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Algebra

Blazing goIITian

Joined:	23 Jun 2009
Post:	448

7 Mar 2010 20:52:42 IST

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integrate x/Sqrt[x^4+a^2]

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integrate x/Sqrt[x^4+a^2]

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aal izz well

Blazing goIITian

Joined: 6 Jun 2009

Posts: 409

8 Mar 2010 10:24:44 IST

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let x^2=a^2 tan@.....differtentiating.......2x dx=a^2 sec^2 @

so we hve........in numerator substitute x dx by a^2 sec^2@

and in denominator x^4 by a^4 tan^2@

solving u'll get a simplified form as integration of {a sec@ / 2}

a/2 is a constant ...so we simply hve to do integration of sec@ which is log(sec@+tan@)

from initial line we hve tan@=x^2 /a^2

and sec@ can be calculated from tan@...

hence u get ur answer......

aqswdefr

Hot goIITian

Joined: 11 Oct 2008

Posts: 175

8 Mar 2010 13:46:38 IST

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u=x^2 ====> du=2xdx

I=1/2 int.1/sqrt(u^2+a^2 ) du

=1/2 ln|u+ sqrt(u^2+ a^2 ) + c

FORESTS

Blazing goIITian

Joined: 23 Jun 2009

Posts: 448

8 Mar 2010 22:05:00 IST

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you both are correct and have a salute from me

krishna chaitanya

Hot goIITian

Joined: 15 Jan 2010

Posts: 139

9 Mar 2010 06:52:58 IST

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http://integrals.wolfram.com/index.jsp

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