} \left (-50-30 x-90 x^2+66 x^3-6 x^4\right )}{768 x^3-672 x^4+243 x^5-42 x^6+3 x^7+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (675 x-540 x^2+198 x^3-36 x^4+3 x^5\right )+e^{\frac {5+3 x^2}{3 x}} \left (1440 x^2-1206 x^3+438 x^4-78 x^5+6 x^6\right )} \, dx=\frac {x}{-x+x^2+\frac {10 x}{-5+x-\frac {x}{e^{\frac {5}{3 x}+x}+x}}} \]
Time = 0.08 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.49 \[ \int \frac {-78 x^3+36 x^4-3 x^5+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (-45 x+30 x^2-3 x^3\right )+e^{\frac {5+3 x^2}{3 x}} \left (-50-30 x-90 x^2+66 x^3-6 x^4\right )}{768 x^3-672 x^4+243 x^5-42 x^6+3 x^7+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (675 x-540 x^2+198 x^3-36 x^4+3 x^5\right )+e^{\frac {5+3 x^2}{3 x}} \left (1440 x^2-1206 x^3+438 x^4-78 x^5+6 x^6\right )} \, dx=\frac {e^{\frac {5}{3 x}+x} (-5+x)+(-6+x) x}{x \left (16-7 x+x^2\right )+e^{\frac {5}{3 x}+x} \left (15-6 x+x^2\right )} \]
Integrate[(-78*x^3 + 36*x^4 - 3*x^5 + E^((2*(5 + 3*x^2))/(3*x))*(-45*x + 3 0*x^2 - 3*x^3) + E^((5 + 3*x^2)/(3*x))*(-50 - 30*x - 90*x^2 + 66*x^3 - 6*x ^4))/(768*x^3 - 672*x^4 + 243*x^5 - 42*x^6 + 3*x^7 + E^((2*(5 + 3*x^2))/(3 *x))*(675*x - 540*x^2 + 198*x^3 - 36*x^4 + 3*x^5) + E^((5 + 3*x^2)/(3*x))* (1440*x^2 - 1206*x^3 + 438*x^4 - 78*x^5 + 6*x^6)),x]
(E^(5/(3*x) + x)*(-5 + x) + (-6 + x)*x)/(x*(16 - 7*x + x^2) + E^(5/(3*x) + x)*(15 - 6*x + 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.
| \(\displaystyle \int \frac {-3 x^5+36 x^4-78 x^3+e^{\frac {2 \left (3 x^2+5\right )}{3 x}} \left (-3 x^3+30 x^2-45 x\right )+e^{\frac {3 x^2+5}{3 x}} \left (-6 x^4+66 x^3-90 x^2-30 x-50\right )}{3 x^7-42 x^6+243 x^5-672 x^4+768 x^3+e^{\frac {2 \left (3 x^2+5\right )}{3 x}} \left (3 x^5-36 x^4+198 x^3-540 x^2+675 x\right )+e^{\frac {3 x^2+5}{3 x}} \left (6 x^6-78 x^5+438 x^4-1206 x^3+1440 x^2\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-3 e^{2 x+\frac {10}{3 x}} \left (x^2-10 x+15\right ) x-3 \left (x^2-12 x+26\right ) x^3-e^{x+\frac {5}{3 x}} \left (6 x^4-66 x^3+90 x^2+30 x+50\right )}{3 x \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{3} \int -\frac {3 \left (x^2-12 x+26\right ) x^3+3 e^{2 x+\frac {10}{3 x}} \left (x^2-10 x+15\right ) x+2 e^{x+\frac {5}{3 x}} \left (3 x^4-33 x^3+45 x^2+15 x+25\right )}{x \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{3} \int \frac {3 \left (x^2-12 x+26\right ) x^3+3 e^{2 x+\frac {10}{3 x}} \left (x^2-10 x+15\right ) x+2 e^{x+\frac {5}{3 x}} \left (3 x^4-33 x^3+45 x^2+15 x+25\right )}{x \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (\frac {3 \left (x^2-10 x+15\right )}{\left (x^2-6 x+15\right )^2}-\frac {10 \left (3 x^4-9 x^3+22 x^2-15 x-75\right )}{x \left (x^2-6 x+15\right )^2 \left (x^3+e^{x+\frac {5}{3 x}} x^2-7 x^2-6 e^{x+\frac {5}{3 x}} x+16 x+15 e^{x+\frac {5}{3 x}}\right )}+\frac {10 \left (3 x^6-42 x^5+250 x^4-751 x^3+985 x^2+285 x-1200\right )}{\left (x^2-6 x+15\right )^2 \left (x^3+e^{x+\frac {5}{3 x}} x^2-7 x^2-6 e^{x+\frac {5}{3 x}} x+16 x+15 e^{x+\frac {5}{3 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{3} \left (-\frac {3 (5-x)}{x^2-6 x+15}+200 \int \frac {1}{\left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx-1100 i \sqrt {\frac {2}{3}} \int \frac {1}{\left (-2 x+2 i \sqrt {6}+6\right ) \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx+60 \int \frac {x}{\left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx-30 \int \frac {x^2}{\left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx+275 \left (2-i \sqrt {6}\right ) \int \frac {1}{\left (2 x-2 i \sqrt {6}-6\right ) \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx+275 \left (2+i \sqrt {6}\right ) \int \frac {1}{\left (2 x+2 i \sqrt {6}-6\right ) \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx-1100 i \sqrt {\frac {2}{3}} \int \frac {1}{\left (2 x+2 i \sqrt {6}-6\right ) \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx-1800 \int \frac {x}{\left (x^2-6 x+15\right )^2 \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )^2}dx+35 i \sqrt {\frac {2}{3}} \int \frac {1}{\left (-2 x+2 i \sqrt {6}+6\right ) \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )}dx-\frac {10}{3} \int \frac {1}{x \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )}dx+\frac {50}{3} \left (2-i \sqrt {6}\right ) \int \frac {1}{\left (2 x-2 i \sqrt {6}-6\right ) \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )}dx+\frac {50}{3} \left (2+i \sqrt {6}\right ) \int \frac {1}{\left (2 x+2 i \sqrt {6}-6\right ) \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )}dx+35 i \sqrt {\frac {2}{3}} \int \frac {1}{\left (2 x+2 i \sqrt {6}-6\right ) \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )}dx-1800 \int \frac {1}{\left (x^2-6 x+15\right )^2 \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )}dx+360 \int \frac {x}{\left (x^2-6 x+15\right )^2 \left (x \left (x^2-7 x+16\right )+e^{x+\frac {5}{3 x}} \left (x^2-6 x+15\right )\right )}dx\right )\) |
Int[(-78*x^3 + 36*x^4 - 3*x^5 + E^((2*(5 + 3*x^2))/(3*x))*(-45*x + 30*x^2 - 3*x^3) + E^((5 + 3*x^2)/(3*x))*(-50 - 30*x - 90*x^2 + 66*x^3 - 6*x^4))/( 768*x^3 - 672*x^4 + 243*x^5 - 42*x^6 + 3*x^7 + E^((2*(5 + 3*x^2))/(3*x))*( 675*x - 540*x^2 + 198*x^3 - 36*x^4 + 3*x^5) + E^((5 + 3*x^2)/(3*x))*(1440* x^2 - 1206*x^3 + 438*x^4 - 78*x^5 + 6*x^6)),x]
3.1.67.3.1 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_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(90\) vs. \(2(34)=68\).
Time = 0.26 (sec) , antiderivative size = 91, normalized size of antiderivative = 2.46
| method | result | size |
| risch | \(\frac {-5+x}{x^{2}-6 x +15}-\frac {10 x}{\left (x^{2}-6 x +15\right ) \left ({\mathrm e}^{\frac {3 x^{2}+5}{3 x}} x^{2}+x^{3}-6 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}} x -7 x^{2}+15 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}}+16 x \right )}\) | \(91\) |
| norman | \(\frac {-6 x -5 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}}+x^{2}+{\mathrm e}^{\frac {3 x^{2}+5}{3 x}} x}{{\mathrm e}^{\frac {3 x^{2}+5}{3 x}} x^{2}+x^{3}-6 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}} x -7 x^{2}+15 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}}+16 x}\) | \(101\) |
| parallelrisch | \(\frac {3 x^{2}+3 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}} x -18 x -15 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}}}{3 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}} x^{2}+3 x^{3}-18 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}} x -21 x^{2}+45 \,{\mathrm e}^{\frac {3 x^{2}+5}{3 x}}+48 x}\) | \(105\) |
int(((-3*x^3+30*x^2-45*x)*exp(1/3*(3*x^2+5)/x)^2+(-6*x^4+66*x^3-90*x^2-30* x-50)*exp(1/3*(3*x^2+5)/x)-3*x^5+36*x^4-78*x^3)/((3*x^5-36*x^4+198*x^3-540 *x^2+675*x)*exp(1/3*(3*x^2+5)/x)^2+(6*x^6-78*x^5+438*x^4-1206*x^3+1440*x^2 )*exp(1/3*(3*x^2+5)/x)+3*x^7-42*x^6+243*x^5-672*x^4+768*x^3),x,method=_RET URNVERBOSE)
(-5+x)/(x^2-6*x+15)-10*x/(x^2-6*x+15)/(exp(1/3*(3*x^2+5)/x)*x^2+x^3-6*exp( 1/3*(3*x^2+5)/x)*x-7*x^2+15*exp(1/3*(3*x^2+5)/x)+16*x)
Time = 0.25 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.65 \[ \int \frac {-78 x^3+36 x^4-3 x^5+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (-45 x+30 x^2-3 x^3\right )+e^{\frac {5+3 x^2}{3 x}} \left (-50-30 x-90 x^2+66 x^3-6 x^4\right )}{768 x^3-672 x^4+243 x^5-42 x^6+3 x^7+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (675 x-540 x^2+198 x^3-36 x^4+3 x^5\right )+e^{\frac {5+3 x^2}{3 x}} \left (1440 x^2-1206 x^3+438 x^4-78 x^5+6 x^6\right )} \, dx=\frac {x^{2} + {\left (x - 5\right )} e^{\left (\frac {3 \, x^{2} + 5}{3 \, x}\right )} - 6 \, x}{x^{3} - 7 \, x^{2} + {\left (x^{2} - 6 \, x + 15\right )} e^{\left (\frac {3 \, x^{2} + 5}{3 \, x}\right )} + 16 \, x} \]
integrate(((-3*x^3+30*x^2-45*x)*exp(1/3*(3*x^2+5)/x)^2+(-6*x^4+66*x^3-90*x ^2-30*x-50)*exp(1/3*(3*x^2+5)/x)-3*x^5+36*x^4-78*x^3)/((3*x^5-36*x^4+198*x ^3-540*x^2+675*x)*exp(1/3*(3*x^2+5)/x)^2+(6*x^6-78*x^5+438*x^4-1206*x^3+14 40*x^2)*exp(1/3*(3*x^2+5)/x)+3*x^7-42*x^6+243*x^5-672*x^4+768*x^3),x, algo rithm=\
(x^2 + (x - 5)*e^(1/3*(3*x^2 + 5)/x) - 6*x)/(x^3 - 7*x^2 + (x^2 - 6*x + 15 )*e^(1/3*(3*x^2 + 5)/x) + 16*x)
Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (24) = 48\).
Time = 0.24 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.78 \[ \int \frac {-78 x^3+36 x^4-3 x^5+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (-45 x+30 x^2-3 x^3\right )+e^{\frac {5+3 x^2}{3 x}} \left (-50-30 x-90 x^2+66 x^3-6 x^4\right )}{768 x^3-672 x^4+243 x^5-42 x^6+3 x^7+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (675 x-540 x^2+198 x^3-36 x^4+3 x^5\right )+e^{\frac {5+3 x^2}{3 x}} \left (1440 x^2-1206 x^3+438 x^4-78 x^5+6 x^6\right )} \, dx=- \frac {10 x}{x^{5} - 13 x^{4} + 73 x^{3} - 201 x^{2} + 240 x + \left (x^{4} - 12 x^{3} + 66 x^{2} - 180 x + 225\right ) e^{\frac {x^{2} + \frac {5}{3}}{x}}} - \frac {5 - x}{x^{2} - 6 x + 15} \]
integrate(((-3*x**3+30*x**2-45*x)*exp(1/3*(3*x**2+5)/x)**2+(-6*x**4+66*x** 3-90*x**2-30*x-50)*exp(1/3*(3*x**2+5)/x)-3*x**5+36*x**4-78*x**3)/((3*x**5- 36*x**4+198*x**3-540*x**2+675*x)*exp(1/3*(3*x**2+5)/x)**2+(6*x**6-78*x**5+ 438*x**4-1206*x**3+1440*x**2)*exp(1/3*(3*x**2+5)/x)+3*x**7-42*x**6+243*x** 5-672*x**4+768*x**3),x)
-10*x/(x**5 - 13*x**4 + 73*x**3 - 201*x**2 + 240*x + (x**4 - 12*x**3 + 66* x**2 - 180*x + 225)*exp((x**2 + 5/3)/x)) - (5 - x)/(x**2 - 6*x + 15)
Time = 0.23 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.38 \[ \int \frac {-78 x^3+36 x^4-3 x^5+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (-45 x+30 x^2-3 x^3\right )+e^{\frac {5+3 x^2}{3 x}} \left (-50-30 x-90 x^2+66 x^3-6 x^4\right )}{768 x^3-672 x^4+243 x^5-42 x^6+3 x^7+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (675 x-540 x^2+198 x^3-36 x^4+3 x^5\right )+e^{\frac {5+3 x^2}{3 x}} \left (1440 x^2-1206 x^3+438 x^4-78 x^5+6 x^6\right )} \, dx=\frac {x^{2} + {\left (x - 5\right )} e^{\left (x + \frac {5}{3 \, x}\right )} - 6 \, x}{x^{3} - 7 \, x^{2} + {\left (x^{2} - 6 \, x + 15\right )} e^{\left (x + \frac {5}{3 \, x}\right )} + 16 \, x} \]
integrate(((-3*x^3+30*x^2-45*x)*exp(1/3*(3*x^2+5)/x)^2+(-6*x^4+66*x^3-90*x ^2-30*x-50)*exp(1/3*(3*x^2+5)/x)-3*x^5+36*x^4-78*x^3)/((3*x^5-36*x^4+198*x ^3-540*x^2+675*x)*exp(1/3*(3*x^2+5)/x)^2+(6*x^6-78*x^5+438*x^4-1206*x^3+14 40*x^2)*exp(1/3*(3*x^2+5)/x)+3*x^7-42*x^6+243*x^5-672*x^4+768*x^3),x, algo rithm=\
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (34) = 68\).
Time = 0.34 (sec) , antiderivative size = 100, normalized size of antiderivative = 2.70 \[ \int \frac {-78 x^3+36 x^4-3 x^5+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (-45 x+30 x^2-3 x^3\right )+e^{\frac {5+3 x^2}{3 x}} \left (-50-30 x-90 x^2+66 x^3-6 x^4\right )}{768 x^3-672 x^4+243 x^5-42 x^6+3 x^7+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (675 x-540 x^2+198 x^3-36 x^4+3 x^5\right )+e^{\frac {5+3 x^2}{3 x}} \left (1440 x^2-1206 x^3+438 x^4-78 x^5+6 x^6\right )} \, dx=\frac {x^{2} + x e^{\left (\frac {3 \, x^{2} + 5}{3 \, x}\right )} - 6 \, x - 5 \, e^{\left (\frac {3 \, x^{2} + 5}{3 \, x}\right )}}{x^{3} + x^{2} e^{\left (\frac {3 \, x^{2} + 5}{3 \, x}\right )} - 7 \, x^{2} - 6 \, x e^{\left (\frac {3 \, x^{2} + 5}{3 \, x}\right )} + 16 \, x + 15 \, e^{\left (\frac {3 \, x^{2} + 5}{3 \, x}\right )}} \]
integrate(((-3*x^3+30*x^2-45*x)*exp(1/3*(3*x^2+5)/x)^2+(-6*x^4+66*x^3-90*x ^2-30*x-50)*exp(1/3*(3*x^2+5)/x)-3*x^5+36*x^4-78*x^3)/((3*x^5-36*x^4+198*x ^3-540*x^2+675*x)*exp(1/3*(3*x^2+5)/x)^2+(6*x^6-78*x^5+438*x^4-1206*x^3+14 40*x^2)*exp(1/3*(3*x^2+5)/x)+3*x^7-42*x^6+243*x^5-672*x^4+768*x^3),x, algo rithm=\
(x^2 + x*e^(1/3*(3*x^2 + 5)/x) - 6*x - 5*e^(1/3*(3*x^2 + 5)/x))/(x^3 + x^2 *e^(1/3*(3*x^2 + 5)/x) - 7*x^2 - 6*x*e^(1/3*(3*x^2 + 5)/x) + 16*x + 15*e^( 1/3*(3*x^2 + 5)/x))
Timed out. \[ \int \frac {-78 x^3+36 x^4-3 x^5+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (-45 x+30 x^2-3 x^3\right )+e^{\frac {5+3 x^2}{3 x}} \left (-50-30 x-90 x^2+66 x^3-6 x^4\right )}{768 x^3-672 x^4+243 x^5-42 x^6+3 x^7+e^{\frac {2 \left (5+3 x^2\right )}{3 x}} \left (675 x-540 x^2+198 x^3-36 x^4+3 x^5\right )+e^{\frac {5+3 x^2}{3 x}} \left (1440 x^2-1206 x^3+438 x^4-78 x^5+6 x^6\right )} \, dx=\int -\frac {{\mathrm {e}}^{\frac {x^2+\frac {5}{3}}{x}}\,\left (6\,x^4-66\,x^3+90\,x^2+30\,x+50\right )+{\mathrm {e}}^{\frac {2\,\left (x^2+\frac {5}{3}\right )}{x}}\,\left (3\,x^3-30\,x^2+45\,x\right )+78\,x^3-36\,x^4+3\,x^5}{{\mathrm {e}}^{\frac {2\,\left (x^2+\frac {5}{3}\right )}{x}}\,\left (3\,x^5-36\,x^4+198\,x^3-540\,x^2+675\,x\right )+{\mathrm {e}}^{\frac {x^2+\frac {5}{3}}{x}}\,\left (6\,x^6-78\,x^5+438\,x^4-1206\,x^3+1440\,x^2\right )+768\,x^3-672\,x^4+243\,x^5-42\,x^6+3\,x^7} \,d x \]
int(-(exp((x^2 + 5/3)/x)*(30*x + 90*x^2 - 66*x^3 + 6*x^4 + 50) + exp((2*(x ^2 + 5/3))/x)*(45*x - 30*x^2 + 3*x^3) + 78*x^3 - 36*x^4 + 3*x^5)/(exp((2*( x^2 + 5/3))/x)*(675*x - 540*x^2 + 198*x^3 - 36*x^4 + 3*x^5) + exp((x^2 + 5 /3)/x)*(1440*x^2 - 1206*x^3 + 438*x^4 - 78*x^5 + 6*x^6) + 768*x^3 - 672*x^ 4 + 243*x^5 - 42*x^6 + 3*x^7),x)
int(-(exp((x^2 + 5/3)/x)*(30*x + 90*x^2 - 66*x^3 + 6*x^4 + 50) + exp((2*(x ^2 + 5/3))/x)*(45*x - 30*x^2 + 3*x^3) + 78*x^3 - 36*x^4 + 3*x^5)/(exp((2*( x^2 + 5/3))/x)*(675*x - 540*x^2 + 198*x^3 - 36*x^4 + 3*x^5) + exp((x^2 + 5 /3)/x)*(1440*x^2 - 1206*x^3 + 438*x^4 - 78*x^5 + 6*x^6) + 768*x^3 - 672*x^ 4 + 243*x^5 - 42*x^6 + 3*x^7), x)