If∫xlog(1+x1)dx=f(x)log(x+1)+g(x)x2+Ax+C, then (a)f(x)=21x2 (b) g(x)=logx (c)A=1 (d) none of these

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$I f \int x lo g (1 + \frac{1}{x}) d x = f (x) lo g (x + 1) + g (x) x^{2} + A x + C,$ then (a) $f (x) = \frac{1}{2} x^{2}$ (b) $g (x) = lo g x$ (c) $A = 1$ (d) none of these

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I f \int x lo g (1 + \frac{1}{x}) d x = f (x) lo g (x + 1) + g (x) x^{2} + A x + C,

then (a)

f (x) = \frac{1}{2} x^{2}

(b)

g (x) = lo g x

(c)

A = 1

(d) none of these

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Question Text

I f \int x lo g (1 + \frac{1}{x}) d x = f (x) lo g (x + 1) + g (x) x^{2} + A x + C,

then (a)

f (x) = \frac{1}{2} x^{2}

(b)

g (x) = lo g x

(c)

A = 1

(d) none of these