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# Integration Q watch

1. (Original post by ps1265A)
That's why I'm confused. The exercise I'm doing ONLY concerns the 2 methods I mentioned right at the beginning of the post.

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Both of those that you mentioned arevspecific cases of the inverse chain rule
2. (Original post by TenOfThem)
Both of those that you mentioned arevspecific cases of the inverse chain rule
And I cannot use either of them for this Q? Having tried both, my answer would be no

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3. (Original post by ps1265A)
And I cannot use either of them for this Q? Having tried both, my answer would be no

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If in doubt, use the general formulation of inverse chain rule:
4. (Original post by ps1265A)
And I cannot use either of them for this Q? Having tried both, my answer would be no

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No ... Since they are specific rules that only apply to specific cases

Are they not presented as specific cases in your textbook? It seems odd that the book is just presenting them without the general context.
5. (Original post by ps1265A)
Integrate xe^x^2

So I am going to use the rule f'(x)/f(x) ... However it's not a fraction, can I still apply it here?

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the derivative of e^f(x) is f'(x)e^f(x).
therefore the derivative of e^x^2 is 2xe^x^2.
integration is the inverse of differentiation... [ you do some maths] ... Ta da an answer!
6. (Original post by ps1265A)
And I cannot use either of them for this Q? Having tried both, my answer would be no

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As TenOfThem says, you're trying to remember lots of specific rules when you should be looking at the general principle of what's going on.

Try differentiating and compare with the answer you're trying to get.

Next try differentiating for various functions f(x) and see what form the answers come out in.
7. put it in the form you want, you know you're looking for f'(x)e^f(x) so write that integral out and say to yourself 'what constant do i need to pull out to make my new integral look like my old one' it's not a tricky question
8. (Original post by TenOfThem)
No ... Since they are specific rules that only apply to specific cases

Are they not presented as specific cases in your textbook? It seems odd that the book is just presenting them without the general context.
The book has simply stated the 2 rules. And there is an exercise of questions in which you use the rules. That's why I'm confused because one of the rules is supposed to work apparently.

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9. (Original post by davros)
As TenOfThem says, you're trying to remember lots of specific rules when you should be looking at the general principle of what's going on.

Try differentiating and compare with the answer you're trying to get.

Next try differentiating for various functions f(x) and see what form the answers come out in.
I know how to get to the answer using different integration techniques. But my concern is whether or not the answer can be brought by inspection, but it seems as it cannot.

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10. (Original post by ps1265A)
The book has simply stated the 2 rules. And there is an exercise of questions in which you use the rules. That's why I'm confused because one of the rules is supposed to work apparently.

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(Original post by ps1265A)
I know how to get to the answer using different integration techniques. But my concern is whether or not the answer can be brought by inspection, but it seems as it cannot.

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It does not use either of those rules

But

It is just by inspection

Those 2 are specific cases of "by inspection"
11. (Original post by ps1265A)
I know how to get to the answer using different integration techniques. But my concern is whether or not the answer can be brought by inspection, but it seems as it cannot.

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You can get the answer by 'inspection' BUT 'inspection' isn't some magic method that produces the answer out of nowhere - it's the result of understanding how the derivative of various composite functions looks and it comes with experience and practice
12. (Original post by davros)
You can get the answer by 'inspection' BUT 'inspection' isn't some magic method that produces the answer out of nowhere - it's the result of understanding how the derivative of various composite functions looks and it comes with experience and practice
Ah okay thanks! I've come across another Q in that same exercise: y = e^sinx

This is my method:

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13. (Original post by ps1265A)
Ah okay thanks! I've come across another Q in that same exercise: y = e^sinx

This is my method:

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That is totally incorrect

When you differentiate or integrate e^f(x) you do not introduce powers

The differential of e^sinx is cosx e^sinx by the chain rule
14. did you get to the answer of your original question which was- (1/2e^(x^2) +c)?

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