Use integration by parts to establish a reduction formula for the integral.
-$$\int \cot ^ { n } x d x , n \neq 1$$
A) $\int \cot ^ { n } x d x = \frac { - 1 } { n - 1 } \cot ^ { n - 1 } x - \int \cot ^ { n - 2 } x d x$
B) $\int \cot ^ { n } x d x = \frac { - 1 } { n - 1 } \cot ^ { n - 2 } x - \int \cot ^ { n - 1 } x d x$
C) $\int \cot ^ { n } x d x = \frac { 1 } { n - 1 } \cot ^ { n - 1 } x + \int \cot ^ { n - 1 } x d x$
D) $\int \cot ^ { n } x d x = - \cot ^ { n - 1 } x + \frac { 1 } { n - 1 } \int \cot ^ { n - 2 } x d x$

Question

Quizplus · Accepted Answer

To derive the reduction formula for $\int \cot^n x dx$, we use integration by parts, letting $u = \cot^{n-1} x$ and $dv = \cot x dx$. This leads to the formula $\int \cot^n x dx = \frac{-1}{n-1} \cot^{n-1} x - \int \cot^{n-2} x dx$, which matches choice A.

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