用换元法求不定积分,sinx^5+sinx,答案为-2cosx+2/3cosx^3-1/5cosx^5+c,

问题描述:

用换元法求不定积分,sinx^5+sinx,答案为-2cosx+2/3cosx^3-1/5cosx^5+c,

=-(1+sinx^4)d(cosx)
=-[1+(1-cosx^2)^2]d(cosx)
=-(1+1-2cosx^2+cosx^4)d(cosx)
=-2cosx+2/3cosx^3-1/5cosx^5+c