00:01
Alright, in your question you're asked to evaluate this indefinite integral.
00:04
I'm sorry, yeah, evaluate the indefinite integral.
00:07
At first glance, i looked at this question, i'm like, i'm not sure how to do that.
00:11
It didn't stand right out to me, but then i see the pattern, and that's typical with integral, indefinite integrals where you need to find some formula that helps you fall back on.
00:26
And what i recognized was that if i cut this in half, and i think of it as x to the 8th squared, it would still give me the 16th power, but then if i let my u equal this, and i do a u substitution, that's going to give me an x to the 7th power that we have in the numerator.
00:48
So that started the wheels turning, so to speak, and i started to think, okay, what's an integral that's in the form of something over 1 plus x squared? and i thought to myself, okay, the derivative of inverse tangent is 1 over 1 plus x squared.
01:11
So it takes some time to find those patterns, and once you find them, in this case i'm going to use that one, you need to pick a u substitution that will help you match that pattern...