3.90.99 \(\int \frac {e^{8-2 e^{e^{1+x}}-\frac {6}{x^2}} (12-2 e^{1+e^{1+x}+x} x^3)}{x^3} \, dx\)

Optimal. Leaf size=18 \[ e^{8-2 e^{e^{1+x}}-\frac {6}{x^2}} \]

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Rubi [A]  time = 0.44, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6706} \begin {gather*} e^{-\frac {6}{x^2}-2 e^{e^{x+1}}+8} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(8 - 2*E^E^(1 + x) - 6/x^2)*(12 - 2*E^(1 + E^(1 + x) + x)*x^3))/x^3,x]

[Out]

E^(8 - 2*E^E^(1 + x) - 6/x^2)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{8-2 e^{e^{1+x}}-\frac {6}{x^2}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.18, size = 18, normalized size = 1.00 \begin {gather*} e^{8-2 e^{e^{1+x}}-\frac {6}{x^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(8 - 2*E^E^(1 + x) - 6/x^2)*(12 - 2*E^(1 + E^(1 + x) + x)*x^3))/x^3,x]

[Out]

E^(8 - 2*E^E^(1 + x) - 6/x^2)

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fricas [B]  time = 0.60, size = 38, normalized size = 2.11 \begin {gather*} e^{\left (-\frac {2 \, {\left (x^{2} e^{\left (x + e^{\left (x + 1\right )} + 1\right )} - {\left (4 \, x^{2} - 3\right )} e^{\left (x + 1\right )}\right )} e^{\left (-x - 1\right )}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*x^3*exp(x+1)*exp(exp(x+1))+12)*exp(-exp(exp(x+1))+6)^2/x^3/exp(2)^2/exp(3/x^2)^2,x, algorithm="f
ricas")

[Out]

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

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giac [A]  time = 0.15, size = 15, normalized size = 0.83 \begin {gather*} e^{\left (-\frac {6}{x^{2}} - 2 \, e^{\left (e^{\left (x + 1\right )}\right )} + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*x^3*exp(x+1)*exp(exp(x+1))+12)*exp(-exp(exp(x+1))+6)^2/x^3/exp(2)^2/exp(3/x^2)^2,x, algorithm="g
iac")

[Out]

e^(-6/x^2 - 2*e^(e^(x + 1)) + 8)

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maple [A]  time = 0.08, size = 23, normalized size = 1.28

method	result	size
risch	\({\mathrm e}^{-\frac {2 \left ({\mathrm e}^{{\mathrm e}^{x +1}} x^{2}-4 x^{2}+3\right )}{x^{2}}}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2*x^3*exp(x+1)*exp(exp(x+1))+12)*exp(-exp(exp(x+1))+6)^2/x^3/exp(2)^2/exp(3/x^2)^2,x,method=_RETURNVERBO
SE)

[Out]

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

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maxima [A]  time = 0.44, size = 15, normalized size = 0.83 \begin {gather*} e^{\left (-\frac {6}{x^{2}} - 2 \, e^{\left (e^{\left (x + 1\right )}\right )} + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*x^3*exp(x+1)*exp(exp(x+1))+12)*exp(-exp(exp(x+1))+6)^2/x^3/exp(2)^2/exp(3/x^2)^2,x, algorithm="m
axima")

[Out]

e^(-6/x^2 - 2*e^(e^(x + 1)) + 8)

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mupad [B]  time = 7.79, size = 18, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^8\,{\mathrm {e}}^{-\frac {6}{x^2}}\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{\mathrm {e}\,{\mathrm {e}}^x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-4)*exp(-6/x^2)*exp(12 - 2*exp(exp(x + 1)))*(2*x^3*exp(x + 1)*exp(exp(x + 1)) - 12))/x^3,x)

[Out]

exp(8)*exp(-6/x^2)*exp(-2*exp(exp(1)*exp(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((-2*x**3*exp(x+1)*exp(exp(x+1))+12)*exp(-exp(exp(x+1))+6)**2/x**3/exp(2)**2/exp(3/x**2)**2,x)

[Out]

Timed out

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