Stuck on the integration. Help me please

[Kinetica]

Homework Statement

Hello! I am in the middle of the integration process. Can you give me suggestions on how to simplify the last equation? Thank you!

Please see the attached snapshot of my work.

 

[Vargo]

If I do some algebra, I get

(a+b)^3 - (a-c)^3 = 3a^2(b-c) +3a(b^2-c^2) +b^3-c^3

Does that help?

 

[Kinetica]

Hi! I did it and it yields results different from the book answer.
Can here be a simpler method of simplification?

 

[dimension10]

Homework Statement

Hello! I am in the middle of the integration process. Can you give me suggestions on how to simplify the last equation? Thank you!

Please see the attached snapshot of my work.

I just glanced at the problem but I think this really very extremely super-duper basic elementary algebra trick would help:

$$ x^3-y^3=(x-y)(x^2+xy+y^2$$