Help with an integral

Question

Can you help me in calculating the integral>

 

I= dx/sinx(2+cosx-2sinx) 

 

I could really use the help. Thanks to everyone!

Answer 1

Frosina,

 

If I am interpreting this correctly, we are looking for

 

∫{sin(x)*[2 + cos(x) - 2sin(x)]}^-1dx or ∫[2sin(x) + sin(x)cos(x) -2sin²(x)]^-1dx

 

= (1/3)ln[sin(x/2)] - 3ln[cos(x/2)] - 3ln{[cos(x/2)] - [sin(x/2)]} + 5ln{[3cos(x/2)] - [sin(x/2)]}

 

Frosina, my friend, is your professor some sort of sadist?  The only way I was able to solve this was by going to wolfram and using his step-by-step integrator.

 

Here's a handy website:

 

http://www.wolframalpha.com/widgets/view.jsp?id=893912ad72b01acedd76b68aa3ffc4df

 

 

Answer 2

The best thing to do is to go to

integrals.wolfram.com/index.jsp

 

It is free and very good.