What we're going to do in this video is get some practice applying u substitution to definite integrals. So let's say we have the integral. So we're gonna go from x equals one to x equals two, and the integral is two x times x squared plus one to the third power dx. So I already told you that we're gonna apply u substitution, but it's interesting to be able to recognize when to use it. And the key giveaway here is, well I have this x squared plus one business to the third power, but then I also have the derivative of x squared plus one, which is two x right over here. So I could do the substitution. I could say u is equal to x squared plus one, in which case the derivative of u with respect to x is just two x plus zero, or just two x. I could write that in differential form.