Integration Question

[glass python]

interchange the integral and the sum

if you're allowed to do so in this case

and then find out the sum

[atomic wyvern]

how am I supposed to know?

[glass python]

if its a finite sum, meaning if it converges to something

if it diverges yu cant really integrate infinity can you?

[odd orchid]

igotaclue

this integral becomes the sum from k=1 to infinity, of $\int_{-\infty}^{\infty} \frac{cos(\frac{x}{k}}}{x^2 + k^4}$
```Compilation error:```! Argument of \frac  has an extra }.
<inserted text> 
                \par 
l.57 ...{-\infty}^{\infty} \frac{cos(\frac{x}{k}}}
                                                  {x^2 + k^4}$
I've run across a `}' that doesn't seem to match anything.
For example, `\def\a#1{...}' and `\a}' would produce
this error. If you simply proceed now, the `\par' that
I've just inserted will cause me to report a runaway
argument that might be the root of the problem. But if
your `}' was spurious, just type `2' and it will go away.```

[glass python]

dont mind this

but just swap the integral and s

sum

you can do it if it converges

so you want to do the limit test for this series, ill send a website for this