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thercias

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## Homework Statement

Using the integral ∫dx/1+x^2 = pi/2 from 0 to infinity as a guide, introduce a parameter and then differentiate with respect to this parameter to evaluate the integral

∫dx/(x^2+a^2)^3 from 0 to infinity

## Homework Equations

## The Attempt at a Solution

∫(1/1+x^2) = tan^-1(x)

introducing parameter x/a to replace x we get

∫(1/a)/(1+(x/a)^2) = tan^-1(x/a)

∫dx/(a^2+x^2) = 1/a*tan^-1(x/a)

d/da(1/(x^2+a^2)) = -2a/(x^2+a^2)^2

im kind of stuck here. i don't really understand how to do this question, if anyone can help me understand/ lead me to the correct path that would be appreciated.