Trouble Understanding Integration Problem | Solutions Manual Confusion

[jofree87]

I am having a trouble understanding why the solutions manual is using u-substitution here. Am I forgetting a rule or something?

I don't know how to post in the correct notation so I'll post pictures instead.

I am suppose to integrate equation (4) in the picture. The solutions manual shows equation (6) as their answer. The answer I got is this:

= 1/2*R_Ax² - w_oL/4(x²/2 - Lx/3) + C₃

I believe they are using u-substitution for the (x-L/3). Am I doing something wrong?

 

[Char. Limit]

The answer you give and the answer they give differ only by a constant. So both answers are correct.