integral of [(2/(1+x^2)) - |x|]

[t_reason]

Could you please show me how to solve the integral of
[(2/(1+x^2)) - |x|] ?

I think I need to use u substitution but I'm not sure..

 

[galactus]

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

Hint:

\(\displaystyle \L\\\frac{d}{dx}[tan^{-1}(x)]=\frac{1}{1+x^{2}}\)


\(\displaystyle \L\\\int{x}dx=\frac{x^{2}}{2}=\frac{(x)(x)}{2}\;\ and\;\ \int{-x}dx=\frac{-x^{2}}{2}=\frac{(-x)(x)}{2}=\)

Therefore,
\(\displaystyle \L\\\int{|x|}dx=\frac{x|x|}{2}\)

 

[t_reason]

thanks so much.. i figured it out! :]