Question

integral dx/sqrt(x^2-9)

Answer 1

Trig substitution

Answer 2

x=3sec

Answer 3

yes, good!

Answer 4

And dx=?

Answer 5

dx=3sec(theta)tan(theta)

Answer 6

forgot: d(theta)

Answer 7

\(\color{#000000}{ \displaystyle \int\frac{1}{\sqrt{(3\sec \theta)^2~-~9}}(3\sec\theta \tan\theta~d\theta) }\)

Answer 8

Stuck?

Answer 9

3 integra (1/sqrt3(sec(u)^2-9))(tan(u)/cos(u))

Answer 10

You probably know that \(\color{#000000}{ (a\cdot b)^n=a^n\cdot b^n }\), and not just \(\color{#000000}{ \displaystyle a\cdot b^n }\).

Answer 11

it is a hint to where your mistake is.

Answer 12

\(\color{#000000}{ \displaystyle \int\frac{1}{\sqrt{(3\sec \theta)^2~-~9}}(3\sec\theta \tan\theta~d\theta) }\)

\(\color{#000000}{ \displaystyle 3 \int\frac{\sec\theta \tan\theta}{\sqrt{3^2\sec^2\theta~-~9~}~~}d\theta }\)

Answer 13

\(\color{#000000}{ \displaystyle 3 \int\frac{\sec\theta \tan\theta}{\sqrt{9(\sec^2\theta~-1)~}~~}d\theta }\)

\(\color{#000000}{ \displaystyle 3 \int\frac{\sec\theta \tan\theta}{3\sqrt{\sec^2\theta-1}~~}d\theta }\)

\(\color{#000000}{ \displaystyle \int\frac{\sec\theta \tan\theta}{\sqrt{\sec^2\theta-1}~~}d\theta }\)

Answer 14

continue ....

Answer 15

Yes, you will have to integrate in terms of theta, but then to solve and simplify everything in terms of x...

Answer 16

First finish integrating with \(\theta\).

Answer 17

got it, thanks for the help

Answer 18

Oh, alright.
YW

Answer 19

i got ln((1/cos(theta))+tan(theta))+C

Answer 20

good! @garmex now write in terms of x..

Answer 21

hello,\[\ln \left| ((\ x+\sqrt{x^2 -9})/3)\right|\]

Answer 22

+C

Answer 23

that's what i ended up with

Answer 24

and thanks for the response

Answer 25

you got it! that's correct! well Done @garmex