I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 5.1 : Indefinite Integrals
6. Determine \(f\left( x \right)\) given that \(f'\left( x \right) = 6{x^8} - 20{x^4} + {x^2} + 9\).
We know that indefinite integrals are asking us to undo a differentiation to so all we are really being asked to do here is evaluate the following indefinite integral.
\[f\left( x \right) = \int{{f'\left( x \right)\,\,dx}} = \int{{6{x^8} - 20{x^4} + {x^2} + 9\,dx}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{2}{3}{x^9} - 4{x^5} + \frac{1}{3}{x^3} + 9x + c}}\]Don’t forget the “+c”! Remember that the original function may have had a constant on it and the “+c” is there to remind us of that.