1.

Let f (x) be a polynomial of degree three such that f(0) = 1, f(1) = 2 and 0 is a critical point of f(x) such that f(x) does not have a local extremum at 0. Them int(f(x))/(x^(2)+1) dx is equal to

Answer»

`x-LOG(x^(2)+1)+TAN^(-1)x+C`
`x+(1//2)log(x^(2)+1)-tan^(-1)x+C`
`(1//2)x^(2)x(1//2)loga(x^(2)+1)-tan^(-1)x+C`
`(1//2)(x^(2)-log(x^(2)+1))+tan^(-1)x+C`

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