# He power series of arctan

1. Mar 31, 2012

### hivesaeed4

How do we get the power series of arctan using integration. Could someone explain this step by step as I'm quite confused about it.

2. Mar 31, 2012

### DonAntonio

$\frac{1}{1+x^2} = 1-\frac{x^2}{2!}+\frac{x^4}{4!}-...$, and since

$(Arctan\, x)'=\frac{1}{1+x^2}$ , then...

DonAntonio

3. Mar 31, 2012

### chiro

Hey hivesaeed4 and welcome to the forums.

To add on to what DonAntonio said, investigate what Taylor series are and how are they are used:

http://en.wikipedia.org/wiki/Taylor_series

4. Apr 1, 2012

### hivesaeed4

Thanks. Thanks alot.