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 functions\[\frac{x^2}{\sqrt{x^6+a^6}}\]

$\begin{array}{1 1} \frac{1}{3}\log\mid x^3+\sqrt{x^6+a^6}\mid+c. \\ \frac{1}{3}\log\mid x^6+\sqrt{x^6+a^6}\mid+c. \\ \frac{1}{6}\log\mid x^3+\sqrt{x^6+a^6}\mid+c. \\ \frac{1}{6}\log\mid x^6+\sqrt{x^6+a^6}\mid+c. \end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $\int\frac{dx}{\sqrt{x^2+a^2}}=\int log\mid x+\sqrt{x^2+a^2}\mid+c.$
Given:$I=\int\frac{x^2}{\sqrt{x^6+a^6}}dx.$
Put $x^3=t.$
 
On differentiating we get,
 
$x^2dx=dt.\Rightarrow x^2dx=\frac{dt}{3}.$
 
Substituting this we get,
 
$I=\frac{1}{3}\int\frac{dt}{\sqrt {t^2+(a^3)^2}}$.
 
On integrating we get,
 
$\;\;\;=\frac{1}{3}[log\mid t+\sqrt{t^2+(a^3)^2}+c.$
 
But $(a^3)^2=a^6.$
 
$\;\;\;=\frac{1}{3}log\mid t+\sqrt{t^2+a^6}\mid+c.$
 
Substituting for t we get,
 
$\;\;\;=\frac{1}{3}log\mid x^3+\sqrt{x^6+a^6}\mid+c.$

 

answered Feb 4, 2013 by sreemathi.v
edited Feb 4, 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
...