What is the integral of: (4sin(x))/(2+cos(x)) and please explain the method. Thank you.

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- December 1st 2008, 11:34 AMcharlie8529Integration
What is the integral of: (4sin(x))/(2+cos(x)) and please explain the method. Thank you.

- December 1st 2008, 12:02 PMSoroban
Hello, charlie8529!

Quote:

We have: .

Let:

Substitute: .

Got it?

- December 1st 2008, 12:03 PMvincisonfire
You want to compute the antiderivative of

That is .

Let

Then you can differentiate both side to find that

We notice that in the integral above we have at the denominator.

This corresponds to

We can now substitute in the integral to simplify the notation.

This should now remember you something.

because we substitute math] u = 2 + cos(x) [/tex].

You may use logarithm properties to express your answer as

where C is a constant number. Don't forget it. I use to and teachers will take off mark any time for this little mistake. - December 1st 2008, 12:15 PMcharlie8529
Thanks for the help guys.