integarte {secx}\{1+2
sin^2(x)},dx
(Quoted from mymathforum, where you cross-posted...)
We are given:
Let's rewrite the integrand:
Now we may state:
That was MarkFL's answer...
Almost simultaneously, galactus wrote:
Let
Notice now we have the form
Continuing:
Since , then (this just comes from looking at a right triangle).
Put all together:
The left most integral is an arctan. The right one is of the form
So, we get after resubbing:
http://www.mymathforum.com/viewtopic...start=0#p89474