作业帮高数：这个积分怎么求?如图
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/19 17:34:04
xNA_i;gfv/-1gB6& J0& QP w1R|gK^{57;?v^vߟ fݓzkWI'Lg ~0Y^,%jՊɽBkԊv;ufJl3ea=?ϐ <'[b X" mRI " PB"mӻ(TYhga,HkE4b "2×S${N瀂ر
8#
QdX a\Y X}p (cO (&"P9
cbc2Õ3˞ ?;}nd Nz;/{^R! v~spq
Z |\TJܥu,ΠXs?4 r>dpBD<}9v\yدfO/ gG"o[j:КSq z[\?
高数：这个积分怎么求?如图
高数：这个积分怎么求?
如图
高数：这个积分怎么求?如图
剩下的应该容易解了.
(2-u)/(u²-1)=(1/2)[1/(u-1) -3/(u+1)]
∫[(2-u)/(u²-1)]du
=∫(1/2)[1/(u-1) -3/(u+1)]du
=(1/2)∫[1/(u-1)]du -(3/2)∫[1/(u+1)]du
=(1/2)∫[1/(u-1)]d(u-1) -(3/2)∫[1/(u+1)]d(u+1)
=(...
全部展开
(2-u)/(u²-1)=(1/2)[1/(u-1) -3/(u+1)]
∫[(2-u)/(u²-1)]du
=∫(1/2)[1/(u-1) -3/(u+1)]du
=(1/2)∫[1/(u-1)]du -(3/2)∫[1/(u+1)]du
=(1/2)∫[1/(u-1)]d(u-1) -(3/2)∫[1/(u+1)]d(u+1)
=(1/2)ln|u-1| -(3/2)ln|u+1| +C
收起