Derive the integral for 1/1 + x2

We need to evaluate the integral of 1/(1+x2)

Solution

Let us assume that

I=\(\int \frac{1}{1+x^{2}}\)

Substitute x= tan u

dx=sec2udu

u = arctan x———-(i)

So

I= \(\int 1/ 1 + tan^{2}u . sec^{2}u du\)

= \(\int 1/sec^{2}u . sec^{2}u du\)

=\(\int 1.du\)

=u

= arctan x (from (i))

So the integral of 1/(1+x2) is arc tanx

Was this answer helpful?

  
   

0 (0)

Upvote (0)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class

Ask
Question