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

question 85

Multiple Choice

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

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

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Definitions:

Hallucinations

Perceived experiences that occur in the absence of actual sensory stimulation.

Delusions

Systematized false beliefs, often of grandeur or persecution.

ECT

Electroconvulsive Therapy, a psychiatric treatment method where seizures are electrically induced in patients to provide relief from mental disorders.

Seizure

A sudden, uncontrolled electrical disturbance in the brain that can cause changes in behavior, movements, feelings, and levels of consciousness.