3.51.24 \(\int e^{-5+x^4+e^{\frac {3 e^{3 x^{-x}}}{x}} (-4 e^{3 x} x-12 e^{2 x} x^2-12 e^x x^3-4 x^4)+e^{\frac {e^{3 x^{-x}}}{x}} (-4 e^x x^3-4 x^4)+e^{\frac {4 e^{3 x^{-x}}}{x}} (e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4)+e^{\frac {2 e^{3 x^{-x}}}{x}} (6 e^{2 x} x^2+12 e^x x^3+6 x^4)} x^{-2-x} (4 x^{5+x}+e^{\frac {2 e^{3 x^{-x}}}{x}} (x^x (24 x^5+e^{2 x} (12 x^3+12 x^4)+e^x (36 x^4+12 x^5))+e^{3 x^{-x}} (-36 e^{2 x} x^3-72 e^x x^4-36 x^5+x^x (-12 e^{2 x} x^2-24 e^x x^3-12 x^4)+(-36 e^{2 x} x^3-72 e^x x^4-36 x^5) \log (x)))+e^{\frac {4 e^{3 x^{-x}}}{x}} (x^x (4 e^{4 x} x^2+4 x^5+e^{3 x} (4 x^2+12 x^3)+e^{2 x} (12 x^3+12 x^4)+e^x (12 x^4+4 x^5))+e^{3 x^{-x}} (-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5+x^x (-4 e^{4 x}-16 e^{3 x} x-24 e^{2 x} x^2-16 e^x x^3-4 x^4)+(-12 e^{4 x} x-48 e^{3 x} x^2-72 e^{2 x} x^3-48 e^x x^4-12 x^5) \log (x)))+e^{\frac {e^{3 x^{-x}}}{x}} (x^x (-16 x^5+e^x (-12 x^4-4 x^5))+e^{3 x^{-x}} (12 e^x x^4+12 x^5+x^x (4 e^x x^3+4 x^4)+(12 e^x x^4+12 x^5) \log (x)))+e^{\frac {3 e^{3 x^{-x}}}{x}} (x^x (-16 x^5+e^{3 x} (-4 x^2-12 x^3)+e^{2 x} (-24 x^3-24 x^4)+e^x (-36 x^4-12 x^5))+e^{3 x^{-x}} (36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5+x^x (12 e^{3 x} x+36 e^{2 x} x^2+36 e^x x^3+12 x^4)+(36 e^{3 x} x^2+108 e^{2 x} x^3+108 e^x x^4+36 x^5) \log (x)))) \, dx\)

Optimal. Leaf size=31 \[ e^{-5+\left (-x+e^{\frac {e^{3 x^{-x}}}{x}} \left (e^x+x\right )\right )^4} \]

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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^(-5 + x^4 + E^((3*E^(3/x^x))/x)*(-4*E^(3*x)*x - 12*E^(2*x)*x^2 - 12*E^x*x^3 - 4*x^4) + E^(E^(3/x^x)/x)*(
-4*E^x*x^3 - 4*x^4) + E^((4*E^(3/x^x))/x)*(E^(4*x) + 4*E^(3*x)*x + 6*E^(2*x)*x^2 + 4*E^x*x^3 + x^4) + E^((2*E^
(3/x^x))/x)*(6*E^(2*x)*x^2 + 12*E^x*x^3 + 6*x^4))*x^(-2 - x)*(4*x^(5 + x) + E^((2*E^(3/x^x))/x)*(x^x*(24*x^5 +
E^(2*x)*(12*x^3 + 12*x^4) + E^x*(36*x^4 + 12*x^5)) + E^(3/x^x)*(-36*E^(2*x)*x^3 - 72*E^x*x^4 - 36*x^5 + x^x*(
-12*E^(2*x)*x^2 - 24*E^x*x^3 - 12*x^4) + (-36*E^(2*x)*x^3 - 72*E^x*x^4 - 36*x^5)*Log[x])) + E^((4*E^(3/x^x))/x
)*(x^x*(4*E^(4*x)*x^2 + 4*x^5 + E^(3*x)*(4*x^2 + 12*x^3) + E^(2*x)*(12*x^3 + 12*x^4) + E^x*(12*x^4 + 4*x^5)) +
E^(3/x^x)*(-12*E^(4*x)*x - 48*E^(3*x)*x^2 - 72*E^(2*x)*x^3 - 48*E^x*x^4 - 12*x^5 + x^x*(-4*E^(4*x) - 16*E^(3*
x)*x - 24*E^(2*x)*x^2 - 16*E^x*x^3 - 4*x^4) + (-12*E^(4*x)*x - 48*E^(3*x)*x^2 - 72*E^(2*x)*x^3 - 48*E^x*x^4 -
12*x^5)*Log[x])) + E^(E^(3/x^x)/x)*(x^x*(-16*x^5 + E^x*(-12*x^4 - 4*x^5)) + E^(3/x^x)*(12*E^x*x^4 + 12*x^5 + x
^x*(4*E^x*x^3 + 4*x^4) + (12*E^x*x^4 + 12*x^5)*Log[x])) + E^((3*E^(3/x^x))/x)*(x^x*(-16*x^5 + E^(3*x)*(-4*x^2
- 12*x^3) + E^(2*x)*(-24*x^3 - 24*x^4) + E^x*(-36*x^4 - 12*x^5)) + E^(3/x^x)*(36*E^(3*x)*x^2 + 108*E^(2*x)*x^3
+ 108*E^x*x^4 + 36*x^5 + x^x*(12*E^(3*x)*x + 36*E^(2*x)*x^2 + 36*E^x*x^3 + 12*x^4) + (36*E^(3*x)*x^2 + 108*E^
(2*x)*x^3 + 108*E^x*x^4 + 36*x^5)*Log[x]))),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 1.27, size = 110, normalized size = 3.55 \begin {gather*} e^{-5+x^4-4 e^{\frac {e^{3 x^{-x}}}{x}} x^3 \left (e^x+x\right )+6 e^{\frac {2 e^{3 x^{-x}}}{x}} x^2 \left (e^x+x\right )^2-4 e^{\frac {3 e^{3 x^{-x}}}{x}} x \left (e^x+x\right )^3+e^{\frac {4 e^{3 x^{-x}}}{x}} \left (e^x+x\right )^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-5 + x^4 + E^((3*E^(3/x^x))/x)*(-4*E^(3*x)*x - 12*E^(2*x)*x^2 - 12*E^x*x^3 - 4*x^4) + E^(E^(3/x^x
)/x)*(-4*E^x*x^3 - 4*x^4) + E^((4*E^(3/x^x))/x)*(E^(4*x) + 4*E^(3*x)*x + 6*E^(2*x)*x^2 + 4*E^x*x^3 + x^4) + E^
((2*E^(3/x^x))/x)*(6*E^(2*x)*x^2 + 12*E^x*x^3 + 6*x^4))*x^(-2 - x)*(4*x^(5 + x) + E^((2*E^(3/x^x))/x)*(x^x*(24
*x^5 + E^(2*x)*(12*x^3 + 12*x^4) + E^x*(36*x^4 + 12*x^5)) + E^(3/x^x)*(-36*E^(2*x)*x^3 - 72*E^x*x^4 - 36*x^5 +
x^x*(-12*E^(2*x)*x^2 - 24*E^x*x^3 - 12*x^4) + (-36*E^(2*x)*x^3 - 72*E^x*x^4 - 36*x^5)*Log[x])) + E^((4*E^(3/x
^x))/x)*(x^x*(4*E^(4*x)*x^2 + 4*x^5 + E^(3*x)*(4*x^2 + 12*x^3) + E^(2*x)*(12*x^3 + 12*x^4) + E^x*(12*x^4 + 4*x
^5)) + E^(3/x^x)*(-12*E^(4*x)*x - 48*E^(3*x)*x^2 - 72*E^(2*x)*x^3 - 48*E^x*x^4 - 12*x^5 + x^x*(-4*E^(4*x) - 16
*E^(3*x)*x - 24*E^(2*x)*x^2 - 16*E^x*x^3 - 4*x^4) + (-12*E^(4*x)*x - 48*E^(3*x)*x^2 - 72*E^(2*x)*x^3 - 48*E^x*
x^4 - 12*x^5)*Log[x])) + E^(E^(3/x^x)/x)*(x^x*(-16*x^5 + E^x*(-12*x^4 - 4*x^5)) + E^(3/x^x)*(12*E^x*x^4 + 12*x
^5 + x^x*(4*E^x*x^3 + 4*x^4) + (12*E^x*x^4 + 12*x^5)*Log[x])) + E^((3*E^(3/x^x))/x)*(x^x*(-16*x^5 + E^(3*x)*(-
4*x^2 - 12*x^3) + E^(2*x)*(-24*x^3 - 24*x^4) + E^x*(-36*x^4 - 12*x^5)) + E^(3/x^x)*(36*E^(3*x)*x^2 + 108*E^(2*
x)*x^3 + 108*E^x*x^4 + 36*x^5 + x^x*(12*E^(3*x)*x + 36*E^(2*x)*x^2 + 36*E^x*x^3 + 12*x^4) + (36*E^(3*x)*x^2 +
108*E^(2*x)*x^3 + 108*E^x*x^4 + 36*x^5)*Log[x]))),x]

[Out]

E^(-5 + x^4 - 4*E^(E^(3/x^x)/x)*x^3*(E^x + x) + 6*E^((2*E^(3/x^x))/x)*x^2*(E^x + x)^2 - 4*E^((3*E^(3/x^x))/x)*
x*(E^x + x)^3 + E^((4*E^(3/x^x))/x)*(E^x + x)^4)

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fricas [B]  time = 1.04, size = 154, normalized size = 4.97 \begin {gather*} e^{\left (x^{4} + {\left (x^{4} + 4 \, x^{3} e^{x} + 6 \, x^{2} e^{\left (2 \, x\right )} + 4 \, x e^{\left (3 \, x\right )} + e^{\left (4 \, x\right )}\right )} e^{\left (\frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, {\left (x^{4} + 3 \, x^{3} e^{x} + 3 \, x^{2} e^{\left (2 \, x\right )} + x e^{\left (3 \, x\right )}\right )} e^{\left (\frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 6 \, {\left (x^{4} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )}\right )} e^{\left (\frac {2 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, {\left (x^{4} + x^{3} e^{x}\right )} e^{\left (\frac {e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*exp(x)^4-16*x*exp(x)^3-24*exp(x)^2*x^2-16*exp(x)*x^3-4*x^4)*exp(x*log(x))+(-12*x*exp(x)^4-48*
x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x)*x^4-12*x^5)*log(x)-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp
(x)*x^4-12*x^5)*exp(3/exp(x*log(x)))+(4*x^2*exp(x)^4+(12*x^3+4*x^2)*exp(x)^3+(12*x^4+12*x^3)*exp(x)^2+(4*x^5+1
2*x^4)*exp(x)+4*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^4+(((12*x*exp(x)^3+36*exp(x)^2*x^2+36*exp(x)*x
^3+12*x^4)*exp(x*log(x))+(36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*log(x)+36*x^2*exp(x)^3+108*e
xp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*exp(3/exp(x*log(x)))+((-12*x^3-4*x^2)*exp(x)^3+(-24*x^4-24*x^3)*exp(x)^2+(-
12*x^5-36*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^3+(((-12*exp(x)^2*x^2-24*exp(x)*x^3-1
2*x^4)*exp(x*log(x))+(-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*log(x)-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*exp(
3/exp(x*log(x)))+((12*x^4+12*x^3)*exp(x)^2+(12*x^5+36*x^4)*exp(x)+24*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x
)))/x)^2+(((4*exp(x)*x^3+4*x^4)*exp(x*log(x))+(12*exp(x)*x^4+12*x^5)*log(x)+12*exp(x)*x^4+12*x^5)*exp(3/exp(x*
log(x)))+((-4*x^5-12*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)+4*x^5*exp(x*log(x)))*exp((
exp(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^3+x^4)*exp(exp(3/exp(x*log(x)))/x)^4+(-4*x*exp(x)^3-12*exp(x)^
2*x^2-12*exp(x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)^3+(6*exp(x)^2*x^2+12*exp(x)*x^3+6*x^4)*exp(exp(3/exp(x*
log(x)))/x)^2+(-4*exp(x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)+x^4-5)/x^2/exp(x*log(x)),x, algorithm="fricas"
)

[Out]

e^(x^4 + (x^4 + 4*x^3*e^x + 6*x^2*e^(2*x) + 4*x*e^(3*x) + e^(4*x))*e^(4*e^(3/x^x)/x) - 4*(x^4 + 3*x^3*e^x + 3*
x^2*e^(2*x) + x*e^(3*x))*e^(3*e^(3/x^x)/x) + 6*(x^4 + 2*x^3*e^x + x^2*e^(2*x))*e^(2*e^(3/x^x)/x) - 4*(x^4 + x^
3*e^x)*e^(e^(3/x^x)/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(((((-4*exp(x)^4-16*x*exp(x)^3-24*exp(x)^2*x^2-16*exp(x)*x^3-4*x^4)*exp(x*log(x))+(-12*x*exp(x)^4-48*
x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x)*x^4-12*x^5)*log(x)-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp
(x)*x^4-12*x^5)*exp(3/exp(x*log(x)))+(4*x^2*exp(x)^4+(12*x^3+4*x^2)*exp(x)^3+(12*x^4+12*x^3)*exp(x)^2+(4*x^5+1
2*x^4)*exp(x)+4*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^4+(((12*x*exp(x)^3+36*exp(x)^2*x^2+36*exp(x)*x
^3+12*x^4)*exp(x*log(x))+(36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*log(x)+36*x^2*exp(x)^3+108*e
xp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*exp(3/exp(x*log(x)))+((-12*x^3-4*x^2)*exp(x)^3+(-24*x^4-24*x^3)*exp(x)^2+(-
12*x^5-36*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^3+(((-12*exp(x)^2*x^2-24*exp(x)*x^3-1
2*x^4)*exp(x*log(x))+(-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*log(x)-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*exp(
3/exp(x*log(x)))+((12*x^4+12*x^3)*exp(x)^2+(12*x^5+36*x^4)*exp(x)+24*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x
)))/x)^2+(((4*exp(x)*x^3+4*x^4)*exp(x*log(x))+(12*exp(x)*x^4+12*x^5)*log(x)+12*exp(x)*x^4+12*x^5)*exp(3/exp(x*
log(x)))+((-4*x^5-12*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)+4*x^5*exp(x*log(x)))*exp((
exp(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^3+x^4)*exp(exp(3/exp(x*log(x)))/x)^4+(-4*x*exp(x)^3-12*exp(x)^
2*x^2-12*exp(x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)^3+(6*exp(x)^2*x^2+12*exp(x)*x^3+6*x^4)*exp(exp(3/exp(x*
log(x)))/x)^2+(-4*exp(x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)+x^4-5)/x^2/exp(x*log(x)),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 1.00, size = 312, normalized size = 10.06

method	result	size
risch	\({\mathrm e}^{4 x^{3} {\mathrm e}^{\frac {x^{2}+4 \,{\mathrm e}^{3 x^{-x}}}{x}}-12 x^{3} {\mathrm e}^{\frac {x^{2}+3 \,{\mathrm e}^{3 x^{-x}}}{x}}+12 x^{3} {\mathrm e}^{\frac {x^{2}+2 \,{\mathrm e}^{3 x^{-x}}}{x}}-4 x^{3} {\mathrm e}^{\frac {x^{2}+{\mathrm e}^{3 x^{-x}}}{x}}+{\mathrm e}^{\frac {4 \,{\mathrm e}^{3 x^{-x}}}{x}} x^{4}-4 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{3 x^{-x}}}{x}} x^{4}+6 \,{\mathrm e}^{\frac {2 \,{\mathrm e}^{3 x^{-x}}}{x}} x^{4}-4 \,{\mathrm e}^{\frac {{\mathrm e}^{3 x^{-x}}}{x}} x^{4}+6 x^{2} {\mathrm e}^{\frac {2 x^{2}+4 \,{\mathrm e}^{3 x^{-x}}}{x}}-12 x^{2} {\mathrm e}^{\frac {2 x^{2}+3 \,{\mathrm e}^{3 x^{-x}}}{x}}+6 x^{2} {\mathrm e}^{\frac {2 x^{2}+2 \,{\mathrm e}^{3 x^{-x}}}{x}}+x^{4}+4 x \,{\mathrm e}^{\frac {3 x^{2}+4 \,{\mathrm e}^{3 x^{-x}}}{x}}-4 x \,{\mathrm e}^{\frac {3 x^{2}+3 \,{\mathrm e}^{3 x^{-x}}}{x}}+{\mathrm e}^{\frac {4 x^{2}+4 \,{\mathrm e}^{3 x^{-x}}}{x}}-5}\)	\(312\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-4*exp(x)^4-16*x*exp(x)^3-24*exp(x)^2*x^2-16*exp(x)*x^3-4*x^4)*exp(x*ln(x))+(-12*x*exp(x)^4-48*x^2*exp
(x)^3-72*exp(x)^2*x^3-48*exp(x)*x^4-12*x^5)*ln(x)-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x)*x^4-
12*x^5)*exp(3/exp(x*ln(x)))+(4*x^2*exp(x)^4+(12*x^3+4*x^2)*exp(x)^3+(12*x^4+12*x^3)*exp(x)^2+(4*x^5+12*x^4)*ex
p(x)+4*x^5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)^4+(((12*x*exp(x)^3+36*exp(x)^2*x^2+36*exp(x)*x^3+12*x^4)*
exp(x*ln(x))+(36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*ln(x)+36*x^2*exp(x)^3+108*exp(x)^2*x^3+1
08*exp(x)*x^4+36*x^5)*exp(3/exp(x*ln(x)))+((-12*x^3-4*x^2)*exp(x)^3+(-24*x^4-24*x^3)*exp(x)^2+(-12*x^5-36*x^4)
*exp(x)-16*x^5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)^3+(((-12*exp(x)^2*x^2-24*exp(x)*x^3-12*x^4)*exp(x*ln(
x))+(-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*ln(x)-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*exp(3/exp(x*ln(x)))+((
12*x^4+12*x^3)*exp(x)^2+(12*x^5+36*x^4)*exp(x)+24*x^5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)^2+(((4*exp(x)*
x^3+4*x^4)*exp(x*ln(x))+(12*exp(x)*x^4+12*x^5)*ln(x)+12*exp(x)*x^4+12*x^5)*exp(3/exp(x*ln(x)))+((-4*x^5-12*x^4
)*exp(x)-16*x^5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)+4*x^5*exp(x*ln(x)))*exp((exp(x)^4+4*x*exp(x)^3+6*exp
(x)^2*x^2+4*exp(x)*x^3+x^4)*exp(exp(3/exp(x*ln(x)))/x)^4+(-4*x*exp(x)^3-12*exp(x)^2*x^2-12*exp(x)*x^3-4*x^4)*e
xp(exp(3/exp(x*ln(x)))/x)^3+(6*exp(x)^2*x^2+12*exp(x)*x^3+6*x^4)*exp(exp(3/exp(x*ln(x)))/x)^2+(-4*exp(x)*x^3-4
*x^4)*exp(exp(3/exp(x*ln(x)))/x)+x^4-5)/x^2/exp(x*ln(x)),x,method=_RETURNVERBOSE)

[Out]

exp(4*x^3*exp((x^2+4*exp(3/(x^x)))/x)-12*x^3*exp((x^2+3*exp(3/(x^x)))/x)+12*x^3*exp((x^2+2*exp(3/(x^x)))/x)-4*
x^3*exp((x^2+exp(3/(x^x)))/x)+exp(4*exp(3/(x^x))/x)*x^4-4*exp(3*exp(3/(x^x))/x)*x^4+6*exp(2*exp(3/(x^x))/x)*x^
4-4*exp(exp(3/(x^x))/x)*x^4+6*x^2*exp(2*(x^2+2*exp(3/(x^x)))/x)-12*x^2*exp((2*x^2+3*exp(3/(x^x)))/x)+6*x^2*exp
(2*(x^2+exp(3/(x^x)))/x)+x^4+4*x*exp((3*x^2+4*exp(3/(x^x)))/x)-4*x*exp(3*(x^2+exp(3/(x^x)))/x)+exp(4*(x^2+exp(
3/(x^x)))/x)-5)

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maxima [B]  time = 6.50, size = 292, normalized size = 9.42 \begin {gather*} e^{\left (x^{4} e^{\left (\frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, x^{4} e^{\left (\frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 6 \, x^{4} e^{\left (\frac {2 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, x^{4} e^{\left (\frac {e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + x^{4} + 4 \, x^{3} e^{\left (x + \frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 12 \, x^{3} e^{\left (x + \frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 12 \, x^{3} e^{\left (x + \frac {2 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, x^{3} e^{\left (x + \frac {e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 6 \, x^{2} e^{\left (2 \, x + \frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 12 \, x^{2} e^{\left (2 \, x + \frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 6 \, x^{2} e^{\left (2 \, x + \frac {2 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + 4 \, x e^{\left (3 \, x + \frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 4 \, x e^{\left (3 \, x + \frac {3 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} + e^{\left (4 \, x + \frac {4 \, e^{\left (\frac {3}{x^{x}}\right )}}{x}\right )} - 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*exp(x)^4-16*x*exp(x)^3-24*exp(x)^2*x^2-16*exp(x)*x^3-4*x^4)*exp(x*log(x))+(-12*x*exp(x)^4-48*
x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp(x)*x^4-12*x^5)*log(x)-12*x*exp(x)^4-48*x^2*exp(x)^3-72*exp(x)^2*x^3-48*exp
(x)*x^4-12*x^5)*exp(3/exp(x*log(x)))+(4*x^2*exp(x)^4+(12*x^3+4*x^2)*exp(x)^3+(12*x^4+12*x^3)*exp(x)^2+(4*x^5+1
2*x^4)*exp(x)+4*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^4+(((12*x*exp(x)^3+36*exp(x)^2*x^2+36*exp(x)*x
^3+12*x^4)*exp(x*log(x))+(36*x^2*exp(x)^3+108*exp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*log(x)+36*x^2*exp(x)^3+108*e
xp(x)^2*x^3+108*exp(x)*x^4+36*x^5)*exp(3/exp(x*log(x)))+((-12*x^3-4*x^2)*exp(x)^3+(-24*x^4-24*x^3)*exp(x)^2+(-
12*x^5-36*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)^3+(((-12*exp(x)^2*x^2-24*exp(x)*x^3-1
2*x^4)*exp(x*log(x))+(-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*log(x)-36*exp(x)^2*x^3-72*exp(x)*x^4-36*x^5)*exp(
3/exp(x*log(x)))+((12*x^4+12*x^3)*exp(x)^2+(12*x^5+36*x^4)*exp(x)+24*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x
)))/x)^2+(((4*exp(x)*x^3+4*x^4)*exp(x*log(x))+(12*exp(x)*x^4+12*x^5)*log(x)+12*exp(x)*x^4+12*x^5)*exp(3/exp(x*
log(x)))+((-4*x^5-12*x^4)*exp(x)-16*x^5)*exp(x*log(x)))*exp(exp(3/exp(x*log(x)))/x)+4*x^5*exp(x*log(x)))*exp((
exp(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^3+x^4)*exp(exp(3/exp(x*log(x)))/x)^4+(-4*x*exp(x)^3-12*exp(x)^
2*x^2-12*exp(x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)^3+(6*exp(x)^2*x^2+12*exp(x)*x^3+6*x^4)*exp(exp(3/exp(x*
log(x)))/x)^2+(-4*exp(x)*x^3-4*x^4)*exp(exp(3/exp(x*log(x)))/x)+x^4-5)/x^2/exp(x*log(x)),x, algorithm="maxima"
)

[Out]

e^(x^4*e^(4*e^(3/x^x)/x) - 4*x^4*e^(3*e^(3/x^x)/x) + 6*x^4*e^(2*e^(3/x^x)/x) - 4*x^4*e^(e^(3/x^x)/x) + x^4 + 4
*x^3*e^(x + 4*e^(3/x^x)/x) - 12*x^3*e^(x + 3*e^(3/x^x)/x) + 12*x^3*e^(x + 2*e^(3/x^x)/x) - 4*x^3*e^(x + e^(3/x
^x)/x) + 6*x^2*e^(2*x + 4*e^(3/x^x)/x) - 12*x^2*e^(2*x + 3*e^(3/x^x)/x) + 6*x^2*e^(2*x + 2*e^(3/x^x)/x) + 4*x*
e^(3*x + 4*e^(3/x^x)/x) - 4*x*e^(3*x + 3*e^(3/x^x)/x) + e^(4*x + 4*e^(3/x^x)/x) - 5)

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mupad [B]  time = 4.25, size = 308, normalized size = 9.94 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{-4\,x\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{-4\,x^3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{4\,x^3\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{12\,x^3\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-12\,x^3\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^4\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}}\,{\mathrm {e}}^{-4\,x^4\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {3}{x^x}}}{x}}}\,{\mathrm {e}}^{-4\,x^4\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}}\,{\mathrm {e}}^{6\,x^4\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}}\,{\mathrm {e}}^{6\,x^2\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{6\,x^2\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-12\,x^2\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{\frac {3}{x^x}}}{x}}\,{\mathrm {e}}^{2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-x*log(x))*exp(exp((2*exp(3*exp(-x*log(x))))/x)*(12*x^3*exp(x) + 6*x^2*exp(2*x) + 6*x^4) - exp((3*exp
(3*exp(-x*log(x))))/x)*(4*x*exp(3*x) + 12*x^3*exp(x) + 12*x^2*exp(2*x) + 4*x^4) - exp(exp(3*exp(-x*log(x)))/x)
*(4*x^3*exp(x) + 4*x^4) + x^4 + exp((4*exp(3*exp(-x*log(x))))/x)*(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x
^2*exp(2*x) + x^4) - 5)*(4*x^5*exp(x*log(x)) - exp((2*exp(3*exp(-x*log(x))))/x)*(exp(3*exp(-x*log(x)))*(72*x^4
*exp(x) + log(x)*(72*x^4*exp(x) + 36*x^3*exp(2*x) + 36*x^5) + 36*x^3*exp(2*x) + exp(x*log(x))*(24*x^3*exp(x) +
12*x^2*exp(2*x) + 12*x^4) + 36*x^5) - exp(x*log(x))*(exp(x)*(36*x^4 + 12*x^5) + exp(2*x)*(12*x^3 + 12*x^4) +
24*x^5)) + exp(exp(3*exp(-x*log(x)))/x)*(exp(3*exp(-x*log(x)))*(12*x^4*exp(x) + exp(x*log(x))*(4*x^3*exp(x) +
4*x^4) + 12*x^5 + log(x)*(12*x^4*exp(x) + 12*x^5)) - exp(x*log(x))*(exp(x)*(12*x^4 + 4*x^5) + 16*x^5)) + exp((
3*exp(3*exp(-x*log(x))))/x)*(exp(3*exp(-x*log(x)))*(108*x^4*exp(x) + 36*x^2*exp(3*x) + 108*x^3*exp(2*x) + exp(
x*log(x))*(12*x*exp(3*x) + 36*x^3*exp(x) + 36*x^2*exp(2*x) + 12*x^4) + log(x)*(108*x^4*exp(x) + 36*x^2*exp(3*x
) + 108*x^3*exp(2*x) + 36*x^5) + 36*x^5) - exp(x*log(x))*(exp(x)*(36*x^4 + 12*x^5) + exp(3*x)*(4*x^2 + 12*x^3)
+ exp(2*x)*(24*x^3 + 24*x^4) + 16*x^5)) - exp((4*exp(3*exp(-x*log(x))))/x)*(exp(3*exp(-x*log(x)))*(12*x*exp(4
*x) + 48*x^4*exp(x) + exp(x*log(x))*(4*exp(4*x) + 16*x*exp(3*x) + 16*x^3*exp(x) + 24*x^2*exp(2*x) + 4*x^4) + 4
8*x^2*exp(3*x) + 72*x^3*exp(2*x) + 12*x^5 + log(x)*(12*x*exp(4*x) + 48*x^4*exp(x) + 48*x^2*exp(3*x) + 72*x^3*e
xp(2*x) + 12*x^5)) - exp(x*log(x))*(exp(x)*(12*x^4 + 4*x^5) + exp(3*x)*(4*x^2 + 12*x^3) + exp(2*x)*(12*x^3 + 1
2*x^4) + 4*x^2*exp(4*x) + 4*x^5))))/x^2,x)

[Out]

exp(exp((4*exp(3/x^x))/x)*exp(4*x))*exp(x^4)*exp(-5)*exp(-4*x*exp((3*exp(3/x^x))/x)*exp(3*x))*exp(4*x*exp((4*e
xp(3/x^x))/x)*exp(3*x))*exp(-4*x^3*exp(exp(3/x^x)/x)*exp(x))*exp(4*x^3*exp((4*exp(3/x^x))/x)*exp(x))*exp(12*x^
3*exp((2*exp(3/x^x))/x)*exp(x))*exp(-12*x^3*exp((3*exp(3/x^x))/x)*exp(x))*exp(x^4*exp((4*exp(3/x^x))/x))*exp(-
4*x^4*exp(exp(3/x^x)/x))*exp(-4*x^4*exp((3*exp(3/x^x))/x))*exp(6*x^4*exp((2*exp(3/x^x))/x))*exp(6*x^2*exp((2*e
xp(3/x^x))/x)*exp(2*x))*exp(6*x^2*exp((4*exp(3/x^x))/x)*exp(2*x))*exp(-12*x^2*exp((3*exp(3/x^x))/x)*exp(2*x))

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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(((((-4*exp(x)**4-16*x*exp(x)**3-24*exp(x)**2*x**2-16*exp(x)*x**3-4*x**4)*exp(x*ln(x))+(-12*x*exp(x)*
*4-48*x**2*exp(x)**3-72*exp(x)**2*x**3-48*exp(x)*x**4-12*x**5)*ln(x)-12*x*exp(x)**4-48*x**2*exp(x)**3-72*exp(x
)**2*x**3-48*exp(x)*x**4-12*x**5)*exp(3/exp(x*ln(x)))+(4*x**2*exp(x)**4+(12*x**3+4*x**2)*exp(x)**3+(12*x**4+12
*x**3)*exp(x)**2+(4*x**5+12*x**4)*exp(x)+4*x**5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)**4+(((12*x*exp(x)**3
+36*exp(x)**2*x**2+36*exp(x)*x**3+12*x**4)*exp(x*ln(x))+(36*x**2*exp(x)**3+108*exp(x)**2*x**3+108*exp(x)*x**4+
36*x**5)*ln(x)+36*x**2*exp(x)**3+108*exp(x)**2*x**3+108*exp(x)*x**4+36*x**5)*exp(3/exp(x*ln(x)))+((-12*x**3-4*
x**2)*exp(x)**3+(-24*x**4-24*x**3)*exp(x)**2+(-12*x**5-36*x**4)*exp(x)-16*x**5)*exp(x*ln(x)))*exp(exp(3/exp(x*
ln(x)))/x)**3+(((-12*exp(x)**2*x**2-24*exp(x)*x**3-12*x**4)*exp(x*ln(x))+(-36*exp(x)**2*x**3-72*exp(x)*x**4-36
*x**5)*ln(x)-36*exp(x)**2*x**3-72*exp(x)*x**4-36*x**5)*exp(3/exp(x*ln(x)))+((12*x**4+12*x**3)*exp(x)**2+(12*x*
*5+36*x**4)*exp(x)+24*x**5)*exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)**2+(((4*exp(x)*x**3+4*x**4)*exp(x*ln(x))+
(12*exp(x)*x**4+12*x**5)*ln(x)+12*exp(x)*x**4+12*x**5)*exp(3/exp(x*ln(x)))+((-4*x**5-12*x**4)*exp(x)-16*x**5)*
exp(x*ln(x)))*exp(exp(3/exp(x*ln(x)))/x)+4*x**5*exp(x*ln(x)))*exp((exp(x)**4+4*x*exp(x)**3+6*exp(x)**2*x**2+4*
exp(x)*x**3+x**4)*exp(exp(3/exp(x*ln(x)))/x)**4+(-4*x*exp(x)**3-12*exp(x)**2*x**2-12*exp(x)*x**3-4*x**4)*exp(e
xp(3/exp(x*ln(x)))/x)**3+(6*exp(x)**2*x**2+12*exp(x)*x**3+6*x**4)*exp(exp(3/exp(x*ln(x)))/x)**2+(-4*exp(x)*x**
3-4*x**4)*exp(exp(3/exp(x*ln(x)))/x)+x**4-5)/x**2/exp(x*ln(x)),x)

[Out]

Timed out

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