∫x^3/(x^8-2) dx∫(x^3-1)/(x^2+1) dx
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∫x^3/(x^8-2)dx∫(x^3-1)/(x^2+1)dx∫x^3/(x^8-2)dx∫(x^3-1)/(x^2+1)dx∫x^3/(x^8-2)dx∫(x^3-1)/(x^2+1)dx1.令t
∫x^3/(x^8-2) dx∫(x^3-1)/(x^2+1) dx
∫x^3/(x^8-2) dx
∫(x^3-1)/(x^2+1) dx
∫x^3/(x^8-2) dx∫(x^3-1)/(x^2+1) dx
1.令t=x^4 dt\4=x^3dx
原式=∫dt\4(t^2-2)=2^(1\2)\16∫{dt\[t-2^(1\2)]-dt\[t+2^(1\2)]}
=2^(1\2)\16In|[t-2^(1\2)]\[t+2^(1\2)]|+C
=2^(1\2)\16In|[x^4-2^(1\2)]\[x^4+2^(1\2)]|+C
2.(x^3-1)\(x^2+1)=x-x\(x^2+1)-1\(x^2+1)
原式=x^2\2-(1\2)In(x^2+1)-arctanx+C
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