Integrals Yielding to Inverse Trigonometric Functions with Audio, Lecture notes of Engineering Mathematics

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Integration of

Inverse Trigonometric Functions

Review

• (^) Recall derivatives of inverse trig functions

2

1 2 1 2 1 2

1

sin , 1

1

1

tan

1

1

sec , 1

1

d du

u u

dx dx u

d du

u

dx u dx

d du

u u

dx dx u u







 







 



. If a=1, you have:



sin u C

1 u

du 1

2

 





tan u C

1 u

du 1

2





u C

u u

du 1

2

sec

Identifying Patterns

• (^) For each of the integrals below, which

inverse trig function is involved?

5

2

4

13 16

dx

 x

2

25 4

dx

x x 

2

9

dx

 x



Try These

• (^) Look for the pattern or how the expression can be

manipulated into one of the patterns

7

Completing the Square

• (^) Try these

2

2

2

dx

x x



2

dx

 x  x