In this tutorial we shall now discuss integral of cosecant cubed of , and this integration can be evaluated by using integration by parts. But first break the power of function from cube into square and one power of the function then we can use integration by parts of that function, because we know that formula for integration cosecant square of from pervious tutorials.
The integral of cosecant cubed of is of the form
First break the power of function into and , now the integral (i) becomes
Considering and as first and second functions respectively from integration by parts, we have
Using formula for integration by parts, we have
Equation (ii) becomes using above formula, we have
Now using trigonometric identity , we have
But from our original problem , putting this value, we have