∫x^3dx/(x^4-x^2+2)
来源：学生作业帮助网 编辑：六六作业网 时间：2025/01/22 19:47:18
∫x^3dx/(x^4-x^2+2)∫x^3dx/(x^4-x^2+2)∫x^3dx/(x^4-x^2+2)∫x³/(x⁴-x²+2)dx=(1/2)∫x²/
∫x^3dx/(x^4-x^2+2)
∫x^3dx/(x^4-x^2+2)
∫x^3dx/(x^4-x^2+2)
∫ x³/(x⁴-x²+2) dx
=(1/2)∫ x²/(x⁴-x²+2) d(x²)
令x²=u
=(1/2)∫ u/(u²-u+2) du
=(1/2)∫ (u-1/2+1/2)/(u²-u+2) du
=(1/4)∫ (2u-1)/(u²-u+2) du + (1/4)∫ 1/(u²-u+2) du
=(1/4)∫ 1/(u²-u+2) d(u²-u) + (1/4)∫ 1/[(u-1/2)²+7/4] du
=(1/4)ln(u²-u+2) + (√7/14)arctan[2(u-1/2)/√7] + C
=(1/4)ln(x⁴-x²+2) + (√7/14)arctan[(2x²-1)/√7] + C
希望可以帮到你,如果解决了问题,请点下面的"选为满意回答"按钮.
asdfasdfasdfasdfadsfd
∫(x^3-x^2+x+1)/(x^2+1) dx∫(x+4)/(x^2-x-2) dx
∫(3x^4+x^2)/(x^2+1)dx
∫x^3dx/(x^4-x^2+2)
∫x/(3+4x+x^2)^1/2dx
∫{√（x^4+x^-4+2)}/x^3dx
∫(x^11)/(x^8+3x^4+2)dx
∫[(x^2-x+6)/(x^3+3x)]dx
∫dx/x(2x+3)^2
∫（x^2+1/x^4)dx
∫dx/根号(4x-x^2)
∫1/(x^4-x^2)dx
∫x/(4+9x^2)dx
∫(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