If int(dx)/(x^2+a x+1)=f(g(x))+c , then ...

If `int(dx)/(x^2+a x+1)=f(g(x))+c ,` then `f(x)` is inverse trigonometric function for `|a|>2` `f(x)` is logarithmic function for `|a|<2` `g(x)` is quadratic function for `|a|>2` `g(x)` is rational function for `|a|<2`

`f(x)` is inverse trigonometric function for `|a| lt 2`

`f(x)` is logarithmic function for `|a| gt 2`

`g(x)` is quadratic function for `|a| lt 2`

`g(x)` is rational function for `|a| gt 2`

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The correct Answer is:

A, B, D

`int(dx)/(x^(2)+ax+1)=int(dx)/((x+(a)/(2))^(2)+(1-(a^(2))/(4)))`

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