# AP Calc - U-Substitution_ Applying Procedures for Integrals.pdf

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© 2017 College Board Page 1 Inner and Outer Functions In each of the following indefinite integrals, some part of the integrand involves a composition of functions of the form ( ( ))f g x. In each case, identify the “outside function”, ( )f x, and the “inside function”, ( )g x, by completing the second and third columns below. Integral Outside function ()f xInside function ()g xExample: ()+4231xxdx4x+31x1. +++22551xdxxx2. ()+31dxxx3. ()()+++3 434227xxxxdx4. +4xdxx5. ()+9321xxdx
© 2017 College Board Page 2 Applying Procedures for U-Substitution The table below gives the same indefinite integrals from the Introductory Activity. This time, let uequal the inside function identified before, determine its differential du, and then use this substitution to construct an equivalent integral in terms of uand duonly. Integral Inside function uduIntegral in terms of uExample: ()+4231xxdx=31ux=23dux dx1.