# How do you integrate #int 1/sqrt(x^2-4x-21)dx# using trigonometric substitution?

See answer below:

Continuation:

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

To integrate ( \int \frac{1}{\sqrt{x^2 - 4x - 21}} , dx ) using trigonometric substitution, we first complete the square in the denominator to express it in the form ( \sqrt{a^2 - x^2} ). Then we use the substitution ( x = a \sec(\theta) ), where ( a ) is a constant. After performing the substitution and simplifying, we integrate with respect to ( \theta ) and then revert back to the variable ( x ) to obtain the final answer.

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

- How do you integrate #int 1/sqrt(e^(2x)+12e^x+27)dx# using trigonometric substitution?
- How do you use Integration by Substitution to find #intdx/(5-3x)#?
- How do you integrate #inte^(x^2)sin^2xdx# using integration by parts?
- How do you integrate #int sin^10xcosx# using substitution?
- What is #f(x) = int xsqrt(5-2) dx# if #f(2) = 3 #?

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