I need some help with 2 and 8.
2) I see that U = sqrt(x-1) and then du=1/(2sqrt(x-1)) but how do I get an integer to sub in for xdx? Usually in our past problems we would have like xdx and u=x^2 so du = 2x and the fraction is 1/2. I guess I'm just not seeing it so some further good instruction would be nice.
8.I have the answer key that my prof gave me and I can't get the answer. I keep coming up with:
y'=1/(x^2+y^2) * 2x +2yy'
y'-2yy' = 2x/(x^2+y^2)
but the answer key says:
I don't see how you get the -2y in the denominator..
So when you integrate 2 you get:
((u+1)^2)/2 * (2/3U^(3/2))
That seems really whacky and I'm guessing I'm not seeing where you're coming from. Another guy I asked said let U = sqrt(x-1) then solve the polynomial but I didn't understand that either. Sorry; I'm not this big of a dunce usually.