Question

Please help me use trigonometric substitution to solve this integral

Answer 1

\[\int\limits_{3}^{6}\frac{ \sqrt{x^2 - 9} }{ x^2 } dx\]

Answer 2

x=3 sec theta

Answer 3

yes i got that far, then x^2 is 9sec^2 theta

Answer 4

and dx = 3 tan theta sec theta

Answer 5

which means x^2 - 9 = 9sec^2 - 9

Answer 6

yup, go ahead

Answer 7

9sec^2 - 9= 9 tan^2
numerator = 3 tan (3 tan sec) d theta

Answer 8

tan ^2 / (3 sec)

Answer 9

this became more complicated!

Answer 10

this is where i am stuck.

Answer 11

any suggestions @experimentX ?