# How do you integrate #(1x^(2)+4x+12)/((x+2)(x^(2)+4)) # using partial fractions?

Write the partial fraction equation:

Substitute the value for A into equation [1]:

Substitute the value for C into equation [2]:

Let (x = 1):

Remove the term for B from equation [3]

Equation [4] gives us the template for the integrals:

Both integrals are well known:

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

To integrate ( \frac{{x^2 + 4x + 12}}{{(x + 2)(x^2 + 4)}} ) using partial fractions:

- Factor the denominator ( (x + 2)(x^2 + 4) ) into linear and irreducible quadratic factors.
- Express ( \frac{{x^2 + 4x + 12}}{{(x + 2)(x^2 + 4)}} ) as the sum of partial fractions with undetermined coefficients.
- Find the values of the coefficients by equating the numerators of the partial fractions with the original function.
- Integrate each partial fraction separately.
- Combine the results to get the final integrated expression.

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