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.

When I try to integrate ln (sqrt (1+x)) it's much harder because there is integral by parts and then a weird substitution inside it which I don't understand. Could I please get a fully explained …

Video transcript - [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 …

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.

So this one is faster. It's simpler. And over time, you might even start being able to do this in your head. This top one, you still didn't mess up by just setting u equal to sine of 5x, we just have to …

Before diving into our practice exercise, gain some risk-free experience performing 𝘶-substitution.

A common challenge when performing 𝘶-substitution is to realize which part should be our 𝘶.

In math, just like in music, there are rules, but it is the creative use of the rules that produces beauty. U-sub and other methods to transform expressions into an integrable form is a skill …

Using 𝘶-substitution in a situation that is a bit different than "classic" 𝘶-substitution. In this case, the substitution helps us take a hairy expression and make it easier to expand and integrate.