Math 22 Integration by Substitution and the General Power Rule

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The General Power Rule

 If  is a differentiable function of , then

Guidelines for Integration by Substitution

1.Let be a function of

2.Rewrite the integral in terms of the variable

3.Find the resulting integral in terms of

4.Rewrite the antiderivative as a function of

5.Check your answer by differentiating (optional)

Exercises 1 Find the indefinite integral


Let , so


Let , so

3) Find an equation of the function that has the given derivative and whose graph passes through the point

Let , so , so
Given passes through , so satisfy the equation .
So, , hence
Therefore, .

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