∫（2x+6）/[(x^2-1)(x^2+1)^2] dx
问题描述：
∫（2x+6）/[(x^2-1)(x^2+1)^2] dx
答
这题要利用有理函数分解原理,将原式拆分原式=(1/2)∫(x+1)/(x^2-1)dx-(1/2)∫(x+9)/(x^2+1)dx-∫(x+1)/(x^2+1)^2dx=(1/2)∫1/(x-1)d(x-1)-(1/2)∫1/(x^2+1)d(x^2+1)-(9/2)∫1/(x^2+1)dx-∫1/(x^2+1)^2d(x^2+1)-∫1/(...