Integrand size = 198, antiderivative size = 23 \[ \int \frac {-240 e^2+e^{6 x} \left (240 x-2 x^3\right )+e^3 \left (-240 x+2 x^3\right )+e^{2 x} \left (e^2 \left (720 x-6 x^3\right )+e \left (480+4 x^3\right )\right )+e^{4 x} \left (-240-4 x^3+e \left (-720 x+6 x^3\right )\right )}{e^{\frac {120}{x^2}+6 x} x^6+e^{\frac {120}{x^2}+4 x} \left (-3 x^5-3 e x^6\right )+e^{\frac {120}{x^2}+2 x} \left (3 x^4+6 e x^5+3 e^2 x^6\right )+e^{\frac {120}{x^2}} \left (-x^3-3 e x^4-3 e^2 x^5-e^3 x^6\right )} \, dx=\frac {e^{-\frac {120}{x^2}}}{\left (\frac {1}{e-e^{2 x}}+x\right )^2} \]
Time = 0.09 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.48 \[ \int \frac {-240 e^2+e^{6 x} \left (240 x-2 x^3\right )+e^3 \left (-240 x+2 x^3\right )+e^{2 x} \left (e^2 \left (720 x-6 x^3\right )+e \left (480+4 x^3\right )\right )+e^{4 x} \left (-240-4 x^3+e \left (-720 x+6 x^3\right )\right )}{e^{\frac {120}{x^2}+6 x} x^6+e^{\frac {120}{x^2}+4 x} \left (-3 x^5-3 e x^6\right )+e^{\frac {120}{x^2}+2 x} \left (3 x^4+6 e x^5+3 e^2 x^6\right )+e^{\frac {120}{x^2}} \left (-x^3-3 e x^4-3 e^2 x^5-e^3 x^6\right )} \, dx=\frac {e^{-\frac {120}{x^2}} \left (e-e^{2 x}\right )^2}{\left (1+e x-e^{2 x} x\right )^2} \]
Integrate[(-240*E^2 + E^(6*x)*(240*x - 2*x^3) + E^3*(-240*x + 2*x^3) + E^( 2*x)*(E^2*(720*x - 6*x^3) + E*(480 + 4*x^3)) + E^(4*x)*(-240 - 4*x^3 + E*( -720*x + 6*x^3)))/(E^(120/x^2 + 6*x)*x^6 + E^(120/x^2 + 4*x)*(-3*x^5 - 3*E *x^6) + E^(120/x^2 + 2*x)*(3*x^4 + 6*E*x^5 + 3*E^2*x^6) + E^(120/x^2)*(-x^ 3 - 3*E*x^4 - 3*E^2*x^5 - E^3*x^6)),x]
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.
| \(\displaystyle \int \frac {e^{6 x} \left (240 x-2 x^3\right )+e^3 \left (2 x^3-240 x\right )+e^{2 x} \left (e^2 \left (720 x-6 x^3\right )+e \left (4 x^3+480\right )\right )+e^{4 x} \left (-4 x^3+e \left (6 x^3-720 x\right )-240\right )-240 e^2}{e^{\frac {120}{x^2}+6 x} x^6+e^{\frac {120}{x^2}+4 x} \left (-3 e x^6-3 x^5\right )+e^{\frac {120}{x^2}+2 x} \left (3 e^2 x^6+6 e x^5+3 x^4\right )+e^{\frac {120}{x^2}} \left (-e^3 x^6-3 e^2 x^5-3 e x^4-x^3\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 e^{-\frac {120}{x^2}} \left (e-e^{2 x}\right ) \left (-2 e^{2 x} \left (x^3+60\right )-e^{4 x} x \left (x^2-120\right )+2 e^{2 x+1} x \left (x^2-120\right )-e^2 x \left (x^2-120\right )+120 e\right )}{x^3 \left (-e^{2 x} x+e x+1\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {e^{-\frac {120}{x^2}} \left (e-e^{2 x}\right ) \left (e^{4 x} x \left (120-x^2\right )-2 e^{2 x+1} x \left (120-x^2\right )+e^2 x \left (120-x^2\right )-2 e^{2 x} \left (x^3+60\right )+120 e\right )}{x^3 \left (-e^{2 x} x+e x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {e^{-\frac {120}{x^2}} \left (120-x^2\right )}{x^5}-\frac {e^{-\frac {120}{x^2}} \left (2 e x^2+2 x+1\right )}{x^3 \left (e^{2 x} x-e x-1\right )^3}-\frac {e^{-\frac {120}{x^2}} \left (2 x^3+3 x^2-240\right )}{x^5 \left (e^{2 x} x-e x-1\right )}-\frac {e^{-\frac {120}{x^2}} \left (2 e x^4+4 x^3+3 x^2-120\right )}{x^5 \left (e^{2 x} x-e x-1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 2 \left (2 \int \frac {e^{1-\frac {120}{x^2}}}{x \left (-e^{2 x} x+e x+1\right )^3}dx-2 \int \frac {e^{1-\frac {120}{x^2}}}{x \left (-e^{2 x} x+e x+1\right )^2}dx-2 \int \frac {e^{-\frac {120}{x^2}}}{x^2 \left (e^{2 x} x-e x-1\right )^3}dx-4 \int \frac {e^{-\frac {120}{x^2}}}{x^2 \left (e^{2 x} x-e x-1\right )^2}dx-2 \int \frac {e^{-\frac {120}{x^2}}}{x^2 \left (e^{2 x} x-e x-1\right )}dx+120 \int \frac {e^{-\frac {120}{x^2}}}{x^5 \left (e^{2 x} x-e x-1\right )^2}dx+240 \int \frac {e^{-\frac {120}{x^2}}}{x^5 \left (e^{2 x} x-e x-1\right )}dx-\int \frac {e^{-\frac {120}{x^2}}}{x^3 \left (e^{2 x} x-e x-1\right )^3}dx-3 \int \frac {e^{-\frac {120}{x^2}}}{x^3 \left (e^{2 x} x-e x-1\right )^2}dx-3 \int \frac {e^{-\frac {120}{x^2}}}{x^3 \left (e^{2 x} x-e x-1\right )}dx+\frac {e^{-\frac {120}{x^2}}}{2 x^2}\right )\) |
Int[(-240*E^2 + E^(6*x)*(240*x - 2*x^3) + E^3*(-240*x + 2*x^3) + E^(2*x)*( E^2*(720*x - 6*x^3) + E*(480 + 4*x^3)) + E^(4*x)*(-240 - 4*x^3 + E*(-720*x + 6*x^3)))/(E^(120/x^2 + 6*x)*x^6 + E^(120/x^2 + 4*x)*(-3*x^5 - 3*E*x^6) + E^(120/x^2 + 2*x)*(3*x^4 + 6*E*x^5 + 3*E^2*x^6) + E^(120/x^2)*(-x^3 - 3* E*x^4 - 3*E^2*x^5 - E^3*x^6)),x]
3.23.46.3.1 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. \(83\) vs. \(2(24)=48\).
Time = 50.98 (sec) , antiderivative size = 84, normalized size of antiderivative = 3.65
| method | result | size |
| parallelrisch | \(\frac {\left (x^{2} {\mathrm e}^{4 x}-2 \,{\mathrm e} \,{\mathrm e}^{2 x} x^{2}+x^{2} {\mathrm e}^{2}\right ) {\mathrm e}^{-\frac {120}{x^{2}}}}{x^{2} \left (x^{2} {\mathrm e}^{4 x}-2 \,{\mathrm e} \,{\mathrm e}^{2 x} x^{2}+x^{2} {\mathrm e}^{2}-2 x \,{\mathrm e}^{2 x}+2 x \,{\mathrm e}+1\right )}\) | \(84\) |
int(((-2*x^3+240*x)*exp(x)^6+((6*x^3-720*x)*exp(1)-4*x^3-240)*exp(x)^4+((- 6*x^3+720*x)*exp(1)^2+(4*x^3+480)*exp(1))*exp(x)^2+(2*x^3-240*x)*exp(1)^3- 240*exp(1)^2)/(x^6*exp(60/x^2)^2*exp(x)^6+(-3*x^6*exp(1)-3*x^5)*exp(60/x^2 )^2*exp(x)^4+(3*x^6*exp(1)^2+6*x^5*exp(1)+3*x^4)*exp(60/x^2)^2*exp(x)^2+(- x^6*exp(1)^3-3*x^5*exp(1)^2-3*x^4*exp(1)-x^3)*exp(60/x^2)^2),x,method=_RET URNVERBOSE)
1/x^2*(x^2*exp(x)^4-2*exp(1)*exp(x)^2*x^2+x^2*exp(1)^2)/exp(60/x^2)^2/(x^2 *exp(x)^4-2*exp(1)*exp(x)^2*x^2+x^2*exp(1)^2-2*x*exp(x)^2+2*x*exp(1)+1)
Leaf count of result is larger than twice the leaf count of optimal. 147 vs. \(2 (22) = 44\).
Time = 0.28 (sec) , antiderivative size = 147, normalized size of antiderivative = 6.39 \[ \int \frac {-240 e^2+e^{6 x} \left (240 x-2 x^3\right )+e^3 \left (-240 x+2 x^3\right )+e^{2 x} \left (e^2 \left (720 x-6 x^3\right )+e \left (480+4 x^3\right )\right )+e^{4 x} \left (-240-4 x^3+e \left (-720 x+6 x^3\right )\right )}{e^{\frac {120}{x^2}+6 x} x^6+e^{\frac {120}{x^2}+4 x} \left (-3 x^5-3 e x^6\right )+e^{\frac {120}{x^2}+2 x} \left (3 x^4+6 e x^5+3 e^2 x^6\right )+e^{\frac {120}{x^2}} \left (-x^3-3 e x^4-3 e^2 x^5-e^3 x^6\right )} \, dx=\frac {e^{\left (\frac {8 \, {\left (x^{3} + 30\right )}}{x^{2}} + \frac {12 \, {\left (x^{3} + 20\right )}}{x^{2}} + 2\right )} - 2 \, e^{\left (\frac {4 \, {\left (x^{3} + 30\right )}}{x^{2}} + \frac {18 \, {\left (x^{3} + 20\right )}}{x^{2}} + 1\right )} + e^{\left (\frac {24 \, {\left (x^{3} + 20\right )}}{x^{2}}\right )}}{x^{2} e^{\left (\frac {12 \, {\left (x^{3} + 30\right )}}{x^{2}} + \frac {12 \, {\left (x^{3} + 20\right )}}{x^{2}}\right )} + {\left (x^{2} e^{2} + 2 \, x e + 1\right )} e^{\left (\frac {20 \, {\left (x^{3} + 30\right )}}{x^{2}}\right )} - 2 \, {\left (x^{2} e + x\right )} e^{\left (\frac {16 \, {\left (x^{3} + 30\right )}}{x^{2}} + \frac {6 \, {\left (x^{3} + 20\right )}}{x^{2}}\right )}} \]
integrate(((-2*x^3+240*x)*exp(x)^6+((6*x^3-720*x)*exp(1)-4*x^3-240)*exp(x) ^4+((-6*x^3+720*x)*exp(1)^2+(4*x^3+480)*exp(1))*exp(x)^2+(2*x^3-240*x)*exp (1)^3-240*exp(1)^2)/(x^6*exp(60/x^2)^2*exp(x)^6+(-3*x^6*exp(1)-3*x^5)*exp( 60/x^2)^2*exp(x)^4+(3*x^6*exp(1)^2+6*x^5*exp(1)+3*x^4)*exp(60/x^2)^2*exp(x )^2+(-x^6*exp(1)^3-3*x^5*exp(1)^2-3*x^4*exp(1)-x^3)*exp(60/x^2)^2),x, algo rithm=\
(e^(8*(x^3 + 30)/x^2 + 12*(x^3 + 20)/x^2 + 2) - 2*e^(4*(x^3 + 30)/x^2 + 18 *(x^3 + 20)/x^2 + 1) + e^(24*(x^3 + 20)/x^2))/(x^2*e^(12*(x^3 + 30)/x^2 + 12*(x^3 + 20)/x^2) + (x^2*e^2 + 2*x*e + 1)*e^(20*(x^3 + 30)/x^2) - 2*(x^2* e + x)*e^(16*(x^3 + 30)/x^2 + 6*(x^3 + 20)/x^2))
Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (20) = 40\).
Time = 0.21 (sec) , antiderivative size = 116, normalized size of antiderivative = 5.04 \[ \int \frac {-240 e^2+e^{6 x} \left (240 x-2 x^3\right )+e^3 \left (-240 x+2 x^3\right )+e^{2 x} \left (e^2 \left (720 x-6 x^3\right )+e \left (480+4 x^3\right )\right )+e^{4 x} \left (-240-4 x^3+e \left (-720 x+6 x^3\right )\right )}{e^{\frac {120}{x^2}+6 x} x^6+e^{\frac {120}{x^2}+4 x} \left (-3 x^5-3 e x^6\right )+e^{\frac {120}{x^2}+2 x} \left (3 x^4+6 e x^5+3 e^2 x^6\right )+e^{\frac {120}{x^2}} \left (-x^3-3 e x^4-3 e^2 x^5-e^3 x^6\right )} \, dx=\frac {2 x e^{2 x} - 2 e x - 1}{x^{4} e^{\frac {120}{x^{2}}} e^{4 x} + x^{4} e^{2} e^{\frac {120}{x^{2}}} + 2 e x^{3} e^{\frac {120}{x^{2}}} + x^{2} e^{\frac {120}{x^{2}}} + \left (- 2 e x^{4} e^{\frac {120}{x^{2}}} - 2 x^{3} e^{\frac {120}{x^{2}}}\right ) e^{2 x}} + \frac {e^{- \frac {120}{x^{2}}}}{x^{2}} \]
integrate(((-2*x**3+240*x)*exp(x)**6+((6*x**3-720*x)*exp(1)-4*x**3-240)*ex p(x)**4+((-6*x**3+720*x)*exp(1)**2+(4*x**3+480)*exp(1))*exp(x)**2+(2*x**3- 240*x)*exp(1)**3-240*exp(1)**2)/(x**6*exp(60/x**2)**2*exp(x)**6+(-3*x**6*e xp(1)-3*x**5)*exp(60/x**2)**2*exp(x)**4+(3*x**6*exp(1)**2+6*x**5*exp(1)+3* x**4)*exp(60/x**2)**2*exp(x)**2+(-x**6*exp(1)**3-3*x**5*exp(1)**2-3*x**4*e xp(1)-x**3)*exp(60/x**2)**2),x)
(2*x*exp(2*x) - 2*E*x - 1)/(x**4*exp(120/x**2)*exp(4*x) + x**4*exp(2)*exp( 120/x**2) + 2*E*x**3*exp(120/x**2) + x**2*exp(120/x**2) + (-2*E*x**4*exp(1 20/x**2) - 2*x**3*exp(120/x**2))*exp(2*x)) + exp(-120/x**2)/x**2
Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (22) = 44\).
Time = 0.27 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.57 \[ \int \frac {-240 e^2+e^{6 x} \left (240 x-2 x^3\right )+e^3 \left (-240 x+2 x^3\right )+e^{2 x} \left (e^2 \left (720 x-6 x^3\right )+e \left (480+4 x^3\right )\right )+e^{4 x} \left (-240-4 x^3+e \left (-720 x+6 x^3\right )\right )}{e^{\frac {120}{x^2}+6 x} x^6+e^{\frac {120}{x^2}+4 x} \left (-3 x^5-3 e x^6\right )+e^{\frac {120}{x^2}+2 x} \left (3 x^4+6 e x^5+3 e^2 x^6\right )+e^{\frac {120}{x^2}} \left (-x^3-3 e x^4-3 e^2 x^5-e^3 x^6\right )} \, dx=\frac {{\left (e^{2} + e^{\left (4 \, x\right )} - 2 \, e^{\left (2 \, x + 1\right )}\right )} e^{\left (-\frac {120}{x^{2}}\right )}}{x^{2} e^{2} + x^{2} e^{\left (4 \, x\right )} + 2 \, x e - 2 \, {\left (x^{2} e + x\right )} e^{\left (2 \, x\right )} + 1} \]
integrate(((-2*x^3+240*x)*exp(x)^6+((6*x^3-720*x)*exp(1)-4*x^3-240)*exp(x) ^4+((-6*x^3+720*x)*exp(1)^2+(4*x^3+480)*exp(1))*exp(x)^2+(2*x^3-240*x)*exp (1)^3-240*exp(1)^2)/(x^6*exp(60/x^2)^2*exp(x)^6+(-3*x^6*exp(1)-3*x^5)*exp( 60/x^2)^2*exp(x)^4+(3*x^6*exp(1)^2+6*x^5*exp(1)+3*x^4)*exp(60/x^2)^2*exp(x )^2+(-x^6*exp(1)^3-3*x^5*exp(1)^2-3*x^4*exp(1)-x^3)*exp(60/x^2)^2),x, algo rithm=\
(e^2 + e^(4*x) - 2*e^(2*x + 1))*e^(-120/x^2)/(x^2*e^2 + x^2*e^(4*x) + 2*x* e - 2*(x^2*e + x)*e^(2*x) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 898950 vs. \(2 (22) = 44\).
Time = 6.98 (sec) , antiderivative size = 898950, normalized size of antiderivative = 39084.78 \[ \int \frac {-240 e^2+e^{6 x} \left (240 x-2 x^3\right )+e^3 \left (-240 x+2 x^3\right )+e^{2 x} \left (e^2 \left (720 x-6 x^3\right )+e \left (480+4 x^3\right )\right )+e^{4 x} \left (-240-4 x^3+e \left (-720 x+6 x^3\right )\right )}{e^{\frac {120}{x^2}+6 x} x^6+e^{\frac {120}{x^2}+4 x} \left (-3 x^5-3 e x^6\right )+e^{\frac {120}{x^2}+2 x} \left (3 x^4+6 e x^5+3 e^2 x^6\right )+e^{\frac {120}{x^2}} \left (-x^3-3 e x^4-3 e^2 x^5-e^3 x^6\right )} \, dx=\text {Too large to display} \]
integrate(((-2*x^3+240*x)*exp(x)^6+((6*x^3-720*x)*exp(1)-4*x^3-240)*exp(x) ^4+((-6*x^3+720*x)*exp(1)^2+(4*x^3+480)*exp(1))*exp(x)^2+(2*x^3-240*x)*exp (1)^3-240*exp(1)^2)/(x^6*exp(60/x^2)^2*exp(x)^6+(-3*x^6*exp(1)-3*x^5)*exp( 60/x^2)^2*exp(x)^4+(3*x^6*exp(1)^2+6*x^5*exp(1)+3*x^4)*exp(60/x^2)^2*exp(x )^2+(-x^6*exp(1)^3-3*x^5*exp(1)^2-3*x^4*exp(1)-x^3)*exp(60/x^2)^2),x, algo rithm=\
(512*x^23*e^(4*(x^3 + x^2 + 60)/x^2 + 10*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + 6*(x^2 + 60)/x^2 + 15*(x^2 + 40)/x^2) - 1024*x^23*e^(4*(x^3 + x^2 + 60) /x^2 + 8*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + (x^2 + 120)/x^2 + 6*(x^2 + 60 )/x^2 + 15*(x^2 + 40)/x^2) + 512*x^23*e^(4*(x^3 + x^2 + 60)/x^2 + 6*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + 2*(x^2 + 120)/x^2 + 6*(x^2 + 60)/x^2 + 15*(x ^2 + 40)/x^2) - 1024*x^23*e^(2*(x^3 + x^2 + 60)/x^2 + 10*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + 6*(x^2 + 60)/x^2 + 18*(x^2 + 40)/x^2) + 2048*x^23*e^(2* (x^3 + x^2 + 60)/x^2 + 8*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + (x^2 + 120)/x ^2 + 6*(x^2 + 60)/x^2 + 18*(x^2 + 40)/x^2) - 1024*x^23*e^(2*(x^3 + x^2 + 6 0)/x^2 + 6*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + 2*(x^2 + 120)/x^2 + 6*(x^2 + 60)/x^2 + 18*(x^2 + 40)/x^2) + 512*x^23*e^(10*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + 6*(x^2 + 60)/x^2 + 21*(x^2 + 40)/x^2) - 1024*x^23*e^(8*(x^3 + 60 )/x^2 + 6*(x^3 + 20)/x^2 + (x^2 + 120)/x^2 + 6*(x^2 + 60)/x^2 + 21*(x^2 + 40)/x^2) + 512*x^23*e^(6*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + 2*(x^2 + 120) /x^2 + 6*(x^2 + 60)/x^2 + 21*(x^2 + 40)/x^2) - 1024*x^22*e^(4*(x^3 + x^2 + 60)/x^2 + 11*(x^3 + 60)/x^2 + 3*(x^3 + 20)/x^2 + 6*(x^2 + 60)/x^2 + 15*(x ^2 + 40)/x^2) + 1536*x^22*e^(4*(x^3 + x^2 + 60)/x^2 + 10*(x^3 + 60)/x^2 + 6*(x^3 + 20)/x^2 + (x^2 + 120)/x^2 + 4*(x^2 + 60)/x^2 + 15*(x^2 + 40)/x^2) + 1536*x^22*e^(4*(x^3 + x^2 + 60)/x^2 + 10*(x^3 + 60)/x^2 + 6*(x^3 + 20)/ x^2 + 8*(x^2 + 60)/x^2 + 12*(x^2 + 40)/x^2) + 768*x^22*e^(4*(x^3 + x^2 ...
Timed out. \[ \int \frac {-240 e^2+e^{6 x} \left (240 x-2 x^3\right )+e^3 \left (-240 x+2 x^3\right )+e^{2 x} \left (e^2 \left (720 x-6 x^3\right )+e \left (480+4 x^3\right )\right )+e^{4 x} \left (-240-4 x^3+e \left (-720 x+6 x^3\right )\right )}{e^{\frac {120}{x^2}+6 x} x^6+e^{\frac {120}{x^2}+4 x} \left (-3 x^5-3 e x^6\right )+e^{\frac {120}{x^2}+2 x} \left (3 x^4+6 e x^5+3 e^2 x^6\right )+e^{\frac {120}{x^2}} \left (-x^3-3 e x^4-3 e^2 x^5-e^3 x^6\right )} \, dx=\int \frac {240\,{\mathrm {e}}^2-{\mathrm {e}}^{6\,x}\,\left (240\,x-2\,x^3\right )+{\mathrm {e}}^3\,\left (240\,x-2\,x^3\right )+{\mathrm {e}}^{4\,x}\,\left (\mathrm {e}\,\left (720\,x-6\,x^3\right )+4\,x^3+240\right )-{\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^2\,\left (720\,x-6\,x^3\right )+\mathrm {e}\,\left (4\,x^3+480\right )\right )}{{\mathrm {e}}^{\frac {120}{x^2}}\,\left ({\mathrm {e}}^3\,x^6+3\,{\mathrm {e}}^2\,x^5+3\,\mathrm {e}\,x^4+x^3\right )-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{\frac {120}{x^2}}\,\left (3\,{\mathrm {e}}^2\,x^6+6\,\mathrm {e}\,x^5+3\,x^4\right )-x^6\,{\mathrm {e}}^{6\,x}\,{\mathrm {e}}^{\frac {120}{x^2}}+{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{\frac {120}{x^2}}\,\left (3\,\mathrm {e}\,x^6+3\,x^5\right )} \,d x \]
int((240*exp(2) - exp(6*x)*(240*x - 2*x^3) + exp(3)*(240*x - 2*x^3) + exp( 4*x)*(exp(1)*(720*x - 6*x^3) + 4*x^3 + 240) - exp(2*x)*(exp(2)*(720*x - 6* x^3) + exp(1)*(4*x^3 + 480)))/(exp(120/x^2)*(3*x^4*exp(1) + 3*x^5*exp(2) + x^6*exp(3) + x^3) - exp(2*x)*exp(120/x^2)*(6*x^5*exp(1) + 3*x^6*exp(2) + 3*x^4) - x^6*exp(6*x)*exp(120/x^2) + exp(4*x)*exp(120/x^2)*(3*x^6*exp(1) + 3*x^5)),x)
int((240*exp(2) - exp(6*x)*(240*x - 2*x^3) + exp(3)*(240*x - 2*x^3) + exp( 4*x)*(exp(1)*(720*x - 6*x^3) + 4*x^3 + 240) - exp(2*x)*(exp(2)*(720*x - 6* x^3) + exp(1)*(4*x^3 + 480)))/(exp(120/x^2)*(3*x^4*exp(1) + 3*x^5*exp(2) + x^6*exp(3) + x^3) - exp(2*x)*exp(120/x^2)*(6*x^5*exp(1) + 3*x^6*exp(2) + 3*x^4) - x^6*exp(6*x)*exp(120/x^2) + exp(4*x)*exp(120/x^2)*(3*x^6*exp(1) + 3*x^5)), x)