logo

Ask Questions, Get Answers

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

Evaluate : $ \int\large\frac{x^2}{1+x^3}$$dx $

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 $I=\int f(x)dx.$
Step 1:
$I=\int\large\frac{x^2}{1+x^3}$$dx$
Let $1+x^3=t$
On differentiating with respect to $x$
$3x^2dx=dt$
$x^2dx=\large\frac{dt}{3}$
$I=\int \large\frac{dt/3}{1+x^3}$
$\;\;=\large\frac{1}{3}\int \large\frac{dt}{t}$
Step 2:
On integrating we get,
$\large\frac{1}{3}$$\log \mid t\mid+c$
Substituting for $t$ we get,
$I=\large\frac{1}{3}$$\log \mid 1+x^3\mid +c$
answered Sep 26, 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
...