∫x^3/(x^8-2) dx∫(x^3-1)/(x^2+1) dx

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/27 18:03:08
∫x^3/(x^8-2) dx∫(x^3-1)/(x^2+1) dx
x){Ա"X_"BHS!(j A6IEJaXِdޓKJl+LRJbL cӾO$4J⌀fii%2%PX]0Wƭ3I5mglBRah0҃+/ [BP$HlgLebQrIb^T<;P@

∫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