In this tutorial we shall explain the integration of the cosine inverse function . It is an important integral function, but it has no direct method to find it. We shall find the integration of cosine inverse by using the integration by parts method.
The integration of cosine inverse is of the form
When using integration by parts it must have at least two functions, however this has only one function: . So consider the second function as . Now the integration becomes
The first function is and the second function is .
Using the formula for integration by parts, we have
Using the formula above, equation (i) becomes
Multiplying and dividing by -2, we have
Now we can also use this integration of cosine inverse as a formula.