A Definite Integral Simplification There was this question on integration that I am correct with the answers section of my textbook upto a point. So I will only ask this last step of evaluation.
This is what the book says - 

And this is how my simplication ended up in -

As you can see both the book and my first part is same but I get a different final answer than book. The book has 1/2 inside the bracket where I have 1. I just dont know how the book got 1/2 or what I am missing out. Can anyone help me figure it out? :) 

$$\left(\frac{1}{\sqrt{2}}\right)^{2n+1}=\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{2}\right)^n\not=\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)^n$$
