See here for the integral
http://www.mathhelpforum.com/math-he...-integral.html
and here for the LaTeX help
http://www.mathhelpforum.com/math-he...-tutorial.html
OK, the link above (which I edited in and you didn't see) is for using LaTeX to include nice notation in these posts. So for your example you would type
\displaystyle\int _2^4 x^{2x} (1 + \ln x) dx
but wrap it between math and /math tags.
If you want to get the images for yourself, without posting, you may need TeXnic Center - I'll edit in the link. Others may know of better or more easily accessed software, perhaps.
The latex wiki is at http://www.artofproblemsolving.com/W...aTeX:Downloads
You can also write the integral with the equation editor included in Word.
In Word 2007 you simply go to the Insert tab of the ribbon and click equation (you can also press 'Alt' + '='). Word 2007 allows you to type math very quickly in the equation editor using this syntax http://www.unicode.org/notes/tn28/UT...extMath-v2.pdf.
For Word 2003 you can take a look at this tutorial:
http://people.richland.edu/james/misc/editor.pdf
If the equation editor is not available, take a look at this page, which explains how to install it.
There are many programs to write equations. Another option would be, as tom@ballooncalculus already mentioned, LaTeX.
There is a commercially available Word add-on called MathType (I think that's its name) which has a friendly user interface but creates *very* bloated Word documents. As it uses LaTeX under the hood it makes it surprisingly straightforward (although fiddly) to convert a Word doc with MathType in it to pure LaTeX. So, if you get the hang of MathType (which I'm afraid you have to pay for - it comes from Design Science) and later decide to go the whole hog and get a LaTeX editor (I also use TexNic Center exclusively - it's worth the hassle of setting it up) you can easily convert your existing documents.
Be warned: MathType doesn't work with OpenOffice (or it didn't when I was using it).