00:01
Okay, we want to find the indefinite integral of x cubed times arc sine of x squared.
00:06
To do this, let's first start off right away with doing u substitution.
00:10
So let's say that u is equal to x squared, which is within our arc sign.
00:18
So this means that du is equal to 2x, dx, which then follows that dx, if we solve for it, is equal to du over 2x.
00:34
So we want to get everything in terms of you.
00:38
So let's rewrite our integral here.
00:43
So we have the integral of x cubed arc sine of you.
00:57
And plugging in for dx gives us d u over 2x.
01:02
So we still have things in terms of x, but we can resolve that pretty easily here.
01:08
So we have a factor of one half, which can come out.
01:11
That's no problem.
01:12
Then we have then an x cubed times one over x which is just x squared right that's x squared which is the same thing as you same thing as you so this means we go ahead rewrite our integral again we have a factor of one half from our d u integral of u times arc sine of you so now we have our integral in an easier form where we can apply an integral table formula to write out the solution...