Wow, I can't believe I didn't see that. During the exam I tried using root(x) for u but I never thought about root(x)^2 = x. Tunnel vision must have set in- I should have seen that!
So the answer would be arctan(root(x))- I suppose I can console myself knowing I saw arctan(x) correctly...
u = root(x) so du = 1/(2*root(x)).
INT [1 / ( 2 * root(x))] * [1 / (1 + x)] dx
= INT [1 / (1 + x)] du = ln|1 + x|
That doesn't seem to work, though. If I differentiate this function I only get the original function with respect to u, not with respect to x since the value of u is...
Homework Statement
INTEGRATE dx / (2 * root(x)) * (1 + x)
Homework Equations
That's pretty much it!
The Attempt at a Solution
I received this question on a Calc II exam, so I'm only looking for the solution for my own understanding (I'm sure I already got it wrong). My instinct...