求积分第四题，怎么做
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let
u= x^(1/6)
du = (1/6)x^(-5/6) dx
dx = 6u^5. du
∫dx/[x^(1/2) +x^(1/3)]
=∫6u^5. du/(u^3 +u^2)
=6∫u^3. du/(u +1)
=6∫[u^2+u+1 + 1/(u +1)] du
=6[(1/3)u^3+(1/2)u^2+ u + ln|u +1|] +C
=6[(1/3)x^(1/2)+(1/2)x^(1/3)+ x^(1/6) + ln|x^(1/6) +1|] +C
u= x^(1/6)
du = (1/6)x^(-5/6) dx
dx = 6u^5. du
∫dx/[x^(1/2) +x^(1/3)]
=∫6u^5. du/(u^3 +u^2)
=6∫u^3. du/(u +1)
=6∫[u^2+u+1 + 1/(u +1)] du
=6[(1/3)u^3+(1/2)u^2+ u + ln|u +1|] +C
=6[(1/3)x^(1/2)+(1/2)x^(1/3)+ x^(1/6) + ln|x^(1/6) +1|] +C
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