Expert: Abe Mantell - 8/16/2010

Question
Integrate: 1/((cos^2(x) +4sin(x)-5)*cos(x))

AP BC summer assignment Extra credit

Answer
Hello Keith,

I hate to simply just do the problem for you, since it is an extra credit problem!

However, I will guide you along.
1. Express cos^2(x) as 1-sin^2(x), then factor!
2. Make the substitution u=sin(x)...this will greatly
.  simplify the integrand...but will then require partial
.  fraction expansion.
.  You should (eventually) get the integral of: 1/[(u+3)(u+1)u^2]

Let me know if you need help with the details, but do first try!!!

Have fun!

Abe