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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
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