Could use some help here:

1. The integral: 1 / sqrt( e^x - 1 ) dx

2. The integral: sqrt( x^2 - 1) / x dx

Thanks!

Printable View

- February 25th 2008, 12:47 PMcooliointegration problem
Could use some help here:

1. The integral: 1 / sqrt( e^x - 1 ) dx

2. The integral: sqrt( x^2 - 1) / x dx

Thanks! - February 25th 2008, 01:16 PMPaulRS
We have

Let then

We get:

See that

So:

- February 25th 2008, 01:28 PMPeritus
I think you missed the sqrt

-------------------------------------------------------------------------

- February 25th 2008, 01:51 PMKrizalid
- February 25th 2008, 02:41 PMPeritus
- February 25th 2008, 02:51 PMcoolio
Thanks a for the help everyone!

I came across another one that has stumped me:

The integral from -1 to 1: sinx / 1 + x^2 dx

I see 1 / 1+x^2 as the derivative of arctan, but I'm not sure if that is relevant. The only this I could think of was to integrate by parts, but after attempting that, I seem to just be going in circles. - February 25th 2008, 02:52 PMKrizalid
It's a classic problem, the answer is zero, since you're integrating an odd function on a symmetric interval.

- February 25th 2008, 02:57 PMcoolio
- February 25th 2008, 03:01 PMKrizalid
Let substitute

Hence, our original integral satisfies

(Ahh, I just saw you edited your original question: an odd function satisfies When having integrals whose function is odd besides if they're taken on a symmetric interval the answer is zero.) - February 25th 2008, 03:05 PMcoolio
- February 25th 2008, 03:06 PMcoolio