Indefinite integration using trig

[dpc89]

I'm having some difficulty in evaluating the following indefinite integral: (x^2)/(1+(x^2))dx.
I'm trying different methods, but I'm not making progress. I've tried:
1) Using integration by parts with "u=x^2" to get (x^2)(arctanx)-Integral(arctanx)(2x)dx but I cannot integrate the second part (arctanx)
2) Splitting the function into x*x/(1+(x^2)) and then using logs and integration by parts, with "u=x"
3) Using substitution and substituting u for "x^2" or "1+x^2"

Online integrators are giving the indefinite integral as "x-arctanx", but I cannot achieve this.
Thanks in advance.

 

[galactus]

Perhaps the best thing to do is to expand and then integrate.

\(\displaystyle \frac{x^{2}}{1+x^{2}}=1-\frac{1}{x^{2}+1}\)

\(\displaystyle \int dx-\int\frac{1}{x^{2}+1}dx\)

Recognize the right integral?. x is surely easy to integrate.

See now where the x-arctan(x) comes from?.

 

[dpc89]

Just to note, I did manage to get the answer, by substiting tan(theta) for x. This then allowed me to use trig identites (1+tan^2(theta)=sec^2(theta) etc).
I was initially trying to split the fraction up, but over-complicated things so couldn't see how simple this method was. Thanks a lot for your input guys.