Homework Help: Integration HELP!

1. Nov 21, 2008

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?!?!

2. Nov 21, 2008

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

3. Nov 21, 2008

HallsofIvy

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

4. Nov 21, 2008

Dick

5. Nov 21, 2008

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!