qanda-logo
search-icon
Symbol

Calculator search results

Find the integral value
Answer
circle-check-icon
expand-arrow-icon
$\dfrac {(\ln{\left( x \right)}) ^ {2}} {2} + C$
using substitution
$\color{#FF6800}{\int \dfrac {\ln{\left( x \right)}} {x}dx}$
$ $ Substitute $ t = \ln{\left( x \right)} $ to simplify integral calculation $ $
$\color{#FF6800}{\int tdt}$
$\color{#FF6800}{\int tdt}$
$ $ Using $ \int xdx = \dfrac {x ^ {2}} {2} $ , calculate the integral $ $
$\color{#FF6800}{\dfrac {t ^ {2}} {2}}$
$\dfrac {\color{#FF6800}{t} ^ {2}} {2}$
$ $ Change the substituted $ t = \ln{\left( x \right)} $ again $ $
$\dfrac {(\color{#FF6800}{\ln}{\left( \color{#FF6800}{x} \right)}) ^ {2}} {2}$
$\color{#FF6800}{\dfrac {(\ln{\left( x \right)}) ^ {2}} {2}}$
$ $ Add integral constant $ C \in ℝ $ $ $
$\color{#FF6800}{\dfrac {(\ln{\left( x \right)}) ^ {2}} {2} + C}$
Solution search results
Have you found the solution you wanted?
Try again
Try more features at Qanda!
check-iconSearch by problem image
check-iconAsk 1:1 question to TOP class teachers
check-iconAI recommend problems and video lecture