00:01
So i can help you with a few of these, luke.
00:02
Put these underneath the calculus setting after this, but you have 5 times, and you have the cosine of x to the negative 2 power, and then times the sine of x dx.
00:18
And i'm going to do this with reversing the chain rule.
00:21
We want to have the derivative of this cosine of x sitting here.
00:24
So i'm going to put a negative 1, multiply this by negative 1, and this by negative 1.
00:31
So we'll change that to a negative 5.
00:33
So now we can find the negative 5 times, and we just use the power rule.
00:39
We increase the power by 1, so that becomes x to the negative 1, and then over negative 1 plus c.
00:47
So that would end up being 5 over cosine of x.
00:54
Plus c.
00:56
Now for the sixth one, you have, and i'm going to do a trig substitution, the sine of 2x is 2 sine x times the cosine of x over the sine of x times dx, and there should be a dx there, you're missing that, and the sine of x would cancel, so you have integrating 2 2 cosine of x dx.
01:24
And so the antiderivative of the cosine function is the sine function.
01:29
So that's going to be 2 times sine of x plus c.
01:35
On the next one, you can do, i'm trying to get this to move, there we go.
01:41
The seventh one, we have, and i'm going to write it this way, the 4x to the third third power plus 5.
01:48
And i believe, let me enlarge that a little bit.
01:52
I think that says that that is to the fifth power.
01:56
Okay.
01:57
That is to the fifth power.
01:59
And then times, and i'm going to move that 3 out here...