Key takeaway: Sometimes we need to multiply or divide the entire integral by a constant, so we can achieve the appropriate form for u -substitution without changing the value of the integral.

In these series of videos (U-substitution) you introduce the treatment of the derivative operators (dx, du, etc) as fractions. You specify that they really are not, but treat them like that anyway.

Performing u -substitution with definite integrals is very similar to how it's done with indefinite integrals, but with an added step: accounting for the limits of integration.

Finding the indefinite integral of cos (5x)/e^ [sin (5x)]. To do that, we need to perform 𝘶-substitution twice. Created by Sal Khan.

When using 𝘶-substitution in definite integrals, we must make sure we take care of the boundaries of integration.

One way to work these problems is to change the boundaries and then solve in terms of u. The other way, which Sal used here, is to treat it as an indefinite integral (no boundaries) when you do the u …

How do you do u substitution right over here? And the key when you have powers of trig functions, especially when you have one of them as an odd power, what you want to do is separate one of …

But this makes it clear that, yes, u-substitution will work over here. If we set our u equal to natural log of x, then our du is 1/x dx. Let's rewrite this integral. It's going to be equal to pi times the indefinite …

- [Tutor] What we're going to do in this video is give ourselves some practice in the first step of u substitution, which is often the most difficult for those who are first learning it and that's recognizing …

So is it typically a good strategy to choose "u" as something that either is (1) in the denominator, (2) in parenthesis, or (3) under a radical? I'm just looking for good strategies to choosing good "u" candidates.