00:01
We'll be using integration by parts to find this integral here.
00:04
So we're going to let u be equal to arc tan x squared.
00:12
So therefore db is equal to x -cx.
00:17
Now, du is the derivative of u, so that's going to be 1 over 1 plus x squared squared.
00:26
So that'll be x to the power of 4.
00:29
And then changel says we need 2x.
00:32
Okay, so now b is the antiderative of x, so that's going to be one -half x squared, yeah, one -half x squared.
00:43
Okay, so now let's go ahead and put this into integration by quartz formula.
00:47
So we get this as equal to u times v, so that'll be one -half x squared of tan of x squared, and then we minus the integral of b -d -u.
01:03
So the integral of v -d -u.
01:06
So we can see this 2 .1 -half will cancel, and then we have x -cub over 1 plus x -the -power -4.
01:18
Okay, now to solve that, we just need to do a substitution, because if we let u be equal to 1 plus x -the -power 4, then du is going to be 4x -c -c -c -c -cubed d -d -x.
01:31
So if we isolate x cubed dx, we get this is equal to one quarter d u...