Question

∫x²／(x² 1)dx

Answer 1

∫[x²／(x²+1)]dx = ∫[(x²+1-1)／(x²+1)]dx
= ∫[1 - 1／(x²+1)]dx = x - arctanx + C
题目给出的解答不必要， 换元也不规范， 积分变量换为 t， 还 dx。

Answer 2

令X²+1=t，则X=√(t-1)，dX=1/2(t-1)^(-1/2)
∫X²/(X²+1)dX
=∫(X²+1-1)/(X²+1)dX
=∫[1-1/(X²+1)]dX
=X-arctanX+C