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

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

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.

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Given an integral that should be found using u-substitution, determine what u should be.

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.

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 …

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