First we need to compute some integrals
First lets rewrite this interms of sine and cosine
Now by long division
Integrating we get (for the 2nd one let u =cos(x))
Now for the other integral we have
Using termwise division we get
The first integral should be memorized or from a table.
If you really want to do it by hand let u=sec(x)+tan(x) it is not too bad...
Now finally for the particular solution we have
This is what we wanted YEAH!!!