Question

Evaluate the integral: ∫dx/(sqrt((x^2)+16))

Answer 1

Let x=4tanβ, then dx = 4sec²βdβ.  Now

    ∫(4sec²β)/(4secβ)dβ
=  ∫secβdβ
=  ln |tanβ - secβ| + c
=  ln |(x/4) - (√(x²+16)/4| + C
=  ln |x/√(x²+16)
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