两道高等数学不定积分题∫1/8( (x-1)/(x+1) )^4 dx （提示：令(x-1)/(x+1)=1-2/(x+
2个回答

1,问题转化为求∫x/(x+1)^4dx和∫1/(x+1)^4dx

只需求∫x/(x+1)^4dx=∫dx/(x+1)^2-∫xdx/(x+1)^3-∫1/(x+1)^4dx

只需求∫xdx/(x+1)^3=∫dx/(x+1)-∫xdx/(x+1)^2-∫dx/(x+1)^3

只需求∫xdx/(x+1)^2=∫dx/(x+1)-∫dx/(x+1)^2

问题解决.

2注意到d[1/(xcosx-sinx)]=xsinxdx/(xcosx-sinx)^2

原式=∫(sinx/x)*d[1/(xcosx-sinx)]

=(sinx/x)*1/(xcosx-sinx)-∫[(xcosx-sinx)/x^2]*[1/(xcosx-sinx)]dx

=(sinx/x)*1/(xcosx-sinx)-∫dx/x^2

=(sinx/x)*1/(xcosx-sinx)+1/x+C

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