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

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

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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 = {} $$\begin{array}{c}\int \frac{e^{729-\frac{e^{2x}}{x^4}+2x}(4-2x)}{x^5}dx\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (\frac{4e^{729-\frac{e^{2x}}{x^4}+2x}}{x^5}-\frac{2e^{729-\frac{e^{2x}}{x^4}+2x}}{x^4})dx\\ & =-(2\int \frac{e^{729-\frac{e^{2x}}{x^4}+2x}}{x^4}dx)+4\int \frac{e^{729-\frac{e^{2x}}{x^4}+2x}}{x^5}dx\end{array}\end{array}$$

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

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 $$\begin{array}{c}{e}^{(-\frac{e^{\left(2x\right)}}{x^4}+729)}\end{array}$$

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 $$\begin{array}{c}{e}^{(-\frac{e^{\left(2x\right)}}{x^4}+729)}\end{array}$$

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 $$\int \frac{(4-2x){\mathrm{e}}^{2x}{\mathrm{e}}^{-\ln \left(x{\mathrm{e}}^{\frac{{\mathrm{e}}^{2x}}{x^4}}\right)+729}}{x^4}dx$$

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 $$\begin{array}{c}{e}^{(-\frac{e^{\left(2x\right)}}{x^4}+729)}\end{array}$$

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 $$\begin{array}{c}{\mathrm{e}}^{729}{\mathrm{e}}^{-\frac{{\mathrm{e}}^{2x}}{x^4}}\end{array}$$

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 $$\begin{array}{c}{e}^{729}{e}^{-\frac{e^{2x}}{x^4}}\end{array}$$

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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