A tribute to one of my favorite integrals:

To find the integral of secant squared is not a mighty deed,
But when it comes to secant cubed, well, that’s another tale indeed.
Should you make a substitution of the u and du kind?
How ‘bout trying a half-angle rule to save you from this bind?
The beginning of the answer we hold deep within our hearts:
Good ole’ u dv’s the ticket. Integration – yes, by parts!
Now the question is upon us: What is u and what’s dv?
We’ve an acronym for this – it goes L.I.A.T.E.
We can see that a trig function is the thing we’ll set as u,
But this doesn’t solve our problem; we’ve got choices, yes a few.
If u is just a secant, we know du pretty quick.
And with dv secant squared, v as tangent does the trick.
Now our problem’s looking messy: secant tangent minus more.
Secant tangent squared’s the integrand – this is quite a chore!
An identity is apropos – the tangent squared’s a drag.
One less secant squared will do the job and this one’s in the bag.
We consider now the difference – split it up and feast your eyes,
On the integral of secant and – What’s this? – A nice surprise!
It’s the integral of secant cubed; we’re back where we began!
But you needn’t sound so desparate; we can solve for this, we can!
For now we’ve an equation in the thing we’re looking for.
Just add it to both sides and we’ve got one remaining chore.
There’s the issue of the secant that we need to integrate.
That deserves another poem, but for now you’ll have to wait.
It’s in all the basic tables. Find it quickly if you can!
Ah, forget it, I’ll just tell you – log of secant plus a tan.
So there it is, we’ve laid it out. We’ve done it, me and you.
Sec tan plus the log of secant plus a tangent…over two.