# How do you integrate #int 1/(x^2sqrt(16x^2-9))# by trigonometric substitution?

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

To integrate ( \frac{1}{x^2\sqrt{16x^2 - 9}} ) using trigonometric substitution, perform the following steps:

- Recognize the form ( \sqrt{a^2 - x^2} ), which suggests a trigonometric substitution.
- Let ( x = \frac{3}{4}\sec(\theta) ) or ( x = \frac{3}{4}\csc(\theta) ), depending on whether ( a^2 - x^2 ) is in the form ( \sqrt{a^2 - x^2} ) or ( \sqrt{x^2 - a^2} ), respectively.
- Express ( dx ) in terms of ( d\theta ).
- Substitute ( x ) and ( dx ) in terms of ( \theta ).
- Simplify the integral and solve it in terms of ( \theta ).
- Finally, convert back to the original variable ( x ).

Following these steps should lead to the solution of the integral.

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 integrate #int e^(x)/sqrt(e^(2x) +36)dx# using trigonometric substitution?
- How do you integrate #int(x)/((x+4)(x+6)(x+1))# using partial fractions?
- How do you integrate # ln(sqrt(x)) #?
- How do you integrate #int sec^-1x# by integration by parts method?
- How do I find the integral #int1/((w-4)(w+1))dw# ?

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