Hi I have the following integral:
$$\int \frac{2x}{x^2+6x+3}\, dx$$

I made some changes like:
$$\int \dfrac{2x+6-6}{x^2+6x+3}\, dx$$

then I have: 
$$\int \dfrac{2x+6}{x^2+6x+3}\, dx -\int\dfrac{6}{x^2+6x+3}\, dx$$

and thus: $$\ln(x^2+6x+3)-\int\dfrac{6}{x^2+6x+3}\, dx$$

Ok, I have decomposed $$\frac{2x}{x^2+6x+3} $$  in: $$ \frac{3+\sqrt6}{\sqrt6(x+\sqrt 6+3)} + \frac{3-\sqrt6}{\sqrt6 (-x+\sqrt6-3)}$$

How can I integrate this expressions?


Question: QGIS: How to get Symbols saved in GPX Files
Answer: Using pure GDAL, you can preserve the waypoint symbol and type of an original GPX file with

ogr2ogr -f GPX -dsco GPX_USE_EXTENSIONS=YES out.gpx in.gpx waypoints

&lt;wpt lat="51.295094" lon="6.790674"&gt;
  &lt;ele&gt;39.0&lt;/ele&gt;
  &lt;time&gt;2014-10-14T13:56:58Z&lt;/time&gt;
  &lt;name&gt;Push Log Point #1&lt;/name&gt;
  &lt;desc&gt;Lat.=51.295094, Long.=6.790674, Alt.=39.000000m, Speed=3Km/h, Course=45deg.&lt;/desc&gt;
  &lt;sym&gt;Waypoint&lt;/sym&gt;
  &lt;type&gt;Other&lt;/type&gt;
  &lt;extensions&gt;
    &lt;label&gt;&lt;label_text&gt;Push Log Point #1&lt;/label_text&gt;&lt;/label&gt;
  &lt;/extensions&gt;
&lt;/wpt&gt;


So if you have a shapefile in QGIS, create columns with names sym and type and export it to GPX format with GPX_USE_EXTENSIONS=YES (which is default for GPX since QGIS 2.4).

Remember to save into EPSG:4326, as GPX only allows that.

Other features (like label) will be exported in the &lt;extensions&gt; element, and probably ignored by a GPS unit. My output reads as follows:

&lt;wpt lat="51.295094" lon="6.790674"&gt;
  &lt;name&gt;Push Log Point #1&lt;/name&gt;
  &lt;sym&gt;Waypoint&lt;/sym&gt;
  &lt;type&gt;Other&lt;/type&gt;
  &lt;extensions&gt;
    &lt;ogr:elevation&gt;39.0&lt;/ogr:elevation&gt;
    &lt;ogr:label&gt;1&lt;/ogr:label&gt;
  &lt;/extensions&gt;
&lt;/wpt&gt;
&lt;wpt lat="51.295091" lon="6.790663"&gt;
  &lt;name&gt;Push Log Point #2&lt;/name&gt;
  &lt;sym&gt;church&lt;/sym&gt;
  &lt;type&gt;tower&lt;/type&gt;
  &lt;extensions&gt;
    &lt;ogr:elevation&gt;38.0&lt;/ogr:elevation&gt;
    &lt;ogr:label&gt;2&lt;/ogr:label&gt;
  &lt;/extensions&gt;
&lt;/wpt&gt;


The available symbols depend on the GPS units, so you might create a sample GPX file with the unit and test all available symbols. These will not be imported into QGIS, but you can read the file with a text editor.

As an example, symbols of the Garmin Oregon 6xx are listed at this site. You can even create your own symbols and upload them.