大一新生在线求救

let
u=x^(1/12)
du =(1/12)x^(-11/12) dx
dx = 12u^11 du
u^14 =u^4.(u^5-1)(u^5+1) +u^4
u^14/(u^5 - 1)
=u^4.(u^5+1) +u^4/(u^5-1)
=u^9+u^4 +u^4/(u^5-1)
∫√x/[x^(2/3)- x^(1/4)] dx
=∫ [u^6/(u^8 - u^3)] (12u^11 du)
=12∫ [u^14/(u^5 - 1)] du
=12∫ [u^9+u^4 +u^4/(u^5-1)] du
=12[ (1/10)u^10 +(1/5)u^5 + (1/5)ln|u^5-1| ] +C
=(6/5)u^10 +(12/5)u^5 + (12/5)ln|u^5-1| +C
=(6/5)x^(5/6) +(12/5)x^(5/12) + (12/5)ln|x^(5/12)-1| +C