00:01
So to do this integral, what we're going to want to do is expand this factor in the top here.
00:07
And so if we do, we're going to get x squared plus 2x plus 1 divided by x to 1⁄2x.
00:15
And then the next thing we want to do is just split this integral up into the integral of this first term.
00:22
So the first term was x squared divided by x to 1 .5 power dx.
00:27
Plus i'm also going to take out this, well, i guess we'll take it out in another step.
00:33
So the second term is 2 divided by x, or 2 times x divided by x to the 1 half power.
00:39
And then lastly, this last term is 1 divided by x to the 1 half or x negative 1⁄2 power.
00:47
So x squared divided by x to the 1⁄2 power, that's x the 3 halves power.
00:53
And we're going to take this 2 out, x divided by x the 1⁄2 is x the 1⁄2 power.
00:59
And then lastly, plus the integral of x the negative 1f power.
01:04
So each of these integrals is a power rule integral.
01:08
And whenever we're taking the integral of x to the n minus 1 power, this is equal to x the n divided by n.
01:13
And this is derived directly from the power rule for derivatives.
01:17
So that's how we know that this is equal to the integral of x the n minus 1...