U Substitution and Indefinite Integrals

Do you really want to multiply it all out before integrating? NO!

When you integrate a composite function, it is important that the derivative is already there so that it can "disappear" when you do the opposite of integration. This is written as or if then it would be written as

Use a substitute for the "

portion of the function. This is called -Substitution simply

because we use the letter

integrating. It makes the integration much simpler.

Then, du

U Substitution and Indefinite Integrals

U Substitution and Indefinite Integrals

*You can introduce a constant as long as you do it in such a way that the problem remains the same; you CANNOT introduce a variable (like multiplying and dividing by x).

U Substitution and Indefinite Integrals

U Substitution and Indefinite Integrals

U Substitution and Indefinite Integrals

U Substitution and Indefinite Integrals

*Be sure to pay attention to the form of , which would imply the use

of the Log Rule to integrate versus the form of , where n is a

negative number other than 1 and thus the general Power Rule is used.

U Substitution and Indefinite Integrals

U Substitution and Indefinite Integrals