# How do you find the indefinite integral of #int x/(sqrt(9-x^2))#?

By signing up, you agree to our Terms of Service and Privacy Policy

By parts. Set

Notes:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the indefinite integral of (\int \frac{x}{\sqrt{9-x^2}} , dx), use the substitution method. Let (u = 9 - x^2), then (du = -2x , dx).

Substitute (u) and (du) into the integral:

[\int \frac{x}{\sqrt{9-x^2}} , dx = -\frac{1}{2} \int \frac{1}{\sqrt{u}} , du]

Now, integrate (\frac{1}{\sqrt{u}}):

[\int \frac{1}{\sqrt{u}} , du = 2\sqrt{u} + C]

Substitute back (u = 9 - x^2):

[= 2\sqrt{9 - x^2} + C]

So, the indefinite integral of (\int \frac{x}{\sqrt{9-x^2}} , dx) is (2\sqrt{9 - x^2} + C).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7