log-x-2-dx-

Question Number 15235 by arnabpapu550@gmail.com last updated on 08/Jun/17

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

Answered by liday last updated on 18/Jun/17

\int {(l o g \sqrt{x})}^{2} d x = \frac{1}{4} \int {(l o g x)}^{2} d x = \frac{1}{4} [x {(l o g x)}^{2} - \int x \cdot 2 l o g x \cdot \frac{1}{x} d x]

= \frac{1}{4} [x {(l o g x)}^{2} - 2 \int l o g x d x] = \frac{1}{4} [x {(l o g x)}^{2} - 2 (x l o g x - x)]

= \frac{x}{4} [{(l o g x)}^{2} - 2 l o g x + 2]

Commented by liday last updated on 18/Jun/17

a n d + c

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