If $\int \frac{dx}{(x^2 - 2x + 10)^2} = A \left( \tan^{-1} \left( \frac{x-1}{3} \right) + \frac{f(x)}{x^2 - 2x + 10} \right) + C,$ …

Mathematics

Problem

\int \frac{dx}{(x^2 - 2x + 10)^2} = A \left( \tan^{-1} \left( \frac{x-1}{3} \right) + \frac{f(x)}{x^2 - 2x + 10} \right) + C,

where

C

is a constant of integration, then (a)

A = \frac{1}{54}

and

f(x) = 3(x-1)

(b)

A = \frac{1}{27}

and

f(x) = 9(x-1)

(c)

A = \frac{1}{81}

and

f(x) = 3(x-1)

(d)

A = \frac{1}{54}

and

f(x) = 9(x-1)^2