How to Use Log Rule for Integrals with Radical Expressions?

[fluxions22]

Homework Statement

integral of x/square root of 9- x^2

Homework Equations

1/x dx= ln |x| + c

The Attempt at a Solution

3 ln|x| + c

 

[vela]

You need to show more work. At this point, it looks like you're just guessing.

So you have the integral

I=\int \frac{x}{\sqrt{9-x^2}}\,dx

right? I don't see how

\int \frac{dx}{x} = \ln |x| + c

applies at all.

 

[physicsman2]

Try factoring out a 9 in the denominator in the square root. It should be somewhat obvious from there what you need to do.

 

[Mark44]

Try factoring out a 9 in the denominator in the square root. It should be somewhat obvious from there what you need to do.

A simpler approach is to use an ordinary substitution. Using this approach you don't need to factor anything out of the radical.

 

[physicsman2]

A simpler approach is to use an ordinary substitution. Using this approach you don't need to factor anything out of the radical.

Oh whoops, I didn't see the x in the numerator. I thought there was only a 1 in the numerator, which is why I thought that at first. You're right.