(4x^2/(3x^2+2))dx
=(4/3) + (8/9)/(x^2+(2/3)) dx
积分得(4/3)x+(8/9)(√3/√2)arctan[(√3/√2)x] + C
(x^5/(根号x^3+1))
=(1/3)x^3/√(x^3+1) dx^3
令u=x^3
原式=
(1/3)u/√(u+1) du
=(1/3)[√(u+1) - 1/√(u+1)] du
积分得
(2/9)* (u+1)^(3/2) - 2* (u+1)^(1/2) + C
=(2/9)* (x^3+1)^(3/2) - 2* (x^3+1)^(1/2) + C