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Homework Statement
∫√(1+x^{2})/x dx
Homework Equations
The Attempt at a Solution
Let u = 1+x^{2}
du = 2xdx
1/2du=xdx
x=√(u-1)
∫√1+x^{2}/x dx
=∫√u/√(u-1) du
or is it 1/2∫√udu as xdx would remove it. This is where I got confused.
What did you do with the x in the denominator ofHomework Statement
∫√(1+x^{2})/x dx
Homework Equations
The Attempt at a Solution
Let u = 1+x^{2}
du = 2xdx
1/2du=xdx
x=√(u-1)
∫√1+x^{2}/x dx
=∫√u/√(u-1) du
or is it 1/2∫√udu as xdx would remove it. This is where I got confused.
You're missing an x.In my solution attempt, I tried two different ways. In your specific question, I replaced the x in the denominator with √(u-1) , as solving for x in u=1+x^2
There are two ways that I know of to do this integration.Thanks for the help so far. With that little fix, I've now reached the point of
1/2 ∫√u/(u-1) du
I don't know where to go from here. I also am having many people tell me that this method will not work? That Trig-Substitution is the only way to solve this problem... Is that true? Am I just wasting my time?