求助一道高数题,会的帮下忙〜一定有好评!

求助一道高数题,会的帮下忙〜一定有好评!
求助一道高数题,会的帮下忙〜一定有好评!
 

求助一道高数题,会的帮下忙〜一定有好评!
∫dx/[x^(1/2)+x^(1/3)],u=x^1/6,x=u^6,dx=6u^5du
= 6∫u^5du/(u³+u²)
= 6∫u³du/(u+1)
= 6∫[u²-u-1/(u+1)+1]du
= 6[u³-u²-ln|u+1|+u] + c
= 2x^(1/2)-3x^(1/3)+6x^(1/6)-6ln|1+x^(1/6)| + c