3.39.53 \(\int \frac {e^{e^{5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}}+5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}+e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}+\frac {9+8 x^2+3 e^5 x^2}{x^3}} (-135-40 x^2-15 e^5 x^2)}{x^4} \, dx\)

Optimal. Leaf size=32 \[ e^{e^{5 e^{e^{\frac {3}{x}+\frac {5+3 e^5+\frac {9}{x^2}}{x}}}}} \]

________________________________________________________________________________________

Rubi [F]  time = 3.26, 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 (e^{5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}}+5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}+e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}+\frac {9+8 x^2+3 e^5 x^2}{x^3}\right ) \left (-135-40 x^2-15 e^5 x^2\right )}{x^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^(5*E^E^((9 + 8*x^2 + 3*E^5*x^2)/x^3)) + 5*E^E^((9 + 8*x^2 + 3*E^5*x^2)/x^3) + E^((9 + 8*x^2 + 3*E^5*
x^2)/x^3) + (9 + 8*x^2 + 3*E^5*x^2)/x^3)*(-135 - 40*x^2 - 15*E^5*x^2))/x^4,x]

[Out]

-135*Defer[Int][E^(E^(5*E^E^((9 + 8*x^2 + 3*E^5*x^2)/x^3)) + 5*E^E^((9 + 8*x^2 + 3*E^5*x^2)/x^3) + E^((9 + 8*x
^2 + 3*E^5*x^2)/x^3) + (9 + 8*x^2 + 3*E^5*x^2)/x^3)/x^4, x] - 5*(8 + 3*E^5)*Defer[Int][E^(E^(5*E^E^((9 + 8*x^2
+ 3*E^5*x^2)/x^3)) + 5*E^E^((9 + 8*x^2 + 3*E^5*x^2)/x^3) + E^((9 + 8*x^2 + 3*E^5*x^2)/x^3) + (9 + 8*x^2 + 3*E
^5*x^2)/x^3)/x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (e^{5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}}+5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}+e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}+\frac {9+8 x^2+3 e^5 x^2}{x^3}\right ) \left (-135+\left (-40-15 e^5\right ) x^2\right )}{x^4} \, dx\\ &=\int \left (-\frac {135 \exp \left (e^{5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}}+5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}+e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}+\frac {9+8 x^2+3 e^5 x^2}{x^3}\right )}{x^4}-\frac {5 \exp \left (e^{5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}}+5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}+e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}+\frac {9+8 x^2+3 e^5 x^2}{x^3}\right ) \left (8+3 e^5\right )}{x^2}\right ) \, dx\\ &=-\left (135 \int \frac {\exp \left (e^{5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}}+5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}+e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}+\frac {9+8 x^2+3 e^5 x^2}{x^3}\right )}{x^4} \, dx\right )-\left (5 \left (8+3 e^5\right )\right ) \int \frac {\exp \left (e^{5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}}+5 e^{e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}}+e^{\frac {9+8 x^2+3 e^5 x^2}{x^3}}+\frac {9+8 x^2+3 e^5 x^2}{x^3}\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.14, size = 27, normalized size = 0.84 \begin {gather*} e^{e^{5 e^{e^{\frac {9}{x^3}+\frac {8+3 e^5}{x}}}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^(5*E^E^((9 + 8*x^2 + 3*E^5*x^2)/x^3)) + 5*E^E^((9 + 8*x^2 + 3*E^5*x^2)/x^3) + E^((9 + 8*x^2 +
3*E^5*x^2)/x^3) + (9 + 8*x^2 + 3*E^5*x^2)/x^3)*(-135 - 40*x^2 - 15*E^5*x^2))/x^4,x]

[Out]

E^E^(5*E^E^(9/x^3 + (8 + 3*E^5)/x))

________________________________________________________________________________________

fricas [B]  time = 0.65, size = 157, normalized size = 4.91 \begin {gather*} e^{\left (\frac {x^{3} e^{\left (5 \, e^{\left (e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}}\right )}\right )}\right )} + x^{3} e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}}\right )} + 5 \, x^{3} e^{\left (e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}}\right )}\right )} + 3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}} - \frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}} - e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}}\right )} - 5 \, e^{\left (e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-15*x^2*exp(5)-40*x^2-135)*exp((3*x^2*exp(5)+8*x^2+9)/x^3)*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))*exp
(5*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3)))*exp(exp(5*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))))/x^4,x, algorithm="fr
icas")

[Out]

e^((x^3*e^(5*e^(e^((3*x^2*e^5 + 8*x^2 + 9)/x^3))) + x^3*e^((3*x^2*e^5 + 8*x^2 + 9)/x^3) + 5*x^3*e^(e^((3*x^2*e
^5 + 8*x^2 + 9)/x^3)) + 3*x^2*e^5 + 8*x^2 + 9)/x^3 - (3*x^2*e^5 + 8*x^2 + 9)/x^3 - e^((3*x^2*e^5 + 8*x^2 + 9)/
x^3) - 5*e^(e^((3*x^2*e^5 + 8*x^2 + 9)/x^3)))

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {5 \, {\left (3 \, x^{2} e^{5} + 8 \, x^{2} + 27\right )} e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}} + e^{\left (5 \, e^{\left (e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}}\right )}\right )}\right )} + e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}}\right )} + 5 \, e^{\left (e^{\left (\frac {3 \, x^{2} e^{5} + 8 \, x^{2} + 9}{x^{3}}\right )}\right )}\right )}}{x^{4}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-15*x^2*exp(5)-40*x^2-135)*exp((3*x^2*exp(5)+8*x^2+9)/x^3)*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))*exp
(5*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3)))*exp(exp(5*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))))/x^4,x, algorithm="gi
ac")

[Out]

integrate(-5*(3*x^2*e^5 + 8*x^2 + 27)*e^((3*x^2*e^5 + 8*x^2 + 9)/x^3 + e^(5*e^(e^((3*x^2*e^5 + 8*x^2 + 9)/x^3)
)) + e^((3*x^2*e^5 + 8*x^2 + 9)/x^3) + 5*e^(e^((3*x^2*e^5 + 8*x^2 + 9)/x^3)))/x^4, x)

________________________________________________________________________________________

maple [A]  time = 0.20, size = 25, normalized size = 0.78

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{5 \,{\mathrm e}^{{\mathrm e}^{\frac {3 x^{2} {\mathrm e}^{5}+8 x^{2}+9}{x^{3}}}}}}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-15*x^2*exp(5)-40*x^2-135)*exp((3*x^2*exp(5)+8*x^2+9)/x^3)*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))*exp(5*exp
(exp((3*x^2*exp(5)+8*x^2+9)/x^3)))*exp(exp(5*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))))/x^4,x,method=_RETURNVERBOS
E)

[Out]

exp(exp(5*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))))

________________________________________________________________________________________

maxima [A]  time = 0.93, size = 24, normalized size = 0.75 \begin {gather*} e^{\left (e^{\left (5 \, e^{\left (e^{\left (\frac {3 \, e^{5}}{x} + \frac {8}{x} + \frac {9}{x^{3}}\right )}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-15*x^2*exp(5)-40*x^2-135)*exp((3*x^2*exp(5)+8*x^2+9)/x^3)*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))*exp
(5*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3)))*exp(exp(5*exp(exp((3*x^2*exp(5)+8*x^2+9)/x^3))))/x^4,x, algorithm="ma
xima")

[Out]

e^(e^(5*e^(e^(3*e^5/x + 8/x + 9/x^3))))

________________________________________________________________________________________

mupad [B]  time = 2.91, size = 26, normalized size = 0.81 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{5\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^5}{x}}\,{\mathrm {e}}^{8/x}\,{\mathrm {e}}^{\frac {9}{x^3}}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp((3*x^2*exp(5) + 8*x^2 + 9)/x^3))*exp(exp(5*exp(exp((3*x^2*exp(5) + 8*x^2 + 9)/x^3))))*exp((3*x^2
*exp(5) + 8*x^2 + 9)/x^3)*exp(5*exp(exp((3*x^2*exp(5) + 8*x^2 + 9)/x^3)))*(15*x^2*exp(5) + 40*x^2 + 135))/x^4,
x)

[Out]

exp(exp(5*exp(exp((3*exp(5))/x)*exp(8/x)*exp(9/x^3))))

________________________________________________________________________________________

sympy [A]  time = 1.22, size = 26, normalized size = 0.81 \begin {gather*} e^{e^{5 e^{e^{\frac {8 x^{2} + 3 x^{2} e^{5} + 9}{x^{3}}}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-15*x**2*exp(5)-40*x**2-135)*exp((3*x**2*exp(5)+8*x**2+9)/x**3)*exp(exp((3*x**2*exp(5)+8*x**2+9)/x*
*3))*exp(5*exp(exp((3*x**2*exp(5)+8*x**2+9)/x**3)))*exp(exp(5*exp(exp((3*x**2*exp(5)+8*x**2+9)/x**3))))/x**4,x
)

[Out]

exp(exp(5*exp(exp((8*x**2 + 3*x**2*exp(5) + 9)/x**3))))

________________________________________________________________________________________