1. Integral problem

Find the intregral of:

The square root of (1+x^3)

I've tried this for a while, it's tough. Perhaps im missing something.

2. $\displaystyle \int \sqrt{x^3 + 1}~dx$

This integral seems messy. I couldn't come up with a nice way to evaluate.

3. The thing is: it can't be computed in elementary terms.

4. Am I missing something here?

[insert huge great big mathematical flaw]

see post below

5. That's one of the terrible mistakes that a human been can ever do!

$\displaystyle \sqrt{a+b}\ne\sqrt a+\sqrt b.$

(Quite amazing how people covering integration makes those mistakes.)

6. hmm

So this cannot be done easily? The person i'm helping is a senior in HS taking AP calc. 1, so really only u sub seems viable.

7. Replace the "cannot be done easily" by "it can't be done." You may try substitutions, integration by parts but you can't get an easy integral to get rid of the problem.

8. Originally Posted by Krizalid
That's one of the terrible mistakes that a human been can ever do!
i agree. but it's human "being"

(don't worry, a lot of native english speakers don't know that -- funny huh?)

9. Originally Posted by Jhevon
(don't worry, a lot of native english speakers don't know that -- funny huh?)
Ohhh, I felt stupid

If you said so, then it's common

10. Originally Posted by Krizalid
Ohhh, I felt stupid

If you said so, then it's common
yes, i make fun of people about it all the time. except i usually interpret it as them saying "bean"

"wow, you saw a human bean?! that's amazing! just like those walking raisins in that old cartoon show (i forgot what it was called)"

anyway, i always imagine a bean with arms, legs and a face walking down the street

11. Originally Posted by bakeit1
So this cannot be done easily? The person i'm helping is a senior in HS taking AP calc. 1, so really only u sub seems viable.
Where has the question come from? Is there a typo - should it be x^2, not x^3? Is it a definite integral where only an approximate answer is required?

The complete context is essential in questions like this.

My money's on the typo scenario ....

12. Originally Posted by Krizalid
Replace the "cannot be done easily" by "it can't be done." You may try substitutions, integration by parts but you can't get an easy integral to get rid of the problem.
Bah! Someday someone will finally expand the meaning of the term "elementary function" and we'll be able to compute this exactly.

-Dan

13. That'd be nice really, but I do prefer solving nice & interesting problems (Tough ones, of course.)

14. Originally Posted by bakeit1
Find the intregral of:

The square root of (1+x^3)

I've tried this for a while, it's tough. Perhaps im missing something.
Originally Posted by bakeit1
So this cannot be done easily? The person i'm helping is a senior in HS taking AP calc. 1, so really only u sub seems viable.
You be the judge:

15. That's an easy expression to derive. (NOT)

What's the function F? Some variation on the hypergeometric function?

-Dan

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