如图，求详解.17题
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let
u = (x+1)^(1/6)
du = (1/6)(x+1)^(-5/6) dx
dx = 6u^5. du
------
∫dx/[(x+1)^(1/2) +(x+1)^(1/3)]
=∫6u^5. du/[u^3 +u^2]
=6∫u^3/(u +1) du
=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)^(1/2) - (1/2)(x+1)^(1/3) +u - ln|(x+1)^(1/6)+1| ] +C
u = (x+1)^(1/6)
du = (1/6)(x+1)^(-5/6) dx
dx = 6u^5. du
------
∫dx/[(x+1)^(1/2) +(x+1)^(1/3)]
=∫6u^5. du/[u^3 +u^2]
=6∫u^3/(u +1) du
=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)^(1/2) - (1/2)(x+1)^(1/3) +u - ln|(x+1)^(1/6)+1| ] +C
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