Question

Please help me get started on the following integral. (click to see)

Answer 1

\[\int\limits_{}^{}\frac{ dx }{ x^2\sqrt{9x^2-4} }\]

Answer 2

hint : pull out x^2 from the radical

Answer 3

wont i be left with 4/(x^2) within the radical?

Answer 4

wait a sec, let me think a bit

Answer 5

how about a trig substitution

Answer 6

\(x = 2/3sec(\theta)\) ?

Answer 7

this looks nice, go ahead :)

Answer 8

ok and how did we decide upon sec?

Answer 9

sec=(1/cos)

Answer 10

good question,
cuz we have this identity :
sec^2-1 = tan^2

Answer 11

substituting x = 2/3sec(theta), simpifies the radical nicely

Answer 12

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