If-x-log-1-1-x-dx-f-x-log-x-1-g-x-x-2-Ax-C-then-

Question Number 55779 by gunawan last updated on 04/Mar/19

If \int x \log (1 + \frac{1}{x}) d x

= f (x) \cdot \log (x + 1) + g (x) \cdot x^{2} + A x + C,

then

Commented by gunawan last updated on 04/Mar/19

Find A

Commented by gunawan last updated on 04/Mar/19

A =

f (x) =

g (x) =

Answered by MJS last updated on 04/Mar/19

\int x \log (1 + \frac{1}{x}) d x =

= - \frac{1}{2} \log (x + 1) + x^{2} \ln (1 + \frac{1}{x}) + \frac{x}{2} + C

(integration by parts)

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

g (x) = \ln (1 + \frac{1}{x})

A = \frac{1}{2}

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