1. Inverse Trigonometry Integrals

2. Derivative and Antiderivatives that Deal with the Inverse Trigonometry
We know the following to be true:
This shows the following indefinite integral:
But, what if the value in the square root is not 1? Can we still use this antiderivative?

3. Derivative and Antiderivatives that Deal with the Inverse Trigonometry
Investigate the following:
This shows the following indefinite integral:
Now investigate arccos(x).

4. Derivative and Antiderivatives that Deal with the Inverse Trigonometry
Investigate the following:
This shows the following indefinite integral:
This only differs by a minus sign from arcsin(x). It will be omitted from our list.

5. Derivative and Antiderivatives that Deal with the Inverse Trigonometry
Investigate the following:
This shows the following indefinite integral:
Arccot(x) will only differs by a minus sign from this. It will be omitted from our list.

6. Integrals Involving Inverse Trigonometric Functions
If u(x) is a differentiable function and a > 0, then
Arcsec(x) is challenging to prove due to sign changes.

7. Rewrite the integral to resemble the Rule
Example 1
Evaluate:
Rewrite the integral to resemble the Rule
Use the Rule

8. Rewrite the integral to resemble the Rule
Example 2
Evaluate:
Rewrite the integral to resemble the Rule
Still missing things…

9. Manipulate the Numerator so it contains the derivative of the base.
Example 2
Evaluate:
Manipulate the Numerator so it contains the derivative of the base.
Complete the square.

10. 1980 AB Free Response 4