97 Section 5.2 The Natural Logarithmic Function: Integration Section 5.2 The Natural Logarithmic Function: Integration Course Number Objective: In this lesson you learned how to find the antiderivative Instructor of the natural logarithmic function. Date ln| = = u dx u du | + u C Log Rule for Integration Let be a differentiable function of u x. What you should learn 1 ln| | + = dx x C How to use the Log Rule x for Integration to integrate a rational 1 function Example 1: Find 1 . dx x ln| | + x x C 3 Example 2: Find . dx x3 2 (1/3) ln|3 + x3| C x Example 3: Find 4x x2 + 1 . dx (1/2)x2 4x + ln| | + x C If a rational function has a numerator of degree greater than or equal to that of the denominator , division may reveal a form to which you can apply the Log Rule.
Section 5.2 The Natural Logarithmic Function: Integration 97 Section 5.2 The Natural Logarithmic Function: Integration Objective: In this lesson you learned how to find the antiderivative of the natural logarithmic function. Course Number Instructor Date Log Rule for Integration Let u be a differentiable function of x. 1 dx = ln| x | + C x 1 u dx = u du = ln| u | + C What you should learn How to use the Log Rule for Integration to integrate a rational function Example 1: Find 1 dx . x x ln| x | + C Example 2: Find 2 3 x3 dx . (1/3) ln|3 x3| + C Example 3: Find x2 4x + 1 x dx . (1/2)x2 4x + ln| x | + C If a rational function has a numerator of degree greater than or equal to that of the denominator , division may reveal a form to which you can apply the Log Rule.
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