Henry Reed

Integration by Parts

Today, we shall integrate by parts. Yesterday
We integrated by substitution. And tomorrow
We shall differentiate under the integral sign. But today,
Today we shall integrate by parts. Buddleia
In the park is demonstrating its effect on butterflies,
	And today we shall integrate by parts.

This is the integral sign. And this here
Is the hard part, which as you will see
We can handle with this trick. And this is the easy part,
Which in your case you think you have not got. Bronzed girls
In bikinis are sprawled on the grass at their ease,
	Which in your case you have not got.

This is a product of functions, which is differentiated
With a simple formula. And please bear in mind
That an integral sign is needed for every “dx”; this is an easy matter
Understandable even by an engineer. The sunshine
Glistens on butterflies and flowers, and the bodies of the girls,
	None of whom bears in mind an integral sign.

And here is the gist of the idea. The point of this trick
Is to do the easy part twice, and so to avoid
Having to do the hard part at all. We call this
Pretty damned clever. But out in the park
Girls are doing the easy part over and over again,
	Avoiding the hard parts entirely.

Avoiding the hard part entirely; it is perfectly easy
If you bear in mind that an integral sign is needed for every “dx”,
And the idea, and the formula, and some mathematical nous
Which in your case you have not got; and the girls
On the grass are doing the easy part over and over again,
	While today we shall integrate by parts.

Henry Reed (1914-1986) was a poet, radio playwright and translator; he also wrote parodies - which makes him, in a sense, fair game. Much his best-known poem is Naming of Parts.  I did not realise until I had finished this parody that Naming of Parts is part of a sequence called Lessons of War. There's an excellent site where you can read the full text of it, and a hear a reading featuring the poet himself.

I have to confess to a mathematical upbringing. "Integration by parts" is a standard technique in the calculus, which I think I learnt as part of the "A" level syllabus. Engineers and certain other species of infidel are quite happy for symbols like "dx" to float around on their own, but proper mathematicians are never comfortable unless there is an integral sign nearby (that long stretched "S" thing). If you don't know what I'm talking about and wish you did, have a quick look here. 

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© Bob Newman 2006. All rights reserved.

This page last updated 01/09/2006