Substitution Example

Let's make a substitution.

We call this reward substitution.

Well, let's just make a substitution.

So let's make a substitution here.

Can we do something like reward substitution?

But our fantasies of substitution have cost us.

Okay, here's my solution to the 3rd substitution.

So we can start from either substitution rule.

And there's only 1 substitution rule for word.

So here, the substitution is pretty clear, right?

But we said n this substitution comes into this.

So let's make a substitution for y over x.

Now what's this situation? It's not exactly reward substitution.

So now, we can do the substitution with v.

So what we can do is we can do substitution.

But it's a quick substitution, and it saves us some time.

Then I can make a variable substitution that makes it separable.

I'm going to make 1 substitution. That's what I'm doing here.

So what is our integral going to become with this substitution?

Test

Test

Test...

Test

Test

The first is test, re test.

We made the substitution that v is equal to y over x.

And, finally, test and test it again.

And that variable substitution allows this equation to turn into a separable one.

But we're making this substitution that v is equal to y over x.

Let's go back to out original integral before we even made our substitution.

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