∫x^3/(x^8-2) dx∫(x^3-1)/(x^2+1) dx
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/06 09:44:57
∫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
∫x^3/(x^8-2) dx∫(x^3-1)/(x^2+1) dx
∫(2x-3)/(x^2-3x+8)dx
∫(x^11)/(x^8+3x^4+2)dx
∫[(x^2-x+6)/(x^3+3x)]dx
∫dx/x(2x+3)^2
∫(2^x+3^x)²dx
∫x^3/9+X^2 dx.
∫X^2 e^-X^3 dx.
∫（x-3x+2）dx
∫x^3/1+x^2 dx
∫(x-1)^2/x^3 dx
∫3+x/(9-x^2)dx
∫x^3/(9+x^2)dx
∫dx/(x-2)平方(x-3)
∫(X^3)/(1+X^2)dx
∫x^2/x+3dx
∫x^3*e^x^2dx
∫2^x-3dx