求不定积分∫x^2/(x^4-x^2+1)dx

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/07 18:16:41

求不定积分∫x^2/(x^4-x^2+1)dx
求不定积分∫x^2/(x^4-x^2+1)dx

求不定积分∫x^2/(x^4-x^2+1)dx
∫x^2dx/(x^4-x^2+1)
=(1/2)∫xdx^2/[(x^2+1)^2-3x^2]
=(1/4√3)∫(2√3x)dx^2/[(x^2+1+√3x)(x^2+1-√3x)]
=(1/4√3)[∫dx^2/(x^2+1-√3x)-∫dx^2/(x^2+1+√3x)]
=(1/4√3) [∫d(x^2-√3x+1)/(x^2+1-√3x) +∫√3dx/(x^2-√3x+1)
-∫d(x^2+√3x+1)/(x^2+1+√3x)+∫√3dx/(x^2+√3x+1)]
=(1/4√3)[ln|x^2+1-√3x|/|x^2+1+√3x| +√3∫dx/[(x-√3/2)^2+1/4]+√3∫dx/[(x+√3/2)^2+1/4]
=(1/4√3[ln|x^2+1-√3x|/|x^2+1+√3x| +2√3aratn(2x-√3)+2√3arctan(2x+√3)]+C
=(1/4√3)ln[|x^2+1-√3x|/|x^2+1+√3x|] +(1/2)arctan(2x-√3)+(1/2)arctan(2x+√3)+C

求不定积分 ∫(X^2+1)/(X^4+1)dxrt 求不定积分∫1/(x^2+4x+5)dx. ∫x*根号4x^2-1 dx 求不定积分 ∫1/(x^2-4x+3)dx,求不定积分, 求不定积分∫(x^2/(1+x^4))dx 求不定积分 ∫ [(x^4)/(1+x^2)]dx= 求不定积分∫x^2/(1-x^4)dx ∫dx/(x^4(1+x^2))求不定积分 ∫x^2√(1+x^4)dx 求不定积分! 求不定积分:∫[x(e^x)]/[(1+x)^2]dx 求不定积分∫(x^2-3x)/(x+1)dx 对(x+1)/(x^2-4x+3)求不定积分 求dx/[(x-1)(x^2+4x+9)]不定积分? 不定积分习题求不定积分∫（x^2-1)sin2xdx 求不定积分 ∫x/(x^2)dx dx/(4x-x^2)求不定积分 不定积分符号[(x+1)/x^2+xlnx]dx,求不定积分 tan^4x求不定积分 1 tan^4x求不定积分 1/【(1-x^2)^3/2】求不定积分