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# Indefinite Integrals

# Leibniz (Fraction) Notation

To do integration by substitution using Leibniz notation, we think of the derivative function as a fraction of infinitesimally small quantities *du* and *dx*. We change variables by manipulating these infinitesimal quantities.

The general strategy is pretty much the same as before:

- Change variables (substitute in
*u*for some function of*x*). - Integrate.
- Put the original variable back (substitute the function of
*x*back in for*u*).