logo

Ask Questions, Get Answers

X
 
Home  >>  CBSE XII  >>  Math  >>  Integrals

Integrate the function\[\frac{e^{5logx}-e^{4logx}}{e^{3logx}-e^{2logx}}\]

$\begin{array}{1 1}\frac{x^3}{3} + c \\ \frac{x^5}{5}+c \\ \frac{x^4}{4} +c \\ \frac{x^2}{2}+c \end{array} $

1 Answer

Toolbox:
  • (i)$e^{log x}=x$
  • (ii)$alogx=logx^a$
  • (iii)$\int x^ndx=\frac{x^{n+1}}{n+1}+c$
Given $\Large\frac{e^{5logx}-e^{4logx}}{e^{3logx}-e^{2logx}}$
 
But $alogx=logx^a$
 
Hence $\Large\frac{e^{logx^5}-e^{logx^4}}{e^{logx^3}-e^{logx^2}}dx$
 
But $e^{log x}=x$
 
Therefore $ I=\large\frac{x^5-x^4}{x^3-x^2}$$dx$
 
Taking the common factors,
 
$\int \large \frac{x^4(x-1)}{x^2(x-1)}dx$
 
$=\int \frac{x^4}{x^2}dx=\int x^2dx$
 
On integrating we get,
 
$ \large\frac{x^3}{3}+c$
answered Feb 15, 2013 by meena.p
edited Apr 11, 2016 by meena.p
 
Download clay6 mobile appDownload clay6 mobile app
...
X