Improper integral trig substitution, trig sub on zero to infinity, using arctan(infinity)=pi/2.

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We compute a trig sub on zero to infinity for an improper integral requiring a trig substitution and transforming the limits of integration. We take advantage of the secant tangent pythagorean identity and transform the limits of integration, noting that the inverse tangent of infinity is pi/2 (arctan(infinity)=pi/2). The infinity is treated informally without re-expressing the integral as a limit. Integral of 1/(1+x^2)^(3/2).