Integrate ='false' \int \frac {5x^2 + 7x + 3}{x^3 + 2x^2 + x} dx

Question:

Integrate {eq}\int \frac {5x^2 + 7x + 3}{x^3 + 2x^2 + x} dx {/eq}

Integrations Using Partial Fractions

First we find the partial fraction of the given function in order to simplify the solution

Then we integrate the function obtained by partial fraction

Formulas Used

{eq}\displaystyle \begin{align} \int a\cdot f\left(x\right)dx&=a\cdot \int f\left(x\right)dx\\ \int \frac{1}{x}dx&=\ln \left(\left|x\right|\right)\\ \int \frac{1}{x^2}dx&=\frac{-1}{x}\\ \end{align} {/eq}

Answer and Explanation:

Given

{eq}\displaystyle \int \frac {5x^2 + 7x + 3}{x^3 + 2x^2 + x} dx {/eq}

First we find the partial fraction of the given function

{eq}\display...

See full answer below.

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

View this answer

Learn more about this topic:

Loading...
How to Integrate Functions With Partial Fractions

from Math 104: Calculus

Chapter 13 / Lesson 9
6.8K

Related to this Question

Explore our homework questions and answers library