Use Integration by Parts to Establish a Reduction Formula for the Integral

question 23

Multiple Choice

Use integration by parts to establish a reduction formula for the integral.
- $$\int \csc ^ { n } x d x , n \neq 1$$

• A) \(\int \csc ^ { n } x d x = \frac { - 1 } { n - 1 } \csc ^ { n - 2 } x \cot x + \frac { n - 2 } { n - 1 } \int \csc ^ { n - 2 } x d x\)
• B) \(\int \csc ^ { n } x d x = \csc ^ { n - 2 } x \cot x + ( n - 2 ) \int \csc ^ { n - 2 } x d x\)
• C) \(\int \csc ^ { n } x d x = \frac { - 1 } { n - 1 } \csc ^ { n - 2 } x \cot x - \frac { n - 1 } { n } \int \csc ^ { n - 1 } x d x\)
• D) \(\int \csc ^ { n } x d x = \frac { - 1 } { n - 1 } \csc ^ { n - 2 } x \cot x - \frac { n - 2 } { n - 1 } \int \csc ^ { n - 2 } x \cot x d x\)