∫ e−2e e5 _________ ex−x2 −2x+e−2e e5 _________ ex−x2 −2xx (e2x(1−2x)+x4−2x5+e e5 _________ ex−x2 (2e5+xx−4e5x2)+ex(−2x2+4x3)) _______________________________________________________________________________________________________________________________

3.92.55 \(\int \frac {e^{-2 e^{\frac {e^5}{e^x-x^2}}-2 x+e^{-2 e^{\frac {e^5}{e^x-x^2}}-2 x} x} (e^{2 x} (1-2 x)+x^4-2 x^5+e^{\frac {e^5}{e^x-x^2}} (2 e^{5+x} x-4 e^5 x^2)+e^x (-2 x^2+4 x^3))}{e^{2 x}-2 e^x x^2+x^4} \, dx\)

Optimal. Leaf size=27 \[ e^{e^{-2 \left (e^{\frac {e^5}{e^x-x^2}}+x\right )} x} \]

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Rubi [F] time = 148.14, 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*} \int \frac {\exp \left (-2 e^{\frac {e^5}{e^x-x^2}}-2 x+e^{-2 e^{\frac {e^5}{e^x-x^2}}-2 x} x\right ) \left (e^{2 x} (1-2 x)+x^4-2 x^5+e^{\frac {e^5}{e^x-x^2}} \left (2 e^{5+x} x-4 e^5 x^2\right )+e^x \left (-2 x^2+4 x^3\right )\right )}{e^{2 x}-2 e^x x^2+x^4} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(E^(-2*E^(E^5/(E^x - x^2)) - 2*x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)*(E^(2*x)*(1 - 2*x) + x^4 - 2*x^5 +

E^(E^5/(E^x - x^2))*(2*E^(5 + x)*x - 4*E^5*x^2) + E^x*(-2*x^2 + 4*x^3)))/(E^(2*x) - 2*E^x*x^2 + x^4),x]

[Out]

Defer[Int][E^(-2*E^(E^5/(E^x - x^2)) + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)/(E^x - x^2)^2, x] - 2*Defer[Int][(E

^(-2*E^(E^5/(E^x - x^2)) + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)*x)/(-E^x + x^2)^2, x] - 2*Defer[Int][(E^(-2*E^(

E^5/(E^x - x^2)) - x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)*x^2)/(-E^x + x^2)^2, x] - 4*Defer[Int][(E^(5 - 2*E^

(E^5/(E^x - x^2)) - 2*x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x + E^5/(E^x - x^2))*x^2)/(-E^x + x^2)^2, x] + 4*De

fer[Int][(E^(-2*E^(E^5/(E^x - x^2)) - x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)*x^3)/(-E^x + x^2)^2, x] + 2*Defe

r[Int][(E^(5 - 2*E^(E^5/(E^x - x^2)) - 2*x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x + E^5/(E^x - x^2))*x^3)/(-E^x

+ x^2)^2, x] + Defer[Int][(E^(-2*E^(E^5/(E^x - x^2)) - 2*x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)*x^4)/(-E^x +

x^2)^2, x] - 2*Defer[Int][(E^(-2*E^(E^5/(E^x - x^2)) - 2*x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)*x^5)/(-E^x +

x^2)^2, x] - 2*Defer[Int][(E^(5 - 2*E^(E^5/(E^x - x^2)) - 2*x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x + E^5/(E^x

- x^2))*x)/(-E^x + x^2), x]

Rubi steps

Aborted

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Mathematica [A] time = 0.55, size = 29, normalized size = 1.07 \begin {gather*} e^{e^{-2 e^{\frac {e^5}{e^x-x^2}}-2 x} x} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^(-2*E^(E^5/(E^x - x^2)) - 2*x + E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)*(E^(2*x)*(1 - 2*x) + x^4 - 2*

x^5 + E^(E^5/(E^x - x^2))*(2*E^(5 + x)*x - 4*E^5*x^2) + E^x*(-2*x^2 + 4*x^3)))/(E^(2*x) - 2*E^x*x^2 + x^4),x]

[Out]

E^(E^(-2*E^(E^5/(E^x - x^2)) - 2*x)*x)

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fricas [A] time = 0.58, size = 30, normalized size = 1.11 \begin {gather*} e^{\left (x e^{\left (-2 \, x - 2 \, e^{\left (-\frac {e^{10}}{x^{2} e^{5} - e^{\left (x + 5\right )}}\right )}\right )}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x*exp(5)*exp(x)-4*x^2*exp(5))*exp(exp(5)/(exp(x)-x^2))+(1-2*x)*exp(x)^2+(4*x^3-2*x^2)*exp(x)-2*x

^5+x^4)*exp(x/exp(2*exp(exp(5)/(exp(x)-x^2))+2*x))/(exp(x)^2-2*exp(x)*x^2+x^4)/exp(2*exp(exp(5)/(exp(x)-x^2))+

2*x),x, algorithm="fricas")

[Out]

e^(x*e^(-2*x - 2*e^(-e^10/(x^2*e^5 - e^(x + 5)))))

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giac [A] time = 0.14, size = 25, normalized size = 0.93 \begin {gather*} e^{\left (x e^{\left (-2 \, x - 2 \, e^{\left (-\frac {e^{5}}{x^{2} - e^{x}}\right )}\right )}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x*exp(5)*exp(x)-4*x^2*exp(5))*exp(exp(5)/(exp(x)-x^2))+(1-2*x)*exp(x)^2+(4*x^3-2*x^2)*exp(x)-2*x

^5+x^4)*exp(x/exp(2*exp(exp(5)/(exp(x)-x^2))+2*x))/(exp(x)^2-2*exp(x)*x^2+x^4)/exp(2*exp(exp(5)/(exp(x)-x^2))+

2*x),x, algorithm="giac")

[Out]

e^(x*e^(-2*x - 2*e^(-e^5/(x^2 - e^x))))

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maple [A] time = 0.13, size = 25, normalized size = 0.93


method	result	size

risch	\({\mathrm e}^{x \,{\mathrm e}^{-2 \,{\mathrm e}^{\frac {{\mathrm e}^{5}}{{\mathrm e}^{x}-x^{2}}}-2 x}}\)	\(25\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x*exp(5)*exp(x)-4*x^2*exp(5))*exp(exp(5)/(exp(x)-x^2))+(1-2*x)*exp(x)^2+(4*x^3-2*x^2)*exp(x)-2*x^5+x^4

)*exp(x/exp(2*exp(exp(5)/(exp(x)-x^2))+2*x))/(exp(x)^2-2*exp(x)*x^2+x^4)/exp(2*exp(exp(5)/(exp(x)-x^2))+2*x),x

,method=_RETURNVERBOSE)

[Out]

exp(x*exp(-2*exp(exp(5)/(exp(x)-x^2))-2*x))

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maxima [A] time = 0.72, size = 25, normalized size = 0.93 \begin {gather*} e^{\left (x e^{\left (-2 \, x - 2 \, e^{\left (-\frac {e^{5}}{x^{2} - e^{x}}\right )}\right )}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x*exp(5)*exp(x)-4*x^2*exp(5))*exp(exp(5)/(exp(x)-x^2))+(1-2*x)*exp(x)^2+(4*x^3-2*x^2)*exp(x)-2*x

^5+x^4)*exp(x/exp(2*exp(exp(5)/(exp(x)-x^2))+2*x))/(exp(x)^2-2*exp(x)*x^2+x^4)/exp(2*exp(exp(5)/(exp(x)-x^2))+

2*x),x, algorithm="maxima")

[Out]

e^(x*e^(-2*x - 2*e^(-e^5/(x^2 - e^x))))

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mupad [B] time = 6.36, size = 24, normalized size = 0.89 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^5}{{\mathrm {e}}^x-x^2}}}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x*exp(- 2*x - 2*exp(exp(5)/(exp(x) - x^2))))*exp(- 2*x - 2*exp(exp(5)/(exp(x) - x^2)))*(exp(x)*(2*x^

2 - 4*x^3) + exp(exp(5)/(exp(x) - x^2))*(4*x^2*exp(5) - 2*x*exp(5)*exp(x)) + exp(2*x)*(2*x - 1) - x^4 + 2*x^5)

)/(exp(2*x) - 2*x^2*exp(x) + x^4),x)

[Out]

exp(x*exp(-2*x)*exp(-2*exp(exp(5)/(exp(x) - x^2))))

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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(((2*x*exp(5)*exp(x)-4*x**2*exp(5))*exp(exp(5)/(exp(x)-x**2))+(1-2*x)*exp(x)**2+(4*x**3-2*x**2)*exp(x

)-2*x**5+x**4)*exp(x/exp(2*exp(exp(5)/(exp(x)-x**2))+2*x))/(exp(x)**2-2*exp(x)*x**2+x**4)/exp(2*exp(exp(5)/(ex

p(x)-x**2))+2*x),x)

[Out]

Timed out

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