Substitution Part I I. Quiz II. Homework III. Substitution Recall that the chain rule states that (f(g(x)))' = f'(g(x))g'(x) Integrating both sides we get: int[f(g(x)]'dx = int[f'(g(x)g'(x)dx] or
Example: Calculate
Let u = x2 +1 du/dx = 2x or du = 2xdx We substitute: int[u-2 du] = -u-1 + C = (x2 +1)-1 + C Steps: 1) Find the function derivative pair (f and f') 2) Let u = f(x) 3) find du/dx and adjust for constants 4) Substitute 5) Integrate 6) Resubstitute We will try many more examples including those such as int[xsin(x2)dx] int[x sqrt(x - 2)dx]
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