Copyright

Partial Fraction Decomposition. Show the form of the partial fraction decomposition for the...

Question:

Partial Fraction Decomposition. Show the form of the partial fraction decomposition for the integrand below. Generate a system of equations that could be used to complete the decomposition. Rather than continuing the partial fraction decomposition, evaluate the integral using the substitution {eq}u^{2}=1+x^{2} {/eq}

{eq}\int_{0}^{\infty} \frac{x^{3}}{\left(1+x^{2}\right)^{3}} d x {/eq}

Partial Fraction Decomposition:

When you have a rational function {eq}\frac{f(x)}{g(x)} {/eq}, you can rewrite the function as a sum of simpler functions by using the partial fraction decomposition (also called partial fraction expansion). This is the same as the procedure of adding fractions by first finding a common denominator, but done in reverse order. Rewriting an integrand using partial fraction decomposition can result in integrals that are simpler to evaluate. In order to find the partial fraction decomposition, you will need to remember factoring skills and how to solve a system of equations

Answer and Explanation:

Become a Study.com member to unlock this answer! Create your account

View this answer

To find the form of the partial fraction decomposition of the integrand of {eq}\int_{0}^{\infty} \frac{x^{3}}{\left(1+x^{2}\right)^{3}} d x {/eq},...

See full answer below.


Learn more about this topic:

Loading...

Related to this Question

Explore our homework questions and answers library