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Right Screen 2 for II – A3 Example 1: x 5x 2 3 1 dx Solution: Step 1: Let u 5 x 2 1 Step 2: du 10 x dx We chose to let the expression 5 x 2 1 because it is the expression that is raised to a power not equal to one. Took the derivative of both sides of the equation found in step 1 with respect to x. Step 3: du 10 x dx Multiply both sides by dx. 3 2 Now look at your given problem x 5 x 1 dx . We know that u 5 x 2 1 so u substituting this into the given problem yields 3 x u dx Our ultimate goal is setup the problem in terms of u, this means we need to find a correct substitution for x dx. Using the expression in Step 3, we can do the following: Step 4: 1 du x dx 10 Step 5: x 5x 2 Divide both sides by 10. 3 1 1 dx u 3 du 10 Make all appropriate substitutions.