Evaluate the following integral: `int_0^pi1/(3+2sinx+cosx)dx`

Explanation

Given,I=`int_0^pi1/(3+2sinx+cosx)dx`

Put `tan(x/2)=t`

When x=0 ,t=0

when `x=pi,t=oo`

`dx=(2dt)/(1+t^2)`

`sinx=(2t)/(1+t^2)`,`cosx=(1-t^2)/(1+t^2)`

I=`int_0^(oo) 1/(3+2sin(2t)/(1+t^2)+cos(1-t^2)/(1+t^2)) (2dt)/(1+t^2)`

=`2 int _0^oo dt/(2t^2+4t+4)`

...