Ask Questions, Get Answers

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

Integrate the function $\large \frac {\log^{99} x}{x}$

Can you answer this question?

1 Answer

0 votes
  • 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 $\large\frac{dx}{dx}=g'(t).$
  • dx=g'(t)dt.
  • Thus $ I=\int f(g(t).g'(t))dt.$
Given $I=\int \frac{(log x)^{99}}{x}dx.$-------(1)
Let us substitute log x=t.
Differentiating on both sides we get,
Now substituting for log x and $\frac{1}{x}dx$ we get,
$I=\int t^{99}.dt$
On integrating we get,
Substituting back for t we get,
Hence $\int\frac{(log x)^2}{x}dx=\frac{1}{100}(log|x|)^{100}+c$.
answered Dec 24, 2013 by balaji.thirumalai
edited Jan 31, 2014 by yamini.v
Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App