The discussion revolves around the integration of the function ∫x^2√(2+x) using substitution methods. Participants are exploring the use of u-substitution to simplify the integral.
There is an ongoing exploration of different substitution methods. Some participants have suggested specific substitutions, while others are seeking clarification on the original poster's attempts. No consensus has been reached, but there are indications of productive dialogue regarding the approach to the problem.
Participants are discussing the implications of different substitutions and their derivatives, indicating a focus on understanding the mechanics of u-substitution in the context of integration.
HallsofIvy said:Frankly, I really don't know what you mean by
"if I sub 2+x I just get 1, and if I sub x^2 I just get 2x
If I do √(2+x) I just get 1/2(1/√(2+x)) "
You get 1 for what? The integral? Show your work! HOW did you get "1"?
benorin said:Let [itex]J:=\int x^2\sqrt{x+1}dx[/itex]. Put [itex]u=x+1\Rightarrow du=dx[/itex] to get [itex]J=\int (u-1)^2\sqrt{u}du=\int \left( u^\frac{5}{2}-2u^\frac{3}{2}+u^\frac{1}{2}\right)[/itex]