Intergral of (e^(3/x))/(x^2) ?

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In summary, the integral of (e^(3/x))/(x^2) is 3e^(3/x) + C, where C is the constant of integration. To solve this integral, you can use the substitution method and the domain of the function is all real numbers except 0. The integral cannot be further simplified, but can be solved using integration by parts. The function (e^(3/x))/(x^2) has significance in mathematical analysis and probability theory as it represents the probability density function of the inverse chi-squared distribution and is used to model data in various fields.
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BadCompany89
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I know how to do a u substitution, but can it be applied to this equation?
 
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  • #2
u=3/x
du=-3dx/x^2

-1/3 ∫e^u du

etc.
 
  • #3
ah, thanks
 

FAQ: Intergral of (e^(3/x))/(x^2) ?

What is the integral of (e^(3/x))/(x^2)?

The integral of (e^(3/x))/(x^2) is 3e^(3/x) + C, where C is the constant of integration.

How do you solve the integral of (e^(3/x))/(x^2)?

To solve this integral, you can use the substitution method. Let u = 3/x, then du = -3/x^2 dx. This will transform the integral into the form of ∫e^u du, which can be easily solved using the power rule.

What is the domain of the function (e^(3/x))/(x^2)?

The domain of (e^(3/x))/(x^2) is all real numbers except 0. This is because the function is undefined at x = 0 due to the presence of x^2 in the denominator.

Can the integral of (e^(3/x))/(x^2) be simplified further?

No, the integral of (e^(3/x))/(x^2) cannot be further simplified. However, you can use integration by parts to solve it in a different form.

What is the significance of the function (e^(3/x))/(x^2)?

The function (e^(3/x))/(x^2) has significance in mathematical analysis and probability theory. It represents the probability density function of the inverse chi-squared distribution and is used to model data in various fields such as finance and engineering.

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