Question

Evaluate
∫ (logₑx)/(x) ×dx

Answer 1

Answer:

as 1/x is derivative of logx

Step-by-step explanation:

the required answer is (logx)^2/2

hope it helps u..

please mark it as brainliest ANSWER and Don't forget to FOLLOW me......

Answer 2

AnsWer :

$\tt \frac{ {(log \: x) }^{2} }{2} + c.$

Solution :

We have,

$\tt\int \frac{ log \: x \: dx}{x}$

Let,

$\tt log \: x = t.$

Then,

Both sides take.

$\tt \longmapsto \frac{dt}{dx} = \frac{ log \: x }{dx}$

Integration of log x be 1/x.

$\tt \longmapsto dt = \frac{1}{x} dx$

A/Q,

$\tt \longmapsto\int \frac{ log \: x \: dx }{x}$

$\tt \longmapsto \int \: t.dt.$

$\tt \longmapsto \frac{ {t}^{2} }{2} + c.$

Putting the value of t.

$\tt \longmapsto \frac{ {(log \: x) }^{2} }{2} + c.$

$\rule{120}3$

Some information :

$\tt \bullet\int{ log \; x \: dx }= \frac{1}{x}$

$\tt \bullet\: y = x^{2} \: then, \int y dx =\frac{x^{n+1}}{n+1}+c.$