Integration by parts

You misunderstood me. It was a just a caution for the OP.

...

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?

I don't understand how k=1 can even arise by accident.

First and foremost-use the LIATE/ILATE rule to decide which is u and which is v.

Then-

I=int. e^3x sin 2x dx
=sin 2x int e^3x dx - int ( d(sin 2x)/dx . int e^3x dx ) dx
= 1/3 e^3x sin 2x - int( d(sin 2x)/dx . int e^3x dx)) dx
= 1/3 e^3x sin 2x - int(2 cos 2x . 1/3 e^3x) dx
= 1/3 e^3x sin 2x - 2/3 int(cos 2x e^3x) dx
= 1/3 e^3x sin 2x - 2/3 [ 1/3 e^3x cos 2x - int { d(cos 2x)/dx . int (e^3x) dx} dx ]
= 1/3 e^3x sin 2x - 2/3 [ 1/3 e^3x cos 2x - int { (-2 sin 2x) . 1/3 e^3x}dx ]
= 1/3 e^3x sin 2x - 2/3 [1/3 e^3x cos 2x + 2/3 int(sin 2x e^3x) dx]
= 1/3 e^3x sin 2x - 2/9 e^3x cos 2x - 4/9 I

Therefore,
13/9 I = 1/3 e^3x sin 2x - 2/9 e^3x cos 2x

I= 9/13 [1/3 e^3x sin 2x - 2/9 e^3x cos 2x] + k


..typing that was tough, so I'm sorry if I made any typing errors, but this is the sum.


EDIT: I just typed that whole thing out on my cell phone - how can someone neg me?!

Probably because you just gave out a full solution, which is frowned upon.

Wow, we really learn new things every day.

1) Don't try to help someone. I didn't know I wasn't supposed to give the 'full solution' - I thought that if someone is not quite understanding vague explanations, a solution would help that person to solve similar sums in the future.

2) People around here just think it's fun to give someone -ve rating. At least I did something to help. Most people just give half-hearted answers and don't give crap if OP actually understood the Hebrew.

Wow, we really learn new things every day.

1) Don't try to help someone. I didn't know I wasn't supposed to give the 'full solution' - I thought that if someone is not quite understanding vague explanations, a solution would help that person to solve similar sums in the future.

2) People around here just think it's fun to give someone -ve rating. At least I did something to help. Most people just give half-hearted answers and don't give crap if OP actually understood the Hebrew.

I'm afraid that's not how we do things on here. Maybe take a read of this first.

It's helpful but for a problem like this one, giving the seed for thought rather than the answer is far more useful. It's a strange application of integration by parts and it would be quite a bit more helpful if the OP evaluated it with a push.

Secondly, I think you're being disrespectful to those who do give good help on here.

I'm afraid that's not how we do things on here. Maybe take a read of this first.

It's helpful but for a problem like this one, giving the seed for thought rather than the answer is far more useful. It's a strange application of integration by parts and it would be quite a bit more helpful if the OP evaluated it with a push.

Secondly, I think you're being disrespectful to those who do give good help on here.

I hadn't read that before, so I didn't realize that I shouldn't have posted the solution. At the same time, if words weren't able to explain, only the solution can. I posted the solution because of the post that I quoted before it.

Secondly, I did not mean to sound disrespectful to people who give good help. I didn't say that everyone posts randomly. It was said only because it would have been more polite to just inform me nicely that posting solutions isn't the right way to go instead if giving negative rating.

given the integral

$\displaystyle\int e^{3x}\sin(2x)\;dx$

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

This forum is not as helpful as it used to be. A few year's ago there was a race to provide help and then someone decided that being helpful was not the 'thing'. The number of people using this forum has consequently declined. I think it is called negative growth.

Perhaps instead of continuing this discussion about Study Help forum etiquette, the good 'ld days etc, we should ask the OP the slightly more helpful question:

Do you understand how to evaluate integrals that seem to lead you round in circles now?

If yes, the method used to get there doesn't particularly matter. The "Don't give full solutions", while a good general guideline is circumventable (imo) in the case where the OP is the kind of person that Plato has always seemed to me - that is, the sort who actually want to understand and not just get the answer.

On the other hand, If no, then we should probably be endeavouring to explain it further.

People around here just think it's fun to give someone -ve rating. At least I did something to help. Most people just give half-hearted answers and don't give crap if OP actually understood the Hebrew.

Couldn't possibly agree more! I once gave a partial solution to an integral problem after many clueless replies before me, and the post ended getting censored by a section mod (I deleted it then). From that time, I avoid this section (except for today, of course). The rest of TSR is run rather well, but this section is run horribly for some odd reason, which gave it probably the worst quality of any maths forum across the net.

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

$\displaystyle\int e^{3x}\sin(2x) dx = \Im \left(\displaystyle\int e^{(3+2i)x} dx \right)$,

and find that imaginary part.

x

He wouldn't get the marks. That is further maths, he can only use IBP in Core3 and 4.

He wouldn't get the marks. That is further maths, he can only use IBP in Core3 and 4.