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.
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:
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
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