how to integrate the function

[yilmataye]

Can any one help integrating the following function

integral of 1/(1+at^2)^2 dt from positive infintiy to zero.where a is constant

Many thanks!!!

 

[arbabar]

Can any one help integrating the following function

integral of 1/(1+at^2)^2 dt from positive infintiy to zero.where a is constant

Many thanks!!!

follow the Book Calculus by thomos finney. full detail of indefinite integrals.

 

[_Eduardo_]

WolframAlpha is your friend

 

[albbg]

I can also suggest you the use of "maxima" http://maxima.sourceforge.net/
It is a very powerful symbolic math tool under GNU license. Using it I obtained the following answer to you question:

-π/(4•√a) if a≧ 0
j•π•√-a/(4•a) if a<0 (j is the complex operator)

also you can perfom the indefinite integration and see the primitive of your function.

 

[bulx]

never thought a day would come that one could answer like this!

http://integrals.wolfram.com/index.jsp?expr=1%2F%281%2Bax^2%29^2&random=false
-b

 

[_Eduardo_]

never thought a day would come that one could answer like this!

Wolfram is amazing! In addition to all information returned, show the steps! (by clicking on "Show Steps")