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Re:

3. ## integral 2

See a different substitution which works better.

4. ## Re:

What made you choose just x^2? How do you determine that?

5. Just intuition, and a lot of experience
Regarding your question about dividing the integral, you can do that as long you know that both function you use are integrable.

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Is this something that comes across often? And is this one of the first things you look for when you are solving these kinds of problems?

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Also two other questions...

1) Do all constants hold over? No matter if they are from the original problem or from the differentiation of U?

2) If there is a plus or minus a number in the original problem, do I put that out in front of the integral and let it hold over, or do I integrate at the same time I integrate Ul?

8. My rule to choose substitution is whatever you don't like replace with a new letter. You tried that, but it didn't give you a simpler integral. I know that I have to change x^4, since a linear expresion did not work, a quadratic on the bottom I can deal with.
If you have square roots, or radical, almost all the times works by using a new variable for the whole radical.

9. Originally Posted by qbkr21
Also two other questions...

1) Do all constants hold over? No matter if they are from the original problem or from the differentiation of U?

2) If there is a plus or minus a number in the original problem, do I put that out in front of the integral and let it hold over, or do I integrate at the same time I integrate Ul?
1) yes,constant hold over,
int{af(x)}=aint{f(x)}if f is integrable.
2) the abouve rule works for all real constants.
Make sure that the constant is a factor of the function and not a term