Question

log x-1/(log x)² ,Integrate the given function defined on proper domain w.r.t. x.

Answer 1

HELLO DEAR,


YOUR QUESTIONS IS-------------- 1/logx - 1/(logx)² , Integrate the given function defined on proper domain w.r.t. x.


NOW, $\bold{\int[1/logx - 1/(logx)^2]\,dx}$

put logx = t
=> x = e^t
=> dx = e^t.dt

so, $\bold{\int[1/t - 1/t^2]e^t.dt}$

we know if the integral is in the form of e^x[f(x) + f'(x)] so, your integral is e^xf(x) + c

therefore,
$\bold{I = e^t*1/t + C}$

put the value of t in the equation

$\bold{I = x/logx + c}$



I HOPE ITS HELP YOU DEAR,
THANKS