# Math Help - integration problem

1. ## integration problem

how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees)

2. Originally Posted by prasum
how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees)
Prove the following identity: $\frac{1 + \sin (2x)}{\cos (x) + \sin (x)} = \cos (x) + \sin (x)$.

Now the integration is trivial.

3. thanks for the suggestion. please tell me how to prove the identity

4. Originally Posted by prasum
thanks for the suggestion. please tell me how to prove the identity
$\frac{1+sin(2x)}{cosx+sinx} \times \frac{cosx+sinx}{cosx+sinx}$

Now simplify.

I hope you know that sin2x = 2sinx.cosx