Question

steps to calculate Integral of dx/(9+4x^2)

Answer 1

what ways of integration have you learned?

Answer 2

@toby-san You're in which grade?

Answer 3

i mean, let x = (3/2)tanθ :)

Answer 4

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

Answer 5

now, can evaluate that integral ?

Answer 6

* can u

Answer 7

hint :
multiple by (secθ+tanθ)/(secθ + tanθ) then integrate by u-subt

Answer 8

http://www.wolframalpha.com/input/?i=integrate%20%20dx%2F(9%2B4x%5E2)%20&t=crmtb01

Answer 9

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

Answer 10

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