Converting Integral into Power Series: Is This Step Valid?

[iloveannaw]

Homework Statement

Hi, we're supposed to put the following integral into a power series:

$$\int \frac{arctan(t)}{t} dt$$

with 0 < t < x.

Homework Equations

n/a

The Attempt at a Solution

I just want to know whether this step is ok.

$$\int \frac{arctan(t)}{t} dt = \int \frac{1}{t} \int \frac{dy}{1-(-y^2)} dt$$

with 0 < y < t and 0 < t < x

Happy Easter!

 

[upsidedowntop]

I agree with it.