Evaluate the Integral $\int f ^ { - 1 } ( x ) d x = x f ^ { - 1 } ( x ) - \int f ( y ) d y , y = f ^ { - 1 } ( x )$

question 184

Multiple Choice

Evaluate the integral.
-Use the formula $\int f ^ { - 1 } ( x ) d x = x f ^ { - 1 } ( x ) - \int f ( y ) d y , y = f ^ { - 1 } ( x )$ to evaluate the integral. $\int \cot ^ { - 1 } x d x$

• A) \(x \cot ^ { - 1 } x - \ln \sin x + C\)
• B) \(x \cot ^ { - 1 } x + \ln \sin \left( \cot ^ { - 1 } x \right) + C\)
• C) \(x \cot ^ { - 1 } x - \ln \sin \left( \cot ^ { - 1 } x \right) + C\)
• D) \(x \cot ^ { - 1 } x - x + C\)