一道积分题 ∫1/(x+x^1/3)dx

题目

一道积分题 ∫1/(x+x^1/3)dx

答案

设t³=x,则dx=3t²dt
∫1/(x+x^1/3)dx
=∫1/(t^3+t)*3t^2dt
=∫3t/(t^2+1)dt
=∫3/2*d(t^2+1)/(t^2+1)
=3/2*ln(t^2+1)+C
=3/2*ln[x^(2/3)+1]+C