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integrate the following integral of logx\x^2.dx on (0,infinity)

integrate the following 
 
integral of logx\x^2.dx   on (0,infinity)

Grade:

2 Answers

Arun
25763 Points
one year ago
Dear student
 
log x /x² dx
Let log x = t then x = e^t
 
Also 1/x dx = dt
 
Hence it will be
 
t e^-t dt
 
Now you can do it by product rule
Vikas TU
14149 Points
one year ago

Since you should be doing such question once you know the concept, I will skip the solution here and just give the steps.

Put logx = t

Therefore dx/x = dt and x = exp(t) Limits will change accordingly.

Now substitute all of the above in the integral.

Use method of integration by parts. (that is the u,v integral method)

You will get the integral's answer in terms of t, in which you substitute the new limits and get the answer.

Note : Answer is 1.

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