The problem I would have with the notation

\(
\int dx 2x^3
\)

Is that identifying the integrand becomes problematic and ambiguous. For instance, it would not be hard to construct a problem for which the solution worked out to be

\(
\( \int 2 dx \) \(x^3 \)
\)

Which they would then write as

\(
\( \int dx 2 \) \(x^3 \)
\)

and since they would probably leave off the parens, might easily write it as

\(
\int dx 2x^3
\)

A more likely case would be something like

\(
\int \( 2x^2 + 3 \) dx
\)

which they might write as

\(
\int dx 2x^2 + 3
\)

But now we don't know if the 3 is part of the integrand or not.

If they use a rule that the integration operator is applied to the next factor, then the ambiguity goes away because they would need to write it as

\(
\int dx \( 2x^2 + 3 \)
\)

But the question is -- would they.

We see all the time where people write

\(
\int 2x^2 + 3 dx
\)

which would properly parse as

\(
\( \int 2x^2 \) + \( 3 dx \)
\)

So it can be argued either way. Using the integral as a single unary prefix operator may make it more likely that people will properly delimit the integrand (since they have no choice) whereas using the integral sign and the differential as the delimiters for the integral make it more likely that you can figure out what was intended even with the write is sloppy with properly delimiting the integrand.

I prefer to use the integral and differential to delimit the integrand AND to properly integrate it one its own, too. But then, as a pilot, I believe in backup systems.

Hi,

My guess is that if they have a problem like:
Integral 2*x^3 dx +3*x

they would write it as:
3*x+Integral dx 2*x^3

leaving the integral for last.

I dont do it this way myself either as i like to use the differential 'dx' last as most people do, and that's what i always see in textbooks too.
There is a video somewhere on the web with professor Leonard Susskind (one of the leading guys on the holographic principle) using this notation and one student calling him on it, and he explains that it's just another way of writing it.
I also note that for math programs like at Wolfram we resort to programized input anyway such as:
integrate(2*x^3+3*x,x,0,3)
to integrate 2*x^3+3 for x over 0 to 3.
So that's sort of another notation too i guess. That makes it VERY clear what we want to do so like that too

There's also the implied and explicit multiplication signs that sometimes have different meaning. Sometimes 2x^3 might mean 2*x^3 or might mean (2*x)^2, and also leaving out the sign between the dx and the 2*x^3 in the integral could tell us it is not a multiplication like:
(Integral dx) *2*x^3 which would translate in regular notation to 2*x^3*Integral 1 dx, which would be much different than what we really want, so with no multiplication sign between the dx and 2 maybe that tells us we have to include the 2*x^3 as part of the integrand.
I suppose it could get more complicated with multiple integrals too, either they are part of the previous integrand or another separate integral, etc. I dont really know for sure how this works so i continue to use the more well known form with the 'dx' last

 

@MrAl @WBahn @DickCappels Guys thanks for ur responces , I have no problem with u method I'm just asking about the method used in the questio n

Hello again,

What is the source for your question, as to where it came from? I ask because no one here seems to know what kind of method they are trying to use. Maybe we are just overlooking something simple, but it might help to find out where this came from and what method they were tyring to use to get the result.