3.17.94 \(\int \frac {e^{729-\frac {e^{2 x}}{x^4}+2 x} (4-2 x)}{x^5} \, dx\)

Optimal. Leaf size=14 \[ e^{729-\frac {e^{2 x}}{x^4}} \]

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Rubi [F]  time = 0.46, 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 {e^{729-\frac {e^{2 x}}{x^4}+2 x} (4-2 x)}{x^5} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(729 - E^(2*x)/x^4 + 2*x)*(4 - 2*x))/x^5,x]

[Out]

4*Defer[Int][E^(729 - E^(2*x)/x^4 + 2*x)/x^5, x] - 2*Defer[Int][E^(729 - E^(2*x)/x^4 + 2*x)/x^4, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {4 e^{729-\frac {e^{2 x}}{x^4}+2 x}}{x^5}-\frac {2 e^{729-\frac {e^{2 x}}{x^4}+2 x}}{x^4}\right ) \, dx\\ &=-\left (2 \int \frac {e^{729-\frac {e^{2 x}}{x^4}+2 x}}{x^4} \, dx\right )+4 \int \frac {e^{729-\frac {e^{2 x}}{x^4}+2 x}}{x^5} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 14, normalized size = 1.00 \begin {gather*} e^{729-\frac {e^{2 x}}{x^4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(729 - E^(2*x)/x^4 + 2*x)*(4 - 2*x))/x^5,x]

[Out]

E^(729 - E^(2*x)/x^4)

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fricas [A]  time = 0.78, size = 12, normalized size = 0.86 \begin {gather*} e^{\left (-\frac {e^{\left (2 \, x\right )}}{x^{4}} + 729\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4-2*x)*exp(x)^2*exp(-log(x*exp(exp(x)^2/x^4))+729)/x^4,x, algorithm="fricas")

[Out]

e^(-e^(2*x)/x^4 + 729)

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giac [A]  time = 0.16, size = 12, normalized size = 0.86 \begin {gather*} e^{\left (-\frac {e^{\left (2 \, x\right )}}{x^{4}} + 729\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4-2*x)*exp(x)^2*exp(-log(x*exp(exp(x)^2/x^4))+729)/x^4,x, algorithm="giac")

[Out]

e^(-e^(2*x)/x^4 + 729)

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maple [F]  time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\left (4-2 x \right ) {\mathrm e}^{2 x} {\mathrm e}^{-\ln \left (x \,{\mathrm e}^{\frac {{\mathrm e}^{2 x}}{x^{4}}}\right )+729}}{x^{4}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4-2*x)*exp(x)^2*exp(-ln(x*exp(exp(x)^2/x^4))+729)/x^4,x)

[Out]

int((4-2*x)*exp(x)^2*exp(-ln(x*exp(exp(x)^2/x^4))+729)/x^4,x)

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maxima [A]  time = 0.58, size = 12, normalized size = 0.86 \begin {gather*} e^{\left (-\frac {e^{\left (2 \, x\right )}}{x^{4}} + 729\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4-2*x)*exp(x)^2*exp(-log(x*exp(exp(x)^2/x^4))+729)/x^4,x, algorithm="maxima")

[Out]

e^(-e^(2*x)/x^4 + 729)

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mupad [B]  time = 1.13, size = 13, normalized size = 0.93 \begin {gather*} {\mathrm {e}}^{729}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{2\,x}}{x^4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(2*x)*exp(729 - log(x*exp(exp(2*x)/x^4)))*(2*x - 4))/x^4,x)

[Out]

exp(729)*exp(-exp(2*x)/x^4)

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sympy [A]  time = 0.20, size = 12, normalized size = 0.86 \begin {gather*} e^{729} e^{- \frac {e^{2 x}}{x^{4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4-2*x)*exp(x)**2*exp(-ln(x*exp(exp(x)**2/x**4))+729)/x**4,x)

[Out]

exp(729)*exp(-exp(2*x)/x**4)

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