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

The rational function can be expressed as the sum of partial fractions:

We can equate the numerators since the denominators are equal:

So that:

and incorporating:

and making use of logarithmic properties:

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

To integrate ( \frac{1}{(x + 1)(x + 2)} ) using partial fractions:

- Decompose the fraction into partial fractions.
- Write ( \frac{1}{(x + 1)(x + 2)} ) as ( \frac{A}{x + 1} + \frac{B}{x + 2} ).
- Find the values of ( A ) and ( B ) by equating numerators.
- Multiply both sides by the common denominator ( (x + 1)(x + 2) ).
- Simplify and solve for ( A ) and ( B ).
- Integrate each partial fraction separately.
- Combine the results to get the final integral.

The integral of ( \frac{1}{(x + 1)(x + 2)} ) using partial fractions is ( A\ln|x + 1| + B\ln|x + 2| + C ), where ( A ) and ( B ) are constants obtained from the partial fraction decomposition, and ( C ) is the constant of integration.

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

- How do you use substitution to integrate #(1+2tanx)#?
- How do you integrate #int e^(3x)cosx# by integration by parts method?
- How do you integrate #int 1/sqrt(1-4x^2)# by trigonometric substitution?
- How do you use partial fractions to find the integral #int 1/(x^2-1)dx#?
- How do I find the integral #intt^2/(t+4)dt# ?

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