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The Natural Logarithmic Function and Integration

# The Natural Logarithmic Function and Integration - Try...

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The Natural Logarithmic The Natural Logarithmic Function & Integration Function & Integration Section 5.2

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Log Rule for Integration Log Rule for Integration Let u be a differentiable function of x . 1. 2. C u du u + = ln 1 C dx x + = x ln 1
Alternative form of Log Rule Alternative form of Log Rule C u dx u u + = ln '

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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. Look at Example 5
Guidelines for Integration Guidelines for Integration Memorize a basic list of integration formulas. Find a formula that resembles all or part of the integrand, and, by trial and error, find a choice of u that will

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Unformatted text preview: Try altering the integrand by using a trig. identity, multiplication & division by the same quantity, or addition and subtraction of the same quantity. Be creative. If you have access to computer software that will find antiderivatives symbolically, use it. Integrals of the 6 Basic Trig Integrals of the 6 Basic Trig Functions Functions C u du u +-= ∫ cos sin C u du u +-= ∫ cos sin ∫ + = C u du u sin cos C u du u +-= ∫ cos ln tan C u du u + = ∫ sin ln cot C u u du u + + = ∫ tan sec ln sec C u u du u + +-= ∫ cot csc ln csc Joke Time Joke Time What’s ? Natural log cabin + sea = Houseboat ∫ cabin dcabin...
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