log-x-x-2-dx-

Question Number 93481 by mashallah last updated on 13/May/20

\int (\log x / x^{2}) dx =

Commented by abdomathmax last updated on 15/May/20

I = \int \frac{l n x}{x^{2}} d x b y p a r t s

I = - \frac{l n x}{x} - \int (- \frac{1}{x}) \times \frac{d x}{x} = - \frac{l n x}{x} + \int \frac{d x}{x^{2}}

= - \frac{l n x}{x} - \frac{1}{x} + C = - \frac{1 + l n x}{x} + C

Answered by john santu last updated on 13/May/20

\int \frac{\ln x}{x^{2}} dx = \int \ln (x) . x^{- 2} dx = W

[by parts]

u = \ln (x) \Rightarrow du = \frac{dx}{x}

v = \int x^{- 2} dx = - x^{- 1}

W = - x^{- 1} \ln (x) + \int x^{- 1} . \frac{dx}{x}

W = - \frac{\ln (x)}{x} - \frac{1}{x} + c

W = - \frac{\ln (x) + 1}{x} + c