logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Integrals
0 votes

Integrate the function$\frac{(\large log \; x)^2}{\large x}$

This question has appeared in model paper 2012

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • Method of substitution:
  • Given $\int f(x)dx$ can be transformed into another form by changing independent variable x to t by substituting x=g(t).
  • Consider $I=\int f(x)dx.$
  • Put x=g(t) so that $\frac{dx}{dx}=g'(t).
  • dx=g'(t)dt.
  • Thus $ I=\int f(g(t).g'(t))dt.$
Given $I=\int \frac{(log x)^2}{x}dx.$-------(1)
 
Let us substitute log x=t.
 
Differentiating on both sides we get,
 
$\frac{1}{x}dx=dt$.
 
Now substituting for log x and $\frac{1}{x}dx$ we get,
 
$I=\int t^2.dt$
 
On integrating we get,
 
$\frac{t^3}{3}+c$.
 
Substituting back for t we get,
 
$\frac{1}{3}(log|x|)^3+c$
 
Hence $\int\frac{(log x)^2}{x}dx=\frac{1}{3}(log|x|)^3+c$.

 

answered Jan 28, 2013 by sreemathi.v
edited Jan 28, 2013 by sreemathi.v
 
Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...