5.6 U-substitution technique indef int Part I - 5.6...

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5.6Evaluating IndefiniteIntegral Using theChain rule in reverseSubstitution Methodaka U-Substitution
OutsideInsideDerivativeofInsideIntegration by SubstitutionCuFdxuuf)(')(
Integration bySubstitution1.Picku = f(x),oftenthe “inside function.”2.Compute using differentials3.Substitute to express the integral in terms ofu.4.Integrate the resulting integral.5.Substitute to get the answer in terms ofx.( )dufx dxStart with(( ))( )gf xfx dxIf() we get:( )( )uf xg u dug uC
Integration by SubstitutionEx.Consider the integral:Sub to getIntegrateBack SubstituteFinding the“u” that works well is the most complicated task in integrating using U-subInside FunctionDerivative ofInside Function32pick+5, then3uxdux dx1010uC9u du103510xCdxxx93253
IntegrateLet u = x2+ 1du = 2x dxIntegrateLet u = 5xdu = 5 dxx2122xdxdxxdu2u 22xdu2xCu33x2133Cdxx5cos5dxdu55cos5uduCusinCx5sin
Substitution and the General Power RuleWhat would you let u = in the following examples?

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