_ ^ ( x) ^2 ;dx = - Vidyadip

MCQ

$\int_{}^{} {{{(\log x)}^2}\;dx = } $

A
$x{(\log x)^2} - 2x\log x - 2x + c$
B
$x{(\log x)^2} - 2x\log x - x + c$
✓
$x{(\log x)^2} - 2x\log x + 2x + c$
D
$x{(\log x)^2} - 2x\log x + x + c$

✓

Answer

Correct option: C.

$x{(\log x)^2} - 2x\log x + 2x + c$

c
(c)$\int_{}^{} {{{(\log x)}^2}dx} $. Put $\log x = t \Rightarrow {e^t} = x \Rightarrow dx = {e^t}dt,$

then it reduces to $\int_{}^{} {{t^2}.\,{e^t}dt = {t^2}{e^t} - 2t{e^t} + 2{e^t} + c} $

$ = x{(\log x)^2} - 2x\log x + 2x + c$.

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