# integration problem

• Aug 1st 2009, 05:57 PM
sma4
integration problem
can anyone help me with this, it's been bothering me for the last few days

$\displaystyle \int\sqrt{1+\sin^2 x}dx$

i've tried doing substitution but with little success, and i don't think partial integration does the trick
• Aug 1st 2009, 06:58 PM
skeeter
Quote:

Originally Posted by sma4
can anyone help me with this, it's been bothering me for the last few days

$\displaystyle \int\sqrt{1+\sin^2 x}dx$

i've tried doing substitution but with little success, and i don't think partial integration does the trick

I believe this elliptical integral cannot be integrated using elementary methods.

I don't have the background to explain ... maybe someone more knowledgeable will comment.
• Aug 1st 2009, 09:59 PM
mr fantastic
Quote:

Originally Posted by sma4
can anyone help me with this, it's been bothering me for the last few days

$\displaystyle \int\sqrt{1+\sin^2 x}dx$

i've tried doing substitution but with little success, and i don't think partial integration does the trick

The integral cannot be found using a finite number of elementary functions. What is the exact problem that has led you to this integral?
• Aug 2nd 2009, 02:24 AM
sma4
Quote:

Originally Posted by mr fantastic
What is the exact problem that has led you to this integral?

I don't understand what you are asking for. I found this problem in my exercise book. The original question is as i wrote above, with no additional details. Is it missing something?
• Aug 2nd 2009, 03:51 AM
mr fantastic
Quote:

Originally Posted by sma4
I don't understand what you are asking for. I found this problem in my exercise book. The original question is as i wrote above, with no additional details. Is it missing something?

I assumed that you probably incorrectly obtained this integral from the real problem. Clearly that's not the case. Does your book expect you to solve it using elliptic functions? If not, then yes, it's probably either missing something or there's a typographical error.
• Aug 2nd 2009, 04:38 AM
sma4
Quote:

Originally Posted by mr fantastic
Does your book expect you to solve it using elliptic functions? If not, then yes, it's probably either missing something or there's a typographical error.

The book doesn't expect nor have I learnt elliptical integrals since i am still a high school student. I will ask my teacher for further clarifications, maybe I'm missing the details. Thank you for your time.