How to do the indefinite integral

[cloudage]

Homework Statement

I hope someone can help me with this integral. It is really an improper integral, but I cannot figure out how to do the indefinite integral on it:

integral[e^1/x/x³].

Any help would be appreciated, thanks.

Homework Equations

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The Attempt at a Solution

I tried integration by parts, substitution and using the table of integrals. I couldn't get any of them to work.

 

[Mark44]

I would be included to split it up as (1/x) *[ (1/x^2)*e^(1/x)] and try integration by parts on that. IOW, u = 1/x, and dv = (1/x^2)*e^(1/x)dx.

I don't know that this would work, but that's what I would start with.

 

[tt2348]

This is definately a U substitution problem, when things are kinda odd inside an exponential, its the best method to try.

pick u=1/x,
that means du= (-1/x^2) dx.

so
$$\int \frac{e^{1/x}}{x^{3}} dx$$ = $$\int \frac{-1}{x} e^{1/x}(\frac{-1}{x^{2}}dx)$$

 

[cloudage]

Thank you so much! The substitution did the trick!

 

[tt2348]

perfect. Now if only I could get help with my cray cray math.