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So I understand the first thing we would so is bring the constant out and do

**u substitution**but what I don't understand is how we can make the substitution u = \(\displaystyle \frac{x}{2}\) when there clearly is no \(\displaystyle \frac{x}{2}\) in the problem. I also understand how to factor out a 4 in the denominator thus getting us this

\(\displaystyle \int \frac{1}{\frac{x^2}{4} + 1} \)

but then I don't understand how we can say u = \(\displaystyle \frac{x}{2}\) then \(\displaystyle du = 1/2dx\)

when \(\displaystyle \frac{x}{2}\) is no where in the problem..What am I missing