Home » Ask & Discuss » Mathematics. » Integral Calculus « Back to Discussion

Integral Calculus

Blazing goIITian

Joined:	28 Apr 2009
Post:	997

10 Jul 2009 18:08:34 IST

0 People liked this

288

integrate this

None

integrate this

$\int [x-1] dx/[x+1]\sqrt{{x}^{3}+{x}^{2}+x}$

Share this article on:

Comments (3)

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

10 Jul 2009 19:06:42 IST

Like 0 people liked this

koi to batao

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

10 Jul 2009 19:11:52 IST

Like 0 people liked this

is this an integrable function?

®µD®A

Blazing goIITian

Joined: 12 Apr 2008

Posts: 2717

10 Jul 2009 20:33:09 IST

Like 3 people liked this

I will have a go.. :D

Let, $I=int rac{(x-1)dx}{(x+1)sqrt{x^3+x^2+x}}$

$=int rac{(x^2-1)dx}{(x+1)^2sqrt{x^3+x^2+x}}\\=int rac{x^2(1-1/x^2)dx}{(x^2+2x+1)sqrt{x^3+x^2+x}}$

Let,

$x+ rac{1}{x}=t\\Rightarrow (1-1/x^2)dx=dt$

Now we have,I= int rac{dt}{(t+2)sqrt{t+1}}

Let t+1=z^2 herefore dt=2z dz

so , $int rac{dt}{(t+2)sqrt{t+1}}=int rac{2z dz}{(z^2+1)sqrt{z^2}}=2int rac{dz}{z^2+1}$

$=2 an^{-1}(z)+C=2 an^{-1}(sqrt{t+1})+C=2 an^{-1}sqrt{ rac{x^2+x+1}{x}}+C$

I hope it is correct .....

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

Free Sign Up!

Preparing for IIT-JEE ?

Arihant Revision Package for IIT JEE - Books, Practice Tests + Rank Predictor

@ INR 1,995/-

For Quick Info

Find Posts by Topics

Physics.

Topics

9395

20091

3672

2186

7617

2827

2638

Mathematics.

Chemistry.

Biology

Institutes

Parents

Board

Fun Zone