Evaluate the following integral ∫dx/(x^2 √(4+x^2 ))
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total answers (1)
total answers (1)
Mathematics
Put x=2 tanθ , dx=2 〖sec〗^2 θ dθ
need an explanation for this answer? contact us directly to get an explanation for this answer∫dx/(x^2 √(4+x^2 ))=∫(2 〖sec〗^2 θ dθ)/((4 〖tan〗^2 θ) √(4+4〖tan〗^2 θ))
=∫(2 〖sec〗^2 θ dθ)/(4 〖tan〗^2 θ)(2 secθ )
=1/4 ∫(secθ dθ)/(〖tan〗^2 θ)=1/4 ∫〖〖sin〗^(-2) θ〗 cosθ dθ
=(-1)/(4 sinθ )+c