Problem in solving Integral

[claudiocamera]

Solving a problem I came across a power density function in the form S(w) = w^2/( w^2 + a^2) where "a" is given constant , I must find the Power, in order to do that, I need to solve the integral in all the frequency range which means from -∞ to + ∞:

∫ [ w^2/( w^2 + a^2)] dw = ??? I am clueness! How to solve this ? I tried by parts and by fration expansion, but apparently I made some mistake . Can anybody help ?

Thanks
Claudio

 

[v_rayalu]

\[\int \frac{w^2}{w^2+a^2} dw = \int \left( 1- \frac{a^2}{w^2+a^2} \right)dw = w - a \tan^{-1}\frac{w}{a}\]

Hope this helps

Venkat

 

[hr_rezaee]

Hi
in matlab:

syms w
syms a
int( w^2/( w^2 + a^2),w )

ans =
w-a*atan(w/a)

 

[hnejati]

the answer in the range of -inf to +inf is undefined or infinity so the power is inf or a is a function of w