00:01
All right, here we have the integral of x minus 1 over x squared times x squared plus 2 over x to the fifth.
00:06
So let's say we try a u substitution and let you be equal to this piece where we have x squared plus 2 over x.
00:15
We'd write that as x squared plus while 2x to the minus 1 is the same thing as just 2 over x.
00:24
Then differentiating what we get we get that du is going to be equal to while we get 2.
00:33
2x plus while we get a the negative one comes down we get a minus 2 times x to the minus 2 which is minus 2 over x which becomes over x squared right because we get minus 2 times x to the minus 2 which is minus 2 over x squared oh and then we look at this and we see that we have an x minus well, 1 over x squared.
01:04
So if we divide, i guess, everything by 2, we get that, well, 1 half du is going to be equal to what we want, the x minus 1 over x squared.
01:17
Okay, so then we can make a you substitution, and we can let you be equal to, well, x squared plus 2x to minus 1 is the same thing as x squared plus 2 over x.
01:30
So therefore, we then get that, this integral.
01:35
We can well pull out a one -half in front...