Question

这道不定积分题怎么做

Answer 1

换元法。

Answer 2

let
u = x^(1/6)
6u^5 du = dx
∫ dx/[ √x .(1+x^(1/3)) ]
=∫ 6u^5 du /[ u^3 .(1+u^2 ) ]
=6∫ [ u^2 /(1+u^2 ) ] du
=6∫ [ 1 -1/(1+u^2 ) ] du
=6( u - arctanu ) + C
=6[ x^(1/6) - arctan(x^(1/6)) ] + C