# How do you evaluate the integral #int dx/((x+1)(x+3)(x+5))#?

There are a variety of possible methods, but that which sticks out to me is the method of partial fractions. The denominator is already factored for you, so we have:

Multiply both sides by the denominator of the LHS.

Now we replace A, B, and C in the above partial fractions and substitute into the integral.

We can split this into three separate integrals and use a substitution to solve, but it is easily done mentally to give the final answer:

Or, equivalently:

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

To evaluate the integral of dx/((x+1)(x+3)(x+5)), we can use partial fraction decomposition. After decomposition, the integral becomes A/(x+1) + B/(x+3) + C/(x+5), where A, B, and C are constants to be determined. Then, integrate each term separately to obtain the final result.

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

- How do you integrate #int e^x sin sqrtx dx # using integration by parts?
- How do you use partial fraction decomposition to decompose the fraction to integrate #1/(1+e^x) #?
- How do you integrate #(ln x) ^ 2 / x ^ 2#?
- How do you integrate #x*arctan(x) dx#?
- How come integration of sin²2x cos 2x dx become [sin^3 (2x) ]/6?

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