I need help getting the antiderivative.
Find f.
f '(x)= (3x + sqrt(x) + 4)/(x^2); f(1)= -1
I got: f '(x)= 3/x + 1/x^(3/2) + 4/x^2
I broke it up so each piece is under x^2.
Is this wrong?
What you have done is in the right direction, I would write:
$\displaystyle f'(x)=3x^{-1}+x^{-\frac{3}{2}}+4x^{-2}$
Now use the power rule for integration term by term, then use the given point (1,-1) to determine the constant of integration, or use the boundaries as limits for definite integrals. The first method is probably more familiar.