integral of (x^3)/ [sqrt[(x^2)+4] ]

use the substitution
x = 2tanθ

dx = 2 ((secθ)^2) dθ

simplify and then use another substituion

secθ = t

secθ tanθ dθ = dt

simplify and integrate
then resubstitute

change secθ in terms of tanθ

then again resubstitute

remembering that x =2 tanθ or tanθ = (x/2)

integration formulae

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