Normalizing a Non-Normalized Wavefunction

[physixchic]

I am given a non-normalized wavefunction and asked to normalize it. The function and the attempt will be in:
http://i35.tinypic.com/2vahvuc.jpg

 

[CompuChip]

You are correct that you have to calculate
$$\int_{-\infty}^\infty |x| e^{-|x|} \, dx$$
however you are making the step to partial integration too fast. You have two pairs of absolute value signs in your integrand, which you should get rid of first (hint: how can you write |x| e^{-|x|} without absolute value signs when x > 0? And when x < 0?).

When you then do the partial integration you need to evaluate an expression such as the one you had, but between different boundaries which give no problems anymore.