00:01
So in this question, they say, i want to write a formula for capital f, the specific antiderivative of little f.
00:08
If i know that little f of z is equal to 4 over z squared plus e to z to z power, if i know that capital f of 4 is going to be equal to 3.
00:27
So i want to find the antiderivative of this little f.
00:32
I want the antiderivative of 4 over z squared plus e to the z power dz.
00:43
Now, if i wish to integrate 4 over z squared, how can i think of that? i can think of that as 4 z to the negative second.
00:54
So i'm really trying to find an antiderivative of 4 z to the negative second plus e to the z d z this time.
01:05
Now, what's my antiderivative of 4z to the negative second? since this is like a polynomial, i'm going to add 1 to the exponent, 4z to the negative first, and i'm going to divide by the new exponent.
01:22
I divide by negative 1.
01:27
Plus what's my anti -derivative of e to the z? well, i know that the derivative of e to the x is e to the x.
01:35
So the anti -derivative of e to the z is just e to the z.
01:41
So e to the z, now i need a plus c at the end of any antiderivative...