Calc II: Help Solving this Integral

[Hertz]

Homework Statement

$\int \frac{\sqrt{9 - x^2}}{x} dx$

2. The attempt at a solution

x = 3sin(u)
dx = 3cos(u)du
u = arcsin(x/3)

$\int \frac{3\sqrt{cos(u)^2}}{3sin(u)} 3cos(u)du$

$3 \int \frac{cos(u)}{sin(u)} cos(u)du$

Don't really see anywhere to go from here. Apologies if the work is hard to follow, I cut out a few steps because inputting equations is a real pain in my opinion.

 

[Mark44]

Homework Statement

$\int \frac{\sqrt{9 - x^2}}{x} dx$

2. The attempt at a solution

x = 3sin(u)
dx = 3cos(u)du
u = arcsin(x/3)

$\int \frac{3\sqrt{cos(u)^2}}{3sin(u)} 3cos(u)du$

$3 \int \frac{cos(u)}{sin(u)} cos(u)du$

Don't really see anywhere to go from here. Apologies if the work is hard to follow, I cut out a few steps because inputting equations is a real pain in my opinion.

Write cos²(u) as 1 - sin²(u), and then split into two integrals.

 

[Hertz]

Write cos²(u) as 1 - sin²(u), and then split into two integrals.

Ah! Thank you, I'll give it a try