Integration.. HELP!

[twalker40]

1. Evaluate exactly (in terms of \pi) the definite integral \int^{\pi/2}_{-\-\pi/2} \frac{dx}{sinx + 2cosx +3}



2. Relevant equations
How do i do this? Step by step instructions if possible.


3. The attempt at a solution
I've tried to manipulate the integral but still don't get anything. I also set the denominator as u. but then i cannot substitute du.

Help?!?!

[Roberto Bramb]

Substitute trig. objects with parametric formulae:
sinx=2t/(1+t^2), cosx=(1-t^2)/(1+t^2), dx=2dt/(1+t^2)
and your trig. integrale becomes the rational integral
2*Integ[-1,1](1/(t^2+2*t+5)dt = pi/4

[HallsofIvy]

That's clever. Took me a moment to figure out why dx= 2dt/(1+t^2).

[Dick]

It's the 'tan(x/2)' substitution in http://en.wikipedia.org/wiki/Trigonometric_substitution

[twalker40]

awesome... thanks alot guys.

We didn't spend that much time on that identity so it totally slipped my mind. Thanks for the reminder!