3.97.54 \(\int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x (-24 x^4-8 x^6)+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x (-12 x-4 x^3)+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x (-30 x^2-6 x^3-8 x^4)))+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} (-4 x^3-2 x^4)+e^x (24 x^2+12 x^3+8 x^4+4 x^5)+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x (30 x^4+6 x^5+8 x^6)))}{9+6 x^2+e^{2 x} x^2+x^4+e^x (-6 x-2 x^3)} \, dx\)
Optimal. Leaf size=37 \[ \left (-e^{x+e^{4+\frac {x}{x+\frac {3}{-e^x+x}}} x^2}+x^2\right )^2 \]
________________________________________________________________________________________
Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(36*x^3 + 24*x^5 + 4*E^(2*x)*x^5 + 4*x^7 + E^x*(-24*x^4 - 8*x^6) + E^(2*x + 2*E^((-12 + 5*E^x*x - 5*x^2)/(
-3 + E^x*x - x^2))*x^2)*(18 + 12*x^2 + 2*E^(2*x)*x^2 + 2*x^4 + E^x*(-12*x - 4*x^3) + E^((-12 + 5*E^x*x - 5*x^2
)/(-3 + E^x*x - x^2))*(36*x + 36*x^3 + 4*E^(2*x)*x^3 + 4*x^5 + E^x*(-30*x^2 - 6*x^3 - 8*x^4))) + E^(x + E^((-1
2 + 5*E^x*x - 5*x^2)/(-3 + E^x*x - x^2))*x^2)*(-36*x - 18*x^2 - 24*x^3 - 12*x^4 - 4*x^5 - 2*x^6 + E^(2*x)*(-4*
x^3 - 2*x^4) + E^x*(24*x^2 + 12*x^3 + 8*x^4 + 4*x^5) + E^((-12 + 5*E^x*x - 5*x^2)/(-3 + E^x*x - x^2))*(-36*x^3
- 36*x^5 - 4*E^(2*x)*x^5 - 4*x^7 + E^x*(30*x^4 + 6*x^5 + 8*x^6))))/(9 + 6*x^2 + E^(2*x)*x^2 + x^4 + E^x*(-6*x
- 2*x^3)),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [A] time = 2.04, size = 35, normalized size = 0.95 \begin {gather*} \left (e^{x \left (1+e^{5-\frac {3}{3-e^x x+x^2}} x\right )}-x^2\right )^2 \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(36*x^3 + 24*x^5 + 4*E^(2*x)*x^5 + 4*x^7 + E^x*(-24*x^4 - 8*x^6) + E^(2*x + 2*E^((-12 + 5*E^x*x - 5*
x^2)/(-3 + E^x*x - x^2))*x^2)*(18 + 12*x^2 + 2*E^(2*x)*x^2 + 2*x^4 + E^x*(-12*x - 4*x^3) + E^((-12 + 5*E^x*x -
5*x^2)/(-3 + E^x*x - x^2))*(36*x + 36*x^3 + 4*E^(2*x)*x^3 + 4*x^5 + E^x*(-30*x^2 - 6*x^3 - 8*x^4))) + E^(x +
E^((-12 + 5*E^x*x - 5*x^2)/(-3 + E^x*x - x^2))*x^2)*(-36*x - 18*x^2 - 24*x^3 - 12*x^4 - 4*x^5 - 2*x^6 + E^(2*x
)*(-4*x^3 - 2*x^4) + E^x*(24*x^2 + 12*x^3 + 8*x^4 + 4*x^5) + E^((-12 + 5*E^x*x - 5*x^2)/(-3 + E^x*x - x^2))*(-
36*x^3 - 36*x^5 - 4*E^(2*x)*x^5 - 4*x^7 + E^x*(30*x^4 + 6*x^5 + 8*x^6))))/(9 + 6*x^2 + E^(2*x)*x^2 + x^4 + E^x
*(-6*x - 2*x^3)),x]
[Out]
(E^(x*(1 + E^(5 - 3/(3 - E^x*x + x^2))*x)) - x^2)^2
________________________________________________________________________________________
fricas [B] time = 0.55, size = 78, normalized size = 2.11 \begin {gather*} x^{4} - 2 \, x^{2} e^{\left (x^{2} e^{\left (\frac {5 \, x^{2} - 5 \, x e^{x} + 12}{x^{2} - x e^{x} + 3}\right )} + x\right )} + e^{\left (2 \, x^{2} e^{\left (\frac {5 \, x^{2} - 5 \, x e^{x} + 12}{x^{2} - x e^{x} + 3}\right )} + 2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*exp(x)^2*x^3+(-8*x^4-6*x^3-30*x^2)*exp(x)+4*x^5+36*x^3+36*x)*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*
x-x^2-3))+2*exp(x)^2*x^2+(-4*x^3-12*x)*exp(x)+2*x^4+12*x^2+18)*exp(x^2*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2
-3))+x)^2+((-4*x^5*exp(x)^2+(8*x^6+6*x^5+30*x^4)*exp(x)-4*x^7-36*x^5-36*x^3)*exp((5*exp(x)*x-5*x^2-12)/(exp(x)
*x-x^2-3))+(-2*x^4-4*x^3)*exp(x)^2+(4*x^5+8*x^4+12*x^3+24*x^2)*exp(x)-2*x^6-4*x^5-12*x^4-24*x^3-18*x^2-36*x)*e
xp(x^2*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2-3))+x)+4*x^5*exp(x)^2+(-8*x^6-24*x^4)*exp(x)+4*x^7+24*x^5+36*x^
3)/(exp(x)^2*x^2+(-2*x^3-6*x)*exp(x)+x^4+6*x^2+9),x, algorithm="fricas")
[Out]
x^4 - 2*x^2*e^(x^2*e^((5*x^2 - 5*x*e^x + 12)/(x^2 - x*e^x + 3)) + x) + e^(2*x^2*e^((5*x^2 - 5*x*e^x + 12)/(x^2
- x*e^x + 3)) + 2*x)
________________________________________________________________________________________
giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*exp(x)^2*x^3+(-8*x^4-6*x^3-30*x^2)*exp(x)+4*x^5+36*x^3+36*x)*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*
x-x^2-3))+2*exp(x)^2*x^2+(-4*x^3-12*x)*exp(x)+2*x^4+12*x^2+18)*exp(x^2*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2
-3))+x)^2+((-4*x^5*exp(x)^2+(8*x^6+6*x^5+30*x^4)*exp(x)-4*x^7-36*x^5-36*x^3)*exp((5*exp(x)*x-5*x^2-12)/(exp(x)
*x-x^2-3))+(-2*x^4-4*x^3)*exp(x)^2+(4*x^5+8*x^4+12*x^3+24*x^2)*exp(x)-2*x^6-4*x^5-12*x^4-24*x^3-18*x^2-36*x)*e
xp(x^2*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2-3))+x)+4*x^5*exp(x)^2+(-8*x^6-24*x^4)*exp(x)+4*x^7+24*x^5+36*x^
3)/(exp(x)^2*x^2+(-2*x^3-6*x)*exp(x)+x^4+6*x^2+9),x, algorithm="giac")
[Out]
Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time:
0.84Unable to divide, perhaps due to rounding error%%%{16,[0,2,10,11]%%%}+%%%{-128,[0,2,9,12]%%%}+%%%{-48,[0,2
,9,11]%%%}+%%%
________________________________________________________________________________________
maple [B] time = 0.14, size = 79, normalized size = 2.14
|
|
|
| method |
result |
size |
|
|
|
| risch |
\(x^{4}-2 \,{\mathrm e}^{x \left (x \,{\mathrm e}^{\frac {5 \,{\mathrm e}^{x} x -5 x^{2}-12}{{\mathrm e}^{x} x -x^{2}-3}}+1\right )} x^{2}+{\mathrm e}^{2 x \left (x \,{\mathrm e}^{\frac {5 \,{\mathrm e}^{x} x -5 x^{2}-12}{{\mathrm e}^{x} x -x^{2}-3}}+1\right )}\) |
\(79\) |
|
|
|
| |
| |
| |
| |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((4*exp(x)^2*x^3+(-8*x^4-6*x^3-30*x^2)*exp(x)+4*x^5+36*x^3+36*x)*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2-
3))+2*exp(x)^2*x^2+(-4*x^3-12*x)*exp(x)+2*x^4+12*x^2+18)*exp(x^2*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2-3))+x
)^2+((-4*x^5*exp(x)^2+(8*x^6+6*x^5+30*x^4)*exp(x)-4*x^7-36*x^5-36*x^3)*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2
-3))+(-2*x^4-4*x^3)*exp(x)^2+(4*x^5+8*x^4+12*x^3+24*x^2)*exp(x)-2*x^6-4*x^5-12*x^4-24*x^3-18*x^2-36*x)*exp(x^2
*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2-3))+x)+4*x^5*exp(x)^2+(-8*x^6-24*x^4)*exp(x)+4*x^7+24*x^5+36*x^3)/(ex
p(x)^2*x^2+(-2*x^3-6*x)*exp(x)+x^4+6*x^2+9),x,method=_RETURNVERBOSE)
[Out]
x^4-2*exp(x*(x*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2-3))+1))*x^2+exp(2*x*(x*exp((5*exp(x)*x-5*x^2-12)/(exp(x
)*x-x^2-3))+1))
________________________________________________________________________________________
maxima [A] time = 0.48, size = 60, normalized size = 1.62 \begin {gather*} x^{4} - 2 \, x^{2} e^{\left (x^{2} e^{\left (-\frac {3}{x^{2} - x e^{x} + 3} + 5\right )} + x\right )} + e^{\left (2 \, x^{2} e^{\left (-\frac {3}{x^{2} - x e^{x} + 3} + 5\right )} + 2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*exp(x)^2*x^3+(-8*x^4-6*x^3-30*x^2)*exp(x)+4*x^5+36*x^3+36*x)*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*
x-x^2-3))+2*exp(x)^2*x^2+(-4*x^3-12*x)*exp(x)+2*x^4+12*x^2+18)*exp(x^2*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2
-3))+x)^2+((-4*x^5*exp(x)^2+(8*x^6+6*x^5+30*x^4)*exp(x)-4*x^7-36*x^5-36*x^3)*exp((5*exp(x)*x-5*x^2-12)/(exp(x)
*x-x^2-3))+(-2*x^4-4*x^3)*exp(x)^2+(4*x^5+8*x^4+12*x^3+24*x^2)*exp(x)-2*x^6-4*x^5-12*x^4-24*x^3-18*x^2-36*x)*e
xp(x^2*exp((5*exp(x)*x-5*x^2-12)/(exp(x)*x-x^2-3))+x)+4*x^5*exp(x)^2+(-8*x^6-24*x^4)*exp(x)+4*x^7+24*x^5+36*x^
3)/(exp(x)^2*x^2+(-2*x^3-6*x)*exp(x)+x^4+6*x^2+9),x, algorithm="maxima")
[Out]
x^4 - 2*x^2*e^(x^2*e^(-3/(x^2 - x*e^x + 3) + 5) + x) + e^(2*x^2*e^(-3/(x^2 - x*e^x + 3) + 5) + 2*x)
________________________________________________________________________________________
mupad [B] time = 7.74, size = 129, normalized size = 3.49 \begin {gather*} {\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^{\frac {12}{x^2-x\,{\mathrm {e}}^x+3}}\,{\mathrm {e}}^{-\frac {5\,x\,{\mathrm {e}}^x}{x^2-x\,{\mathrm {e}}^x+3}}\,{\mathrm {e}}^{\frac {5\,x^2}{x^2-x\,{\mathrm {e}}^x+3}}}+x^4-2\,x^2\,{\mathrm {e}}^x\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{\frac {12}{x^2-x\,{\mathrm {e}}^x+3}}\,{\mathrm {e}}^{-\frac {5\,x\,{\mathrm {e}}^x}{x^2-x\,{\mathrm {e}}^x+3}}\,{\mathrm {e}}^{\frac {5\,x^2}{x^2-x\,{\mathrm {e}}^x+3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((4*x^5*exp(2*x) - exp(x)*(24*x^4 + 8*x^6) + exp(2*x + 2*x^2*exp((5*x^2 - 5*x*exp(x) + 12)/(x^2 - x*exp(x)
+ 3)))*(exp((5*x^2 - 5*x*exp(x) + 12)/(x^2 - x*exp(x) + 3))*(36*x - exp(x)*(30*x^2 + 6*x^3 + 8*x^4) + 4*x^3*ex
p(2*x) + 36*x^3 + 4*x^5) + 2*x^2*exp(2*x) - exp(x)*(12*x + 4*x^3) + 12*x^2 + 2*x^4 + 18) - exp(x + x^2*exp((5*
x^2 - 5*x*exp(x) + 12)/(x^2 - x*exp(x) + 3)))*(36*x + exp(2*x)*(4*x^3 + 2*x^4) + exp((5*x^2 - 5*x*exp(x) + 12)
/(x^2 - x*exp(x) + 3))*(4*x^5*exp(2*x) - exp(x)*(30*x^4 + 6*x^5 + 8*x^6) + 36*x^3 + 36*x^5 + 4*x^7) - exp(x)*(
24*x^2 + 12*x^3 + 8*x^4 + 4*x^5) + 18*x^2 + 24*x^3 + 12*x^4 + 4*x^5 + 2*x^6) + 36*x^3 + 24*x^5 + 4*x^7)/(x^2*e
xp(2*x) - exp(x)*(6*x + 2*x^3) + 6*x^2 + x^4 + 9),x)
[Out]
exp(2*x)*exp(2*x^2*exp(12/(x^2 - x*exp(x) + 3))*exp(-(5*x*exp(x))/(x^2 - x*exp(x) + 3))*exp((5*x^2)/(x^2 - x*e
xp(x) + 3))) + x^4 - 2*x^2*exp(x)*exp(x^2*exp(12/(x^2 - x*exp(x) + 3))*exp(-(5*x*exp(x))/(x^2 - x*exp(x) + 3))
*exp((5*x^2)/(x^2 - x*exp(x) + 3)))
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*exp(x)**2*x**3+(-8*x**4-6*x**3-30*x**2)*exp(x)+4*x**5+36*x**3+36*x)*exp((5*exp(x)*x-5*x**2-12)/
(exp(x)*x-x**2-3))+2*exp(x)**2*x**2+(-4*x**3-12*x)*exp(x)+2*x**4+12*x**2+18)*exp(x**2*exp((5*exp(x)*x-5*x**2-1
2)/(exp(x)*x-x**2-3))+x)**2+((-4*x**5*exp(x)**2+(8*x**6+6*x**5+30*x**4)*exp(x)-4*x**7-36*x**5-36*x**3)*exp((5*
exp(x)*x-5*x**2-12)/(exp(x)*x-x**2-3))+(-2*x**4-4*x**3)*exp(x)**2+(4*x**5+8*x**4+12*x**3+24*x**2)*exp(x)-2*x**
6-4*x**5-12*x**4-24*x**3-18*x**2-36*x)*exp(x**2*exp((5*exp(x)*x-5*x**2-12)/(exp(x)*x-x**2-3))+x)+4*x**5*exp(x)
**2+(-8*x**6-24*x**4)*exp(x)+4*x**7+24*x**5+36*x**3)/(exp(x)**2*x**2+(-2*x**3-6*x)*exp(x)+x**4+6*x**2+9),x)
[Out]
Timed out
________________________________________________________________________________________