logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
0 votes

Integrate : $\int a^{\large a^{\Large a^{\Large a^{x}}}}.a^{\large a^{\Large a^{x}}}.a^{a^{x}}.a^{x}$$.dx$

$(a)\;\frac{a^{\large a^{\Large a^{\Large a^{x}}}}}{(\log _e a)^4}+c\qquad(b)\;\frac{a^{\large a^{\Large a^{x}}}}{(\log _e a)^4}+c\qquad(c)\;\frac{a^{\large a^{\Large a^{\Large a^{x}}}}}{(\log _e a)^2}+c\qquad (d)\;None$
Can you answer this question?
 
 

1 Answer

0 votes
$a^{\large a^{\Large a^{x}}}=t$
differentiate with x
$ a^{\large a^{\Large a^x}}.\log _e a .a^{\large a^{x}}. \log _e a. a^x. \log _ea. dx =dt$
=> $ a^{\large a^{\Large a^x}}.a^{\large a^{x}}.a^x( \log _ea)^3. dx =dt$
=> $ a^{\large a^{\Large a^x}}.a^{\large a^{x}}.a^x( \log _ea)^3. dx =dt$
=> $ a^{\large a^{\Large a^x}}.a^{\large a^{x}}.a^x. dx =\large\frac{1}{(\log _ea)^3} $$dt$
By putting values we get,
$\qquad= \int a^t \times \large\frac{1}{(\log _ea)^3}$$.dt$
$\qquad= \int a^t . \large\frac{1}{(\log _ea)^3}$$.dt$
$\qquad= \large\frac{1}{(\log _ea)^3}. \frac{at}{\log_ea}$$+c$
$\qquad= \large\frac{a^t}{\log_ea}$$+c$; again put values of t
=>$\large\frac{a^{\large a^{\Large a^{\Large a^{x}}}}}{(\log _e a)^4}+c$
Hence a is the correct answer.
answered Dec 23, 2013 by meena.p
 
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
...