Anti-derivative?

[Awesom-O_2000]

f '(x)= (x)^(1/2)(7x^2-5x+3) and it is also known that f(1)=7. Find f(x).

Honestly I'm not sure where to start--and being that my instructor doesn't even "title" the problems with at least what concept is involved in the problem--I thought I would ask all of you.

Thanks

 

[tkhunny]

I'd start with a simple substitution: u^2 = x. This leave a nice, pretty quartic polynomial that wants some completing the square and a tangent substitution.

On second thought, just complete the square in the denominator and go straight for the tangent substitution.

Let's see what you get.