# How to find this integral

• Feb 7th 2008, 07:53 PM
snoboarder2k6
How to find this integral
Yeah, so I can't figure out how to find the integral with respect to x of the following

cos(x) / (1 + x).

how would I do this?

thanks for any help
• Feb 7th 2008, 08:12 PM
mr fantastic
Quote:

Originally Posted by snoboarder2k6
Yeah, so I can't figure out how to find the integral with respect to x of the following

cos(x) / (1 + x).

how would I do this?

thanks for any help

Why? The reason I ask is this:
• Feb 7th 2008, 08:14 PM
snoboarder2k6
yeah, I did try the integration calculator. I just have no idea what those symbols mean. What's the w/ the Si(...) Ci(...) etc?
That and I want to know how to do it w/o the help of a computer so I can handle it on a test if i need to.

thanks
• Feb 7th 2008, 08:29 PM
mr fantastic
Quote:

Originally Posted by snoboarder2k6
yeah, I did try the integration calculator. I just have no idea what those symbols mean. What's the w/ the Si(...) Ci(...) etc?
That and I want to know how to do it w/o the help of a computer so I can handle it on a test if i need to.

thanks

What it means old son is that there's no answer in terms of a finite number of elementary functions.

If you haven't met the sine-integral Si(x) and cos-integral Ci(x) functions then I would be mighty surprised to see them required on your test ....... Where has the question come from?

Are you sure you not asked to get definite integrals, say form 0 to oo?
• Feb 8th 2008, 05:42 AM
snoboarder2k6
this was part of a larger linear equation, so I'm gonna assume I screwed up somewhere else and that I shouldn't even have to do this.

Thanks for you're help though
• Feb 8th 2008, 08:24 AM
ThePerfectHacker
Quote:

Originally Posted by snoboarder2k6
Yeah, so I can't figure out how to find the integral with respect to x of the following

cos(x) / (1 + x).

how would I do this?

thanks for any help

$\displaystyle \int \frac{\cos (x)}{x+1} dx = \int \frac{\cos [(x+1)-1]}{(x+1)}\left( x+1 \right) ' ~ dx =$$\displaystyle \int \frac{\cos (x+1)\cos 1 + \sin (x+1)\sin 1}{(x+1)} \left( x+1 \right) ' ~ dx = \mbox{Ci}(x+1)\cos 1 + \mbox{Si}(x+1)\sin 1 + k$