5.7 Inverse Trigonometric Functions: Integration

Integrals involving inverse trig functions – Let u be a differentiable function of x, and let a > 0.

1. 2 2

arcsindu u

Caa u

2. 2 2

1arctan

du uC

a u a a

3. 2 2

1sec

uduarc Ca au u a

Why are there only three integrals and not six?

Examples: Find the integral.

1. 21 4

dx

x

2. 2

12

1 9dx

x

3.

2

1

4 3dx

x

4. 4

1

4dx

x x

5. 2

sin

7 cos

xdxx

6. 2

4 3

1

xdx

x

7.

2

2

1 4

xdx

x

Examples: Evaluate the integral.

1. 1

20 4

dx

x

2. 3

23

6

9dx

x

3. 4

21

1

16 5dx

x x