Impropres Integrals

[stiff escarp]

i just need to prove that the second first integral is equal to the second ?

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[stiff escarp]

first integral is equal to the second integral in b)

[eager carbon]

u = 1/t, du = -dt/t²

try this variable substitution from the integral in b)

$\int_{0}^{\infty} \frac{t^{\alpha}}{(1+t^2)(1+t^\alpha)}dt = \int_{0}^{\infty} \frac{1}{t^2 (1 + t^{-2})(1 + t^{-\alpha})} dt$

[shrewd kite]

Rion

[stiff escarp]

then ?

@eager carbon

[eager carbon]

as i said, variable substitution can solve this problem