Evaluate the following integral ∫_0^∞dx/(1+x^2 )^2
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Mathematics
∫_0^∞dx/(1+x^2 )^2
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x=tanθ→dx=〖sec〗^2θ dθ,x=0→θ=0,x=∞→θ=π/2
∴I=∫_0^(π⁄2)(〖sec〗^2 θ)/(1+〖tan〗^2 θ)^2 dθ=∫_0^(π⁄2)〖〖cos〗^2 θ〗 dθ=1/2 ∫_0^(π⁄2)(1+cos2θ ) dθ=π/4