anonymous
  • anonymous
steps to calculate Integral of dx/(9+4x^2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
what ways of integration have you learned?
uri
  • uri
@toby-san You're in which grade?
RadEn
  • RadEn
i mean, let x = (3/2)tanθ :)

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RadEn
  • RadEn
x = (3/2)tanθ dx = (3/4) sec^2 (θ) dθ see ur integral becomes int (3/4) sec^2 (θ)/3secθ dθ = int 1/4 secθ dθ
RadEn
  • RadEn
now, can evaluate that integral ?
RadEn
  • RadEn
* can u
RadEn
  • RadEn
hint : multiple by (secθ+tanθ)/(secθ + tanθ) then integrate by u-subt
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=integrate%20%20dx%2F(9%2B4x%5E2)%20&t=crmtb01
RadEn
  • RadEn
aha, i thought it is sqrt(9+4x^2) . sorry :) try again : x = (3/2)tanθ dx = (3/4) sec^2 (θ) dθ int (3/4) sec^2 (θ)/9sec^2 θ dθ = int 1/12 dθ = θ/12 + c
RadEn
  • RadEn
damn, mistake again x = (3/2)tanθ dx = (3/2) sec^2 (θ) dθ int (3/2) sec^2 (θ)/9sec^2 θ dθ = int 1/6 dθ = θ/6 + c because x = (3/2)tanθ, so tanθ = 2x/3 θ = tan^-1 (2x/3) so, it is 1/6 tan^-1 (2x/3) + c

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