This gives us the equation " title="Rendered by QuickLaTeX.com"/>First, we can find the values of and by evaluating at and , r" />

# Evaluate Integral 8X^2/(X^3+2)^3, Find The Integral 8X^3

Since the denominator is already factored into linear terms we can proceed directly with the partial fraction decomposition. We write,

” title=”Rendered by QuickLaTeX.com”/>

This gives us the equation

” title=”Rendered by QuickLaTeX.com”/>

First, we can find the values of and by evaluating at

and

, respectively. This gives us

Then using these values of and we evaluate at

and

(these are just convenient values, there isn’t anything special about them) to obtain the two equations

Solving these two equations we obtain

and

. Therefore, we have the following partial fraction decomposition:

” title=”Rendered by QuickLaTeX.com”/>

We can now evaluate the integral,

Đang xem: Integral 8x^2/(x^3+2)^3

### Related

Evaluate the integral of (4×2 + x + 1) / (x3 – 1)
Evaluate the integral of (x4+2x-6) / (x3 + x2 – 2x)

### Point out an error, ask a question, offer an alternative solution (to use Latex type at the top of your comment):Cancel reply

ArchivesArchivesSelect Month June 2016 (12) May 2016 (142) April 2016 (150) March 2016 (156) February 2016 (145) January 2016 (155) December 2015 (155) November 2015 (150) October 2015 (155) September 2015 (150) August 2015 (155) July 2015 (155) June 2015 (50)

If you are having trouble with math proofs a great book to learn from is How to Prove It by Daniel Velleman:

A really awesome book that I highly recommend on how to study math and be a math major is Laura Alcock”s, How to Study as a Mathematics Major:

My Complete Math Book Recommendations:
Basics: Calculus, Linear Algebra, and Proof WritingCore Mathematics Subjects.

Cancel