00:01
So we'll first represent this in a different format just to make our lives easier.
00:07
So it's going to be the integral of x to the power n minus 1 times a plus b x to the power n, all to the power negative half d x.
00:26
Right? so since this integrals in terms of x, we can see other variables here like n, and we're going to consider these as constants, right? we'll treat them as constants.
00:41
So a and b are treated as constants, right? so we are going to use use substitution to evaluate this, which basically states that this is basically the chain rule in reverse and we need to represent this integral in terms of view.
01:10
So we'll do that by first, letting.
01:11
U equals to a plus b x to the power n right and the next step is to find the derivative of this equation so d u is equals to n b x to the power n minus 1 d x right now we can get back to our integral so we have the grow of okay so we know that u is equals to a a plus b x to the power n so i're going to have u to the power negative half and you can see that what's left is this x to the power n minus 1 d x which is what we have right here it's just portion right here so if we divide this equation by nb on both sides what we'll end up with is du divided by nb.
02:18
It is equals to x to the power n minus 1 dx...