Integral double check..... !find this integral I have the above integral I am trying to solve that I have taken the time to work out the steps below on paper and needed a couple of extra sets of eyes checking my work and the steps I have shown. I am apologize for the chicken scratch and crudity! Thank you! !worked out steps prior to sets of eyes!

Almost correct. The middle term should be $-\frac 1 {x^2}$.

You forgot to multiply by the 2 outside your integral.