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Right Screen 4 for II – A3 Example: Find x(2 x 1)12 dx Solution: Step 1: let u 2x 1 Step 2: du 2 dx 1 du dx 2 Since we need to find a correct expression to substitute for x dx, and we can’t multiply the expression in Step 2 by x (because that is the variable that we are integrating with respect to), we need to manipulate the expression in Step 1. Step 3: u 1 2 x u 1 x 2 1 u 1 x 2 Now we can make the appropriate substitutions and solve. 12 Step 4: x (2 x 1) dx 1 (u 1) 1 du u 2 2 1 (u 1)(u )12 du 4 1 u13 u12 du 4 1 1 1 u14 u13 C 4 14 13 1 1 u14 u13 C 56 52 1 1 (2 x 1)14 (2 x 1)13 C 56 52