Nis, nis Tu, Tu, Tu...

Now, if I were to integrate both sides, I get uv this should be review is equal to the integral of u prime v, with respect to dt but I'm just doing a little bit of shorthand now plus the integral of uv prime.

The integral of u prime times v.

UV vectors

UV mapping

So the integration by parts just tells us that the integral of uv prime is equal to uv minus the integral of

The integral of u well, let's say uv prime, because that will match what we have up here better is equal to both functions without the derivitives, uv minus the integral of the opposite.

So we have this integral of u prime v is going to be equal to this, uv minus the integral of uv prime.

But we always think of one thing reproductive organs a.k.a. penises and vaginas.

So let's apply this.

So let's apply the integration by parts.

So that's minus 1 over s e to the minus st, times v, sine of at, minus the integral.

But the boundary stays.

Integration by parts. uv.

You know every season when we come to this farm, when somebody wants a can of beans, a little coffee, even some of this floor varnish for a Saturday night, they got to pay you double.

Now, if we take the integral of both sides of this equation, we get uv is equal to the antiderivative of u prime v plus the antiderivative of uv prime.

That equals uv.

We now wield the paintbrush.

Anyway, integral from 0 to infinity.

I'm just rewriting this. e to the minus st s.

It's times minus 1 s, e to the minus st. e to the minus st, that's the uv term right there.

So this Laplace transform, which is this, is equal to uv, which is equal to e to the minus st, times v, f of t, minus the integral and, of course, we're going to have to evaluate this from 0 to infinity.