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# Integration by parts watch

1. given the integral

presumably you use integration by parts, but which bit do I call v and which bit du/dx ?

Actually in general, what's the strategy for deciding which bit to call what? I thought you choose the bit that differentiates to a constant to be v, but in this case, neither of them do.

Ta
2. In this instance it doesn't matter much, it's probably easier to use the trig term.

You will require two iterations, ending up with a similar integral to the one above when you try and work it out the second time.

Calling the integral I, you can then rewrite in the form I = ...
3. Call du/dx e^3x. Easier to intergrate. sin2x can be differentiated easily enough. Then just apply the rule.
4. Not sure if this will help but kinda gives an explanation!

http://www.wolframalpha.com/input/?i...29*sin%282x%29
5. (Original post by marcusmerehay)
In this instance it doesn't matter much, it's probably easier to use the trig term.

You will require two iterations, ending up with a similar integral to the one above when you try and work it out the second time.

Calling the integral I, you can then rewrite in the form I = ...
oh so I'll still have to do in in two stages then?
6. (Original post by Plato's Trousers)
given the integral

presumably you use integration by parts, but which bit do I call v and which bit du/dx ?

Actually in general, what's the strategy for deciding which bit to call what? I thought you choose the bit that differentiates to a constant to be v, but in this case, neither of them do.

Ta
Alternatively, if you want to avoid IBP you could notice that:

,

and find that imaginary part.
7. (Original post by boromir9111)
Not sure if this will help but kinda gives an explanation!

http://www.wolframalpha.com/input/?i...29*sin%282x%29
yeah, I tried Walpha, but it doesn't do it by parts. It uses some kind of general formula
8. (Original post by Farhan.Hanif93)
Alternatively, you could notice that:

,

and find that imaginary part.
um, you're joking right? (you know I won't understand that! )
9. (Original post by Plato's Trousers)
Actually in general, what's the strategy for deciding which bit to call what?
Try googling LIATE Rule, its a rule of thumb which I follow for integration by parts.
Basically you choose 'u' by what come first in the list: Logs, Inverse trig, Algebra, Trig, Exponentials
10. (Original post by Plato's Trousers)
um, you're joking right? (you know I won't understand that! )
My apologies. I thought you were doing an Open University course on it so assumed that you had met complex numbers properly by now.

Do you follow what the others have suggested?
11. http://en.wikipedia.org/wiki/Integration_by_parts

In Examples, from 'An unusual example commonly used...'
12. (Original post by Potassium^2)
Try googling LIATE Rule, its a rule of thumb which I follow for integration by parts.
Basically you choose 'u' by what come first in the list: Logs, Inverse trig, Algebra, Trig, Exponentials
that's cool! I haven't heard of that before.

(Original post by Farhan.Hanif93)
My apologies. I thought you were doing an Open University course on it so assumed that you had met complex numbers properly by now.

Do you follow what the others have suggested?
well, I know what complex numbers are, but I don't see the relevance to this.

Doing it by parts just keeps on generating new products? So I don't see how it helps.

Choosing dv/dx to be e^3x I get

which doesn't really help me, as I have still got a product to integrate. And you keep on getting a product, presumably?
13. (Original post by Plato's Trousers)
well, I know what complex numbers are, but I don't see the relevance to this.
I take it that you've never seen De Moivre's theorem before? Or the definition:

?

Doing it by parts just keeps on generating new products? So I don't see how it helps.

Choosing dv/dx to be e^3x I get

which doesn't really help me, as I have still got a product to integrate. And you keep on getting a product, presumably?
Use IBP again with and notice the integral part that emerges. It will be similar to what you started with. Therefore, if you let , you will have something of the form:

where k is a constant.
14. (Original post by Farhan.Hanif93)
Alternatively, if you want to avoid IBP you could notice that:

,

and find that imaginary part.
oh wait, yes, sorry! I see what you mean now. You're using Euler's relation. That's sneaky

It's just that you first had a Hebrew letter in place of the Im, (before you edited it). Aleph, maybe? I didn't know what that was
15. (Original post by Plato's Trousers)
oh wait, yes, sorry! I see what you mean now. You're using Euler's relation. That's sneaky

It's just that you first had a Hebrew letter in place of the Im, (before you edited it). Aleph, maybe? I didn't know what that was
Good to hear that you've got the idea.

Yeah, I don't know what happened there, slip of the finger I think.
16. (Original post by Farhan.Hanif93)
Good to hear that you've got the idea.

Yeah, I don't know what happened there, slip of the finger I think.
our posts crossed I think. You were posting about de Moivre and I was posting about Euler. I always get those mixed up, what's the difference?
17. (Original post by Farhan.Hanif93)
where k is a constant.
Which won't work if k = 1.
18. (Original post by AgeOfAquarius)
Which won't work if k = 1.
What's your point? I haven't indicated that k is 1. k isn't arbitrary and I have used an equality sign as opposed to an equivalence sign for a reason!
19. (Original post by Plato's Trousers)
our posts crossed I think. You were posting about de Moivre and I was posting about Euler. I always get those mixed up, what's the difference?
A quick google will tell you the answer to your question.
20. (Original post by Farhan.Hanif93)
What's your point? I haven't indicated that k is 1.
You misunderstood me. It was just a caution for the OP.

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