Where to Begin with Integrals to Integration by Parts

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The discussion focuses on strategies for tackling integrals, particularly in the context of integration by parts. A participant expresses confusion about where to start with integrals, specifically referencing the Cauchy formula for iterated integrals. Another contributor advises against expanding the expression and suggests using substitution instead. The conversation highlights integration by parts as a key technique to approach the problem effectively. Overall, the exchange emphasizes the importance of recognizing appropriate methods for solving integrals.
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I've looking at this and I'm dumbfound as to where to begin. Integrals have never been my strong suit.

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This is called the Cauchy formula for iterated integrals (don't mix it up with the Cauchy formula in complex analysis). Ignore the left hand side. Suppose you were asked to answer the right hand side in an exam. What techniques do you know which would help you?
 
What I had in mind is expanding the (x-t)^2, and then multiplying everything out, and then I would have 3 separate integrals due to being able to separate integrals based on addition.
 
No, don't expand. If I wrote (x-t)2 = g(t), would that give you ideas?
 
Ah, integration by parts is the first thing that comes to mind. Don't know how I missed that.
 

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