求不定积分∫[(1+1/x^2)(1-x^2)+xsinx]dx

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 15:23:41
求不定积分∫[(1+1/x^2)(1-x^2)+xsinx]dx求不定积分∫[(1+1/x^2)(1-x^2)+xsinx]dx求不定积分∫[(1+1/x^2)(1-x^2)+xsinx]dx∫[(1

求不定积分∫[(1+1/x^2)(1-x^2)+xsinx]dx
求不定积分∫[(1+1/x^2)(1-x^2)+xsinx]dx

求不定积分∫[(1+1/x^2)(1-x^2)+xsinx]dx
∫[(1+1/x^2)(1-x^2)+xsinx]dx
=∫(1/x^2-x^2 + xsinx) dx
= -1/x - 1/3*x^3 +∫xsinx dx
= -1/x - 1/3*x^3 -∫xdcosx
= -1/x - 1/3*x^3 -xcosx + ∫cosx dx
= -1/x - 1/3*x^3 -xcosx + sinx + C