If $\int {{{dx} \over {{{\left( {{x^2} - 2x + 10} \right)}^2}}}} = A\left( {{{\tan }^{ - 1}}\left( {{{x - 1} \over 3}} \right) + {{f\left( x \right)} \over {{x^2} - 2x + 10}}} \right) + C$ where C is a constant of integration then :

Question

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

where C is a constant of integration then :

A =${1 \over {54}}$ and f(x) = 9(x–1)²

A =${1 \over {54}}$ and f(x) = 3(x–1)

A =${1 \over {81}}$ and f(x) = 3(x–1)

A =${1 \over {27}}$ and f(x) = 9(x–1)²

Solution

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