00:01
Okay, so for number one, you have the integral of 7 over 2 plus 3y, dy.
00:09
So this is a u substitution.
00:12
Let's let u be 2 plus 3y, then du is 3dy.
00:21
So 1 3d2 is equal to dy.
00:27
So we're going to bring the 7 and the 3 out, and this would be the integral of d over u, which is the natural log.
00:42
So it's 7 thirds ln of the natural log of u, which is 2 plus 3y plus c.
00:54
Similarly, for number 2.
00:59
Let's do number 2 down here, and then we'll do number 3 to the right.
01:04
This is the integral of 18x cubed plus 3 over 3 over 3.
01:11
3x to the 4 plus 2x.
01:15
So notice the degree of the denominator is one more than the degree of a numerator.
01:20
That makes it a candidate for u substitution with it being a natural log.
01:25
So u is equal to 3x to the 4th plus 2x.
01:44
So du is 12x cubed plus 2.
01:57
And then dx...