# How do you integrate #int 3/(xsqrt(x^2-9))# by trigonometric substitution?

We have:

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

To integrate ( \frac{3}{x\sqrt{x^2 - 9}} ) using trigonometric substitution, let ( x = 3\sec(\theta) ). Then, ( dx = 3\sec(\theta)\tan(\theta)d\theta ). Substitute these into the integral and simplify. You'll end up with ( \int \frac{3}{x\sqrt{x^2 - 9}}dx = \int \frac{3}{9\sec(\theta)\tan(\theta)}(3\sec(\theta)\tan(\theta))d\theta ). Simplify and solve the integral in terms of ( \theta ). Then, convert back to the original variable ( x ) to get the final answer.

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.

- How do you evaluate the integral #int 1/(x(1+(lnx)^2)#?
- How do you integrate #9sin(ln x) dx#
- How do you integrate #int (x^2-1)/((x)*(x^2+1))# using partial fractions?
- What is #f(x) = int xsqrt(x^2-1) dx# if #f(3) = 0 #?
- How do you use partial fraction decomposition to decompose the fraction to integrate #(x^5 + 1)/(x^6 - x^4)#?

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