蹦出的都是鸟
幼苗
共回答了12个问题采纳率:83.3% 举报
1
∫dx/(x^4 *(1+x^2))
=∫[(1+x^2)^2-2x^2-x^4]dx/[x^4*(1+x^2)]
=∫(1+x^2)dx/x^4-∫2dx/[x^2(1+x^2)]-∫dx/(1+x^2)
=(-1/3)x^(-3)+(-1)x^(-1)-2∫(1+x^2-x^2)dx/[x^2(1+x^2)]-∫dx/(1+x^2)
=-1/3)x^(-3)+x^(-1)-3arctanx+C
2
∫(x^2+2)dx/(1+x+x^2)^2
=∫(x^2+x+1-x-1)dx/(1+x+x^2)
=∫dx/(1+x+x^2)-∫(x+1)dx/(1+x+x^2)^2
=∫dx/[(x+1/2)^2+3/4]-(1/2)∫d(x^2+x+1)/(1+x+x^2)^2 -(1/2)∫dx/[(x+1/2)^2+3/4]
=(1/2)*(√3/2)arctan(√3x/2+√3/4)+(1/2)(1+x+x^2)^(-1)+C
3
∫(1+x)^(1/2)dx/(1-x)^(1/2)
设x=cosu, dx=-sinudu
=∫cos(u/2)(-sinu)du/sin(u/2)
=∫-2(cosu/2)^2du
=∫-(1+cosu)du
=-u-sinu+C
=-arccosx-√(1-x^2)+C
1年前
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