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

Alright, I really wanted to see the difference in bounds graphically, and this is nice. However, I am confused. If (u^3)(du) = 2x(x^2+1) dx, then how are the graphs different? I t

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

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 …

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. …

So let's just start with an example here, so let's say we wanna take the indefinite integral of two x plus one times the square root of x squared plus x, dx, does u substitution apply here and if it …

Doing u-substitution with ln(x)

Integrating with u-substitution Learn 𝘶-substitution intro 𝘶-substitution: multiplying by a constant