# How do you integrate #[((3x^2)+3x+12) / ((x-5)(x^2+9))]dx# using partial fractions?

Please see the explanation

Expand the fraction:

Multiply both sides by the left side denominator:

Let x = 5 to make B and C disapper

Substitute 3 for A:

Let x = 0 to make B disappear:

Substitute 3 for C:

Let x = 1:

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

To integrate the given expression using partial fractions, follow these steps:

- Factor the denominator: (x - 5)(x^2 + 9).
- Express the fraction as a sum of partial fractions with undetermined coefficients: A/(x - 5) + (Bx + C)/(x^2 + 9).
- Clear denominators by multiplying both sides by the common denominator.
- Equate coefficients of like terms on both sides of the equation.
- Solve for the unknown coefficients A, B, and C.
- Once you have the partial fractions, integrate each term separately.
- Finally, sum up the integrals to find the overall integral of the original expression.

The detailed steps would involve solving for A, B, and C by equating coefficients, integrating each term, and then summing them up. If you need further clarification on any of these steps, feel free to ask.

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