∫x^2/(9+4x^2)dx =1/4* ∫4x^2/(9+4x^2)dx
=1/4 * ∫[1-9/(9+4x^2)]dx
=1/4 *∫dx -1/4 * ∫[ 1/(1+(2x/3)^2)]dx
=1/4 *∫dx -1/4 * 3/2* ∫[ 1/(1+(2x/3)^2)]d(2x/3)
=x/4 - 3/8 * arctan(2x/3) + c