1. ## Anti-Derivative

Can anyone explain to me how to get to the second step?
I don't understand how the X^(5/2) - 7(square X) + X^(-1/2) came from.

2. Originally Posted by Brazuca

Can anyone explain to me how to get to the second step?
I don't understand how the X^(5/2) - 7(square X) + X^(-1/2) came from.
remember $\displaystyle \sqrt{x} = x^{\frac{1}{2}}$

$\displaystyle \frac{x^3-7x+1}{x^{\frac{1}{2}}} =$

$\displaystyle \frac{x^3}{x^{\frac{1}{2}}} - \frac{7x}{x^{\frac{1}{2}}} + \frac{1}{x^{\frac{1}{2}}}$

subtract exponents when dividing ... right?

3. We can first split the fraction up to:

(Nevermind, can't get the LaTeX right, just refer above)

Note: $\displaystyle \sqrt{x} = x^{1/2}$

Now, when we divide by x's of different powers, we can subtract the exponents.

$\displaystyle 3 - \frac{1}{2} = \frac{5}{2}$

So that's where the x^5/2 came from...

You should be able to finish it from here, just keep subtracting the powers.

4. I forgot that the bottom part effects each thing on top induvidualy...