Evaluate \int \frac{5x^3 + 50x + 25}{x^4 + 25x^2} dx.

Question:

Evaluate {eq}\int \frac{5x^3 + 50x + 25}{x^4 + 25x^2} dx. {/eq}

Indefinite Integration.

Most of the question needs substitution of the term for integrating. Substitution makes the problem of integration easy and reduce its complexity. The main task is to choose the term for integration.

Answer and Explanation:

Expand

{eq}5(\int \frac{x^3+10x+5} {x^2(x^2+25)}dx) {/eq}

Perform partial fraction decomposition,

{eq}5(\int \frac{3x-1}{5(x^2+25)}dx+\int...

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...
Indefinite Integral: Definition, Rules & Examples

from Calculus: Tutoring Solution

Chapter 7 / Lesson 14
19K

Related to this Question

Explore our homework questions and answers library