ok so basically we are doing lengths and planes of curves.. i m lost to how the solution manual gets this..

the get:

f '(x) = x (x^2 + 2)^ 1/2

= integral ( 0 to 3) x (x^2 + 2)^ 1/2

im ok till here

int ( 0 to 3) x (1 + {x^2 + 2} x^2)^ 1/2

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my question is where did that +1 and x^2 come from how do tthey know they go there?? for other problems how would i know to get those correct values ??