# Thread: How to find this integral

1. ## 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

2. 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:

3. 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

4. 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?

5. 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

6. 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
$\int \frac{\cos (x)}{x+1} dx = \int \frac{\cos [(x+1)-1]}{(x+1)}\left( x+1 \right) ' ~ dx =$ $\int \frac{\cos (x+1)\cos 1 + \sin (x+1)\sin 1}{(x+1)} \left( x+1 \right) ' ~ dx = \mbox{Ci}(x+1)\cos 1 + \mbox{Si}(x+1)\sin 1 + k$