Let's just worry about the indefinite integral.

The indefinite...indefinite... indefinite integral of 2X which is another way of just saying the antiderivative of 2X.

Let's just focus on the indefinite integral for now.

And when you do the integration by parts, this could be an indefinite integral, an improper integral, a definite integral, whatever.

I won't switch back and forth between the definite and indefinite integral.

Then I want to subtract the indefinite integral of f prime of x.

This is essentially just this is the indefinite integral of x squared plus 1.

And we're assuming we're doing the indefinite integral, and we'll evaluate the boundaries later.

And, this notation right over here, this whole expression, is called the indefinite integral.

Indefinite

Indefinite time

Integral

Integral step

Show integral

Integral step

So we'll have a minus a squared over s squared, times the integral from 0 well, I said I'm just worrying about the indefinite integral right now, and we'll evaluate the boundaries later. e to the minus st, sine of at, dt.

The union went out on a strike for an indefinite period.

And that's taking the integral.

Set here the spatial integral step.

Anyway, integral from 0 to infinity.

Minus this integral evaluated at 0.

That's what that double integral represents.

And what's the integral of this?

Let's now do another triple integral, and in this one I won't actually evaluate the triple integral.

So anyway, let's take the anti derivative and evaluate this improper definite integral, or this improper integral.

The integral of u prime times v.

And this is a definite integral, right?

And that's where the integral comes in.

So what's the integral of this thing?

Let's try to set up this integral.

That's the intuition behind the definite integral.

So how do we evaluate this integral?

I'll just use that old integral sign.

What happens if I take the integral?

Let me write a nicer integral sign.

Because the t's are involved in evaluating the boundaries, since we're doing our definite integral or improper integral.

The thought of having this planted on me for an indefinite period appalled me.

So we can rewrite this integral as y.

So what's this integral going to look like?

Generally speaking, this integral cannot be solved analytically.

They're an integral part of the penile skeleton.

I give you an integral factor of 0.004.

How do I take the integral of that?

The integral of 1 is y, the integral of y squared, well that's minus y to the third over 3.

So if we take from zero to infinity, what I'm saying is taking this integral is equivalent to taking this integral.