Trouble Understanding Integration Problem | Solutions Manual Confusion

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The discussion centers on the confusion regarding the use of u-substitution in integration as presented in a solutions manual. The user is attempting to integrate a specific equation and has derived a different answer than the one provided in the manual, which is attributed to the application of u-substitution. Both answers differ only by a constant, confirming that they are both valid solutions. The key takeaway is the importance of recognizing that multiple integration techniques can yield equivalent results in calculus.

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jofree87
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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*RAx2 - woL/4(x2/2 - Lx/3) + C3

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

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

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