Classic u-sub in the form a squared minus u squared

Added: 2026-06-03

[00:00:00]Hi, today we are going to do a U substitution in form a squared minus U squared. I'm going to factor it one because I want to have one over here.

[00:00:09]Now, I will choose U to be X to the power 4 over 9 so that this guy is U squared. In that case, dU is going to be 4 over 9 X cubed dX. See how I have X cubed already and I have a 9 in here.

[00:00:24]So, I'm going to multiply by 4 and I'm going to multiply by 1/4 to even out the expression. Because I chose U to be X squared X to the power 4 over 9, U squared is X to the power 8 over 81. And now my integral becomes dU over 1 minus U squared. That is a table integral of arc sine. The final step is plugging U back in there and we get our answer. What I wanted to show is an example of an integral when you have a squared and U squared. Then you will end up with arc sine of U over A plus C and then you will have a coefficient depending on what the exponent of X you have. Follow me for more calculus and I will see you next time.