How do I evaluate: http://www.wolframalpha.com/input/?i=integral+sqrt((x^2+%2B+1)^2%2F(x^2+-+1)^2)%2C+from+0+to+1%2F2 ?

Any help would be greatly appreciated!

Thanks in advance!

Printable View

- March 18th 2010, 08:00 PMs3aThis looks like a crazy integral...please help
How do I evaluate: http://www.wolframalpha.com/input/?i=integral+sqrt((x^2+%2B+1)^2%2F(x^2+-+1)^2)%2C+from+0+to+1%2F2 ?

Any help would be greatly appreciated!

Thanks in advance! - March 18th 2010, 08:09 PMProve It
- March 18th 2010, 09:00 PMdrumist
- March 19th 2010, 10:54 AMs3a
Where does the 1 come from in the integral? (after the square root step)

- March 19th 2010, 11:05 AMKrizalid
read above, quite obvious from the previous work shown.

and it's worth to mention that - March 19th 2010, 11:17 AMdrumist
When using partial fraction decomposition, you need the numerator to have lower degree than the denominator. In a more complex problem you may have to use polynomial long division to see the reduction, but in this case it's pretty easy to rewrite the expression to get it.

- March 19th 2010, 11:52 AMs3a
I still fail to see where the 1 came from. Here is my new work (attached).

- March 19th 2010, 12:33 PMdrumist
You attempted to use partial fraction decomposition on the following fraction

You cannot do that! Partial fraction decomposition cannot be used on this fraction because the degree of the numerator is not less than the degree of the denominator.

Notice how you got

when you did the work. But now, let's check the answer:

But this doesn't equal the original fraction. - March 19th 2010, 08:04 PMs3a
I forgot to check the degree of the exponents. After having done long division, etc, I get the right answer! Thanks everyone!