Finding f(x) given f'(x)=(x²-1)/x⁵ and f(1/2)=3

[howsockgothap]

Homework Statement

Solve each of the following initial value problems: a) f'(x)=(x²-1)/x⁵ f(1/2)=3

Homework Equations

The Attempt at a Solution

I guess my problem with this is I'm not 100% sure what I'm being asked to do. I know I need to use integration to find the original function. Ok no prob I got -1/2x^-2+1/4^-4. So after that am I just supposed to plug in 3=the original function, substituting 1/2 for x? That doesn't seem right since I'm not getting 3... Am I doing the question incorrectly or have I done my integration wrong?

 

[gb7nash]

Solve each of the following initial value problems: a) f'(x)=(x²-1)/x⁵

You're leaving out the whole problem. Did the question say f(1/2) = 3? Or f(3) = 1/2? As far as your integral goes, it looks fine to me if you mean $$\frac{-1}{2x^2}+\frac{1}{4x^4}$$. However, don't forget to add a constant everytime you take an integral, so just put a +C at the end. After that, just plug in the x and f(x) values to solve for C.

 

[howsockgothap]

Ohhh so I'm solving for C. Thanks!