∫{x^2/[(x-3)(x+2)^2]}dx

x^2/[(x-3)(x+2)^2=(9/25)[1/(x-3)]+(16/25)[1/(x+2)]-(20/25)[1/(x+2)^2]。
原式=(9/25)∫1/(x-3)dx+(16/25)∫1/(x+2)dx-(4/5)∫1/(x+2)^2dx
=(9/25)ln|x-3|+(16/25)ln|x+2|+(4/5)[1/(x+2)]+C。