I=∫(I)log x(II)1x^2dx By integration by parts, I=log x( 1x) ∫1x·( 1x)dx= 1xlog x+∫1x^2dx . I= 1xlog x 1x+C . ...

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Integration by Parts

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Question

Integrate $\int \frac{log x}{x^{2}} d x$

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Solution

$I = \int l o g x (I) \frac{1}{x^{2}} (I I) d x$
By integration by parts,
$I = l o g x (\frac{- 1}{x}) - \int \frac{1}{x} \cdot (\frac{- 1}{x}) d x = \frac{- 1}{x} l o g x + \int \frac{1}{x^{2}} d x$ .
$I = \frac{- 1}{x} l o g x \frac{- 1}{x} + C$ .

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