In order to normalize the wave function I am aware of the following condition:

$$\int_{-\infty}^{\infty} | \psi (x,t) |^2 dx = 1$$

If I am not mistaken what I have to do first is obtaining A so as to ensure that this value meets the stated condition. But what I got does not make sense:

There has to be a mistake here but I do not see where.

My book has the following information about normalization:

Thank you