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

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