Determine convergence of series using integral test

[lha08]

Homework Statement

How can i find if the following series is convergent or divergent using the INTEGRAL TEST?
sigma (n=1 to infinity)= n/(n^4+1)

Homework Equations

The Attempt at a Solution

The answer says that the initial step involves changing it to: 1/2(2x)/(1+(x^2)^2)..but why is that?

 

[tiny-tim]

Hi lha08!

(try using the X² tag just above the Reply box )

sigma (n=1 to infinity)= n/(n^4+1)
…
The answer says that the initial step involves changing it to: 1/2(2x)/(1+(x^2)^2)..but why is that?

Because ∫dy/(1 + y²) is easy.