Question

integration of (log x)*2/x​

Answer 1

ANSWER :–

GIVEN FUNCTION :–

=> ( log x )² / x

${ \bold{ \green{ \huge{ \underline{ solution} : - }}}} \\ \\ { \bold{ = \: ∫ \frac{ {(log(x))}^{2} }{x}dx }} \\ \\ \\ { \bold{put \: \: log(x) = t \: - }} \\ \\ \\ { \bold{ \implies \: \frac{1}{x}.dx =dt }} \\ \\ { \bold{ =∫ {t}^{2}dt }} \\ \\ \\ { \bold{ = \frac{ {t}^{3} }{3} + c}} \\ \\ \\ { \bold{ = \frac{ {( log(x)) }^{3} }{3} }} + c$

${ \bold{ \underline{</strong><strong> </strong><strong>\</strong><strong>huge</strong><strong>{</strong><strong> \red{used \: \: formula}}</strong><strong>}</strong><strong> : - }}</strong><strong> \\ \\ { \bold{(1) \: \frac{d( log(x) )}{dx} = \frac{1}{x} }} \\ \\ \\ { \bold{(2) \:∫ {x}^{n} dx = \frac{ {x}^{n + 1} }{n + 1} + c}}$