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) \(\int \csc ^ { n } x d x = \frac { - 1 } { n - 1 } \csc ^ { n - 2 } x \cot x - \frac { n - 2 } { n - 1 } \int \csc ^ { n - 2 } x \cot x d x\)

---

Definitions:

Healthy Aging

The process of optimizing opportunities for physical, social, and mental well-being throughout the lifespan, especially in older age.

Coping With Pain

Strategies or methods employed by individuals to manage and alleviate pain.

Medical Costs

Expenses associated with healthcare services, including diagnosis, treatment, and prevention of disease, as well as expenditures for medications and medical devices.

Health Care

The organized provision of medical care to individuals or a community through services offered by health professionals.