∫dx⼀((x^2+1)(x^2+x+1))求不定积分

2024-11-02 23:28:39
推荐回答(1个)
回答1:

C = (2/√3)arctan[(2x+1)/√3] + C
原式= (√3/2)∫sec²θ/(3/4*sec²θ)² dθ
arccost +C =arccos(1/x)+C
分母 x^2 * (1+x^2)^(1/2) = t^(-2) * ( 1+1/ t^2 )^(1/2) = t^(-3)