$\smallint \,\,\frac{1}{{x\;}}\,\,\left( {{{\log }_{ex}}\,\,e} \right)\,\,dx$ is equal to

${\log _e}\,\,({\log _e}\,\,ex\,\, - \,\,1)\,\, + \,\,c$

${\log _e}\,\,({\log _e}\,\,x\,\, - \,\,1)\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{1}{{x\;}}\,\,\left( {{{\log }_{ex}}\,\,e} \right)\,\,dx

is equal to

View answer and explanation

Correct option: D

{\log _e}\,\,(1\,\, + \,\,{\log _e}\,\,x)\,\, + \,\,c

Option D (

{\log _e}\,(1\, + \,{\log _e}\,x)\, + \,c

) is correct because after substituting

{\log _e}x = t

, the integral becomes a simple logarithmic form.