Hi, in this problem you are supposed to know how to intergrate (x/(1+x^2)^(1/2))

Question

Hi, in this problem you are supposed to know how to intergrate (x/(1+x^2)^(1/2))dx but I am having trouble figuring out how to do this. It seems when I try to use substitution to find it, I end up getting what I was trying to intergrate in the first place. It is like substitution just leads to a loop. I feel like I need to know some other technique to get this, or am I just doing it wrong? Here is an example of my work so far. (u=(1+x^2)^(1/2), then du/dx=(1/2)((1+x^2)^(-1/2))(2x), so du=(x/(1+x^2)^(1/2))dx, which is the same thing as I was trying to intergrate...)

Explanation / Answer

x/(1+x^2)^1/2 dx

So let u = 1=x^2

Therefore du = 2x dx

Therefore dy/2 = x dx

(1/2) 1/u^(1/2) du

(1/2) u^-(1/2)

(1/2) 2 * u^(1/2)+c

(1+x^2)^(1/2) + c

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