00:01
We are asked to calculate this integral.
00:02
We'll first rewrite this as the integral of negative 2x squared divided by x to the 4 minus x divided by x to the 4 minus 2 divided by x to the 4.
00:21
Then we can cancel x squared in the first term, cancel x in the second term.
00:33
We'll get the integral of negative 2 over x squared minus 1 over x cubed minus 2 over x to the 4.
00:53
Next we'll write this as the integral of negative 2 times x to the negative 2 minus x to the negative 3 minus 2x to the negative 4.
01:12
Now we'll use the power rule.
01:15
Recall that by the power rule we need to add 1 to the exponent and divide by the new exponent.
01:26
The integral of x to the negative 3 is x to the negative 2 divided by negative 2 and the integral of x to the negative 4 is x to the negative 3 divided by negative 3.
01:37
All of this is in substitution from negative 2 to negative 1.
01:44
Now let's simplify.
01:46
We'll get 2 over x plus 1 over 2x squared plus 2 over 3x cubed from negative 1 to negative or from negative 2 to negative 1.
02:06
Now we'll plug in the upper limit of integration first...