du = dx/2x^1/2 = dx/2u
So dx = 2u*du
I know that this is an integral problem, but I'm stuck on some algebra within it. I'm doing a u-substitution on this problem:
So far, so good. Here's where I am stuck. According to Wolfram Alpha, when I do my u-substitution, I should get:
The denominator and the constant are obvious, but I can't see how they get from to in the numerator. Can somebody show this to me? Clearly I have a hole in my algebra abilities.
Right. That's what I got. So, how can Wolfram get u^2 in the numerator. Using u = sqrt(x), their u-substitution comes back as:
So, a sqrt(x) comes back as u^2 in the numerator, but an x in the denominator also comes back as u^2????? This makes absolutely no sense to me. I've used Wolfram enough to trust what they say, but this one has me totally confused.
Yes, I did read it. Thanks for posting it. Right now, however, we are working on partial fractions, and I see a hole in my ability to solve problems of this type, so I am trying to address that specific issue. Your approach is very clever, and in another context, I would happily use it. I need to focus on this issue in the event that I get something of this nature on a test.