Stackers (I tried to be nifty),
I'm currently in a Calculus II course, and we're working through the very basic steps of integrating. I'm really struggling with multiple portions of the substitution method that incorporates the use of u and du. I'm looking at this problem: $$\int (x^6-3x^2)^4(x^5-x)dx$$ Now comes my dilemma. I just cannot, for the life of me, understand how the substitution method would work with this equation. I just need someone to break it down for me a bit better than the book is, I'm supposed to find a value of u that helps the equation look like: $$\int u^4du$$ or something, right? If someone could just step through this problem with me, it'll help me greatly with the other 50 questions I have to do with the same concept. Is there any sort of fool-proof analysis that I can do to each problem to know where and how to assign the values of u and du?
Thanks for your help.