6_8_Student_Notes.pdf - Lesson 8 Integration of...

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Unformatted text preview: Lesson 8: Integration of Transcendental Functions Topic 6.9: Integrating Using Substitution This is a collection of all transcendental functions and their corresponding integration rules. Trigonometric Functions: sin = cos + cos = sin + tan = ln cos + csc = sec = ln sec cot ln csc + cot = ln sin + tan + + + Logarithmic and Exponential Functions: Let u be a differentiable function of x. = + = ln + = + ln Inverse Trigonometric Functions: = arcsin = +C = + 1 arctan 1 arcsec +C + Trigonometric Identities There are times you might need to rewrite or rearrange integrals involving squared terms. sin + cos =1 1 + tan cos = 2 cos cos =1 = sec cot = 1 can also be expressed as cos = can also be expressed as sin = 2 sin sin = 2 sin cos + 1 = csc EX #1: Find the following: A. 1 ln B. C. cos 1 + sin D. E. sin F. sin 2 3 cos 2 cos G. H. 5 + sin 1 EX #2: Find the definite integral: A. C. 1 sin + cos B. D. 2 1+ E. sin F. 5 EX #3: Evaluate by completing the square. A. + + 37 B. 4x EX #4: A. B. Change of Variables Challenge 1 1+ 5 +1 ...
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