# How do you evaluate the integral #int dx/(x^4-16)#?

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

To evaluate the integral ∫ dx/(x^4-16), we can first factor the denominator as the difference of squares: x^4 - 16 = (x^2)^2 - (4)^2 = (x^2 - 4)(x^2 + 4). We can then use partial fraction decomposition to break down the integrand into simpler fractions. The decomposition will be of the form A/(x-2) + B/(x+2) + C/(x^2 + 4), where A, B, and C are constants to be determined. Once we find the values of A, B, and C, we can integrate each term separately. The integral of A/(x-2) and B/(x+2) are straightforward to evaluate using the natural logarithm function. For the term C/(x^2 + 4), we use the arctangent function. Finally, we combine the integrals of each term to obtain the overall result.

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 y^2sqrtydy#?
- How do you find the Improper integral #int (x^2)e^[(-x^2)/2] dx # from x=-∞ to x=∞?
- How do you find the indefinite integral of #int (12/x^4+8/x^5) dx#?
- What is the net area between #f(x) = sqrt(x^2+2x+1) # and the x-axis over #x in [2, 4 ]#?
- How do you find antiderivative of #(1-x)^2#?

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