∫ e−20+4e4+eex (4−ex)+3x−4x2+ex(5−e4−x+x2) _________________________________________________________________ −5+e4+eex+x−x2 (5−e4−e2ex+x −x2+ex(−25−e8+10x−11x2+2x3−x4+e4(10−2x+2x2))+eex (−1+ex(10−2e4−x+2x2)))__________________________________________________________________________________________________________ 25+e8+e2ex−10x+11x2−2x3+x4+e4(−10+2x−2x2)+eex(−10+2e4+2x−2x2) dx

3.15.80 $\int \frac {e^{\frac {-20+4 e^4+e^{e^x} (4-e^x)+3 x-4 x^2+e^x (5-e^4-x+x^2)}{-5+e^4+e^{e^x}+x-x^2}} (5-e^4-e^{2 e^x+x}-x^2+e^x (-25-e^8+10 x-11 x^2+2 x^3-x^4+e^4 (10-2 x+2 x^2))+e^{e^x} (-1+e^x (10-2 e^4-x+2 x^2)))}{25+e^8+e^{2 e^x}-10 x+11 x^2-2 x^3+x^4+e^4 (-10+2 x-2 x^2)+e^{e^x} (-10+2 e^4+2 x-2 x^2)} \, dx$

Optimal. Leaf size=33 \[ e^{4-e^x+\frac {x}{5-e^4-e^{e^x}-x+x^2}} \]

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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[(E^((-20 + 4*E^4 + E^E^x*(4 - E^x) + 3*x - 4*x^2 + E^x*(5 - E^4 - x + x^2))/(-5 + E^4 + E^E^x + x - x^2))*

(5 - E^4 - E^(2*E^x + x) - x^2 + E^x*(-25 - E^8 + 10*x - 11*x^2 + 2*x^3 - x^4 + E^4*(10 - 2*x + 2*x^2)) + E^E^

x*(-1 + E^x*(10 - 2*E^4 - x + 2*x^2))))/(25 + E^8 + E^(2*E^x) - 10*x + 11*x^2 - 2*x^3 + x^4 + E^4*(-10 + 2*x -

2*x^2) + E^E^x*(-10 + 2*E^4 + 2*x - 2*x^2)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A] time = 0.49, size = 30, normalized size = 0.91 \begin {gather*} e^{4-e^x-\frac {x}{-5+e^4+e^{e^x}+x-x^2}} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^((-20 + 4*E^4 + E^E^x*(4 - E^x) + 3*x - 4*x^2 + E^x*(5 - E^4 - x + x^2))/(-5 + E^4 + E^E^x + x -

x^2))*(5 - E^4 - E^(2*E^x + x) - x^2 + E^x*(-25 - E^8 + 10*x - 11*x^2 + 2*x^3 - x^4 + E^4*(10 - 2*x + 2*x^2))

+ E^E^x*(-1 + E^x*(10 - 2*E^4 - x + 2*x^2))))/(25 + E^8 + E^(2*E^x) - 10*x + 11*x^2 - 2*x^3 + x^4 + E^4*(-10 +

2*x - 2*x^2) + E^E^x*(-10 + 2*E^4 + 2*x - 2*x^2)),x]

[Out]

E^(4 - E^x - x/(-5 + E^4 + E^E^x + x - x^2))

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fricas [B] time = 0.96, size = 59, normalized size = 1.79 \begin {gather*} e^{\left (\frac {4 \, x^{2} - {\left (x^{2} - x - e^{4} + 5\right )} e^{x} + {\left (e^{x} - 4\right )} e^{\left (e^{x}\right )} - 3 \, x - 4 \, e^{4} + 20}{x^{2} - x - e^{4} - e^{\left (e^{x}\right )} + 5}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp(x))+(-exp(4)^2+(2*x^2-2*x+10)*exp(4

)-x^4+2*x^3-11*x^2+10*x-25)*exp(x)-exp(4)-x^2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4

)-4*x^2+3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2+2*x-10)*exp(exp(x))+exp(4)^2+(-2*

x^2+2*x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x+25),x, algorithm="fricas")

[Out]

e^((4*x^2 - (x^2 - x - e^4 + 5)*e^x + (e^x - 4)*e^(e^x) - 3*x - 4*e^4 + 20)/(x^2 - x - e^4 - e^(e^x) + 5))

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giac [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((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp(x))+(-exp(4)^2+(2*x^2-2*x+10)*exp(4

)-x^4+2*x^3-11*x^2+10*x-25)*exp(x)-exp(4)-x^2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4

)-4*x^2+3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2+2*x-10)*exp(exp(x))+exp(4)^2+(-2*

x^2+2*x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x+25),x, algorithm="giac")

[Out]

Timed out

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maple [F] time = 1.08, size = 0, normalized size = 0.00 \[\int \frac {\left (-{\mathrm e}^{x} {\mathrm e}^{2 \,{\mathrm e}^{x}}+\left (\left (-2 \,{\mathrm e}^{4}+2 x^{2}-x +10\right ) {\mathrm e}^{x}-1\right ) {\mathrm e}^{{\mathrm e}^{x}}+\left (-{\mathrm e}^{8}+\left (2 x^{2}-2 x +10\right ) {\mathrm e}^{4}-x^{4}+2 x^{3}-11 x^{2}+10 x -25\right ) {\mathrm e}^{x}-{\mathrm e}^{4}-x^{2}+5\right ) {\mathrm e}^{\frac {\left (-{\mathrm e}^{x}+4\right ) {\mathrm e}^{{\mathrm e}^{x}}+\left (-{\mathrm e}^{4}+x^{2}-x +5\right ) {\mathrm e}^{x}+4 \,{\mathrm e}^{4}-4 x^{2}+3 x -20}{{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x -5}}}{{\mathrm e}^{2 \,{\mathrm e}^{x}}+\left (2 \,{\mathrm e}^{4}-2 x^{2}+2 x -10\right ) {\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{8}+\left (-2 x^{2}+2 x -10\right ) {\mathrm e}^{4}+x^{4}-2 x^{3}+11 x^{2}-10 x +25}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp(x))+(-exp(4)^2+(2*x^2-2*x+10)*exp(4)-x^4+

2*x^3-11*x^2+10*x-25)*exp(x)-exp(4)-x^2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4)-4*x^

2+3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2+2*x-10)*exp(exp(x))+exp(4)^2+(-2*x^2+2*

x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x+25),x)

[Out]

int((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp(x))+(-exp(4)^2+(2*x^2-2*x+10)*exp(4)-x^4+

2*x^3-11*x^2+10*x-25)*exp(x)-exp(4)-x^2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4)-4*x^

2+3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2+2*x-10)*exp(exp(x))+exp(4)^2+(-2*x^2+2*

x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x+25),x)

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maxima [A] time = 1.39, size = 28, normalized size = 0.85 \begin {gather*} e^{\left (\frac {x}{x^{2} - x - e^{4} - e^{\left (e^{x}\right )} + 5} - e^{x} + 4\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp(x))+(-exp(4)^2+(2*x^2-2*x+10)*exp(4

)-x^4+2*x^3-11*x^2+10*x-25)*exp(x)-exp(4)-x^2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4

)-4*x^2+3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2+2*x-10)*exp(exp(x))+exp(4)^2+(-2*

x^2+2*x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x+25),x, algorithm="maxima")

[Out]

e^(x/(x^2 - x - e^4 - e^(e^x) + 5) - e^x + 4)

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mupad [B] time = 1.96, size = 208, normalized size = 6.30 \begin {gather*} {\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{{\mathrm {e}}^x}}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^4\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^4}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{\frac {3\,x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {4\,x^2}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{\frac {5\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {20}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(exp(x)*(x + exp(4) - x^2 - 5) - 4*exp(4) - 3*x + 4*x^2 + exp(exp(x))*(exp(x) - 4) + 20)/(x + exp(e

xp(x)) + exp(4) - x^2 - 5))*(exp(4) + exp(exp(x))*(exp(x)*(x + 2*exp(4) - 2*x^2 - 10) + 1) + exp(x)*(exp(8) -

10*x - exp(4)*(2*x^2 - 2*x + 10) + 11*x^2 - 2*x^3 + x^4 + 25) + x^2 + exp(2*exp(x))*exp(x) - 5))/(exp(8) - 10*

x + exp(2*exp(x)) - exp(4)*(2*x^2 - 2*x + 10) + exp(exp(x))*(2*x + 2*exp(4) - 2*x^2 - 10) + 11*x^2 - 2*x^3 + x

^4 + 25),x)

[Out]

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

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

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

(-(4*x^2)/(x + exp(exp(x)) + exp(4) - x^2 - 5))*exp((5*exp(x))/(x + exp(exp(x)) + exp(4) - x^2 - 5))*exp(-20/(

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

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sympy [B] time = 2.43, size = 54, normalized size = 1.64 \begin {gather*} e^{\frac {- 4 x^{2} + 3 x + \left (4 - e^{x}\right ) e^{e^{x}} + \left (x^{2} - x - e^{4} + 5\right ) e^{x} - 20 + 4 e^{4}}{- x^{2} + x + e^{e^{x}} - 5 + e^{4}}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*exp(exp(x))**2+((-2*exp(4)+2*x**2-x+10)*exp(x)-1)*exp(exp(x))+(-exp(4)**2+(2*x**2-2*x+10)*e

xp(4)-x**4+2*x**3-11*x**2+10*x-25)*exp(x)-exp(4)-x**2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x**2-x+5)*exp(x

)+4*exp(4)-4*x**2+3*x-20)/(exp(exp(x))+exp(4)-x**2+x-5))/(exp(exp(x))**2+(2*exp(4)-2*x**2+2*x-10)*exp(exp(x))+

exp(4)**2+(-2*x**2+2*x-10)*exp(4)+x**4-2*x**3+11*x**2-10*x+25),x)

[Out]

exp((-4*x**2 + 3*x + (4 - exp(x))*exp(exp(x)) + (x**2 - x - exp(4) + 5)*exp(x) - 20 + 4*exp(4))/(-x**2 + x + e

xp(exp(x)) - 5 + exp(4)))

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