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.

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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.

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

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.

The key to it is to just play around a little bit with trigonometric identities so that you can get the integral to a point that you can use the reverse chain rule or you can use U substitution, which …

- [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 …

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 …

Limits of combined functions: products and quotients Conclusions from direct substitution (finding limits) Next steps after indeterminate form (finding limits)

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.