求定积分∫(2-3)u^2/(u^2-1)du
问题描述:
求定积分∫(2-3)u^2/(u^2-1)du
答
那个2-3是积分区间么
先分子-1+1
提出一个1来
后面把分母分解为(u-1)(u+1)
式子就能拆成两部分
还不会的话追问吧
答
∫[2,3]u^2/(u^2-1)du
=∫[2,3][1+1/(u^2-1)]du
=∫[2,3][1+1/2*1/(u-1)-1/2*1/(u+1)]du
=[u+1/2ln(u+1)+1/2ln(u-1)][2,3]
=1+1/2ln4-1/2ln3+1/2ln2
=1+3/2*ln2-1/2ln3