Evaluate the Integral $\int f ^ { - 1 } ( x ) d x = x f ^ { - 1 } ( x ) - \int x \left( \frac { d } { d x } f ^ { - 1 } ( x ) \right) d x$

question 458

Multiple Choice

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

• A) \(x \cot ^ { - 1 } x + \ln x + C\)
• B) \(x \cot ^ { - 1 } x + x + C\)
• C) \(x \cot ^ { - 1 } x + \ln \sqrt { x ^ { 2 } + 1 } + C\)
• D) \(x \cot ^ { - 1 } x - \ln \sqrt { x ^ { 2 } + 1 } + C\)

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