Need help with an anti-derivative

[PowerMacG5]

Originally posted by: LordMorpheus

Originally posted by: Marauder911

Originally posted by: ClueLis

Originally posted by: Marauder911

Originally posted by: ClueLis
Substitute u=x^2. This will leave you with 1/(2sqrt(u)sqrt(u^2+1)). Break it up using partial fraction decomposition to obtain 1/2(A/sqrt(u)+B/sqrt(u^2+1)), which will be much easier to integrate.

Okay, when I try that, I get
1=A(sqrt(u^2+1))+B(sqrt(u))

I cannot figure out how to solve for A and B.

That's what I just noticed, too.

Ah, ok. Anyone else have any suggestions?

Well, let U=0, that meanst that A must equal 1.

hmmmmm. That means that B varies with U.
edit: does this integral even converge?

1/x doesn't. 1/x^2 DOES converge, though, and x^2 = sqrt(X^4)


you know, if the original X^4 had been X^5, this would have been many, many, many times easier.

What chapter are you covering? This might be easier if i knew to seperate the fractions or use parts or something like that.

We are covering indefinite integrals, and indefinite forms of limits. The integral isn't possible to be evaluated by any means that are common according to my teacher. Which then to me boils down to that even after Calc II in college you still couldn't evaluate it because AP Calculus BC covers material through Calc II.