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.

The substitution method is a technique for solving a system of equations. This article reviews the technique with multiple examples and some practice problems for you to try on your own.

Unit 2: Integration techniques Unit mastery: 0% Integrating with u-substitution Integrating using long division and completing the square Integrating using trigonometric identities Trigonometric …

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

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

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.

Learn AP®︎ Calculus AB—everything you need to know about limits, derivatives, and integrals to pass the AP® test.

Practice The fundamental theorem of calculus and definite integrals Get 3 of 4 questions to level up!

Yes, the limit as x->c of f (x) is f (c). This property is equivalent to the epsilon-delta definition of continuity, and it's why we can use direct substitution for most familiar functions.