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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`

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Knowledge Check

  • int [f(x)g"(x) - f"(x)g(x)]dx is

    A
    f/g'
    B
    f'g - fg'
    C
    fg' - f'g
    D
    None of these

  • If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

    A
    g(x)(f(x) + f'(x)) + c
    B
    g(x)(f(x) - f'(x)) + c
    C
    g(x)(f(x) f'(x)) + c
    D
    None of these

  • For the function f(x)=2x^2-In|x|

    A
    set of critical points is `{0,1//2}`
    B
    f(x) is increasing in `(-oo-1//2)uu[0,1//2]`
    C
    f(x) is decreasing in `(-1//2,0)uu[1//2,oo)`
    D
    none of the above

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