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

Integral Calculus

Cool goIITian

Joined:	13 Feb 2009
Post:	43

30 Nov 2009 20:34:33 IST

0 People liked this

948

int x^2 / ( xsinx+cosx)^2

None

int x^2 / ( xsinx+cosx)^2

Share this article on:

Comments (2)

kabi

Blazing goIITian

Joined: 11 Jan 2009

Posts: 575

2 Dec 2009 13:04:11 IST

Like 1 people liked this

i have 2 method

1st method

I = integration ( x sec(x) x cos(x)/(xsinx +cos(x))² dx

integration by parts

=x sec(x) int ( xcosx /(xsinx +cos(x))² dx) - int [ ( xsecxtanx+secx) int (xsinx +cos(x))² ]dx

= -xsecx / ( xsinx+cosx) + int (sec^2x)dx

= -xsecx / ( xsinx+cosx) +tanx +c

thank u

kabi

Blazing goIITian

Joined: 11 Jan 2009

Posts: 575

2 Dec 2009 13:04:27 IST

Like 1 people liked this

well

2 nd method This way is my way to solve this

look

(x sin(x)+cos(x) ) = Sqrt(1 +x² ) cos( x -tan^-1(x))

so ur question become

int ( x² sec² (x -tan^-1x ))/(1+x²) dx

put x-tan^(-1)x = t

x²/(1+x²)dx =dt

= int sec^2 t dt

= tan (x -tan^-1(x)) +C

thank u

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