Ask Questions, Get Answers

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

Integrate the function$\frac{\large 2x}{\large 1+x^2}$

Can you answer this question?

1 Answer

0 votes
  • $(i)\;Method \;of \;substitution:$
  • 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 $\frac{dx}{dt}=g'(t)$.
  • dx=g'(t)dt.
  • Thus $I=\int f(x)dx=\int f(g(t).g'(t))dt.$
$(ii)\;\int\frac{1}{x}dx=log x+c$.
Given $I=\int\frac{2x}{1+x^2}dx.$
Let $1+x^2=t.$
Differentiating on both sides we get,
2x dx=dt.
Substituing for $(1+x^2)$ and 2xdx we get,
$I=\int \frac{dt}{t}.$
Now integrating we get,
$I=log t+c$.
Now substituting back for t we get,
Hence $\int\frac{2x}{1+x^2}dx=log(1+x^2)+c.$


answered Jan 28, 2013 by sreemathi.v
Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App