# integration problem

#### prasum

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

#### mr fantastic

MHF Hall of Fame
how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees)
Prove the following identity: $$\displaystyle \frac{1 + \sin (2x)}{\cos (x) + \sin (x)} = \cos (x) + \sin (x)$$.

Now the integration is trivial.

#### prasum

thanks for the suggestion. please tell me how to prove the identity(Wink)

#### harish21

thanks for the suggestion. please tell me how to prove the identity(Wink)
$$\displaystyle \frac{1+sin(2x)}{cosx+sinx} \times \frac{cosx+sinx}{cosx+sinx}$$

Now simplify.

I hope you know that sin2x = 2sinx.cosx