1. Help with Integration

How do you integrate (x-1)/sqrt(x)?

Thanks.

2. Originally Posted by Savior_Self
How do you integrate (x-1)/sqrt(x)?

Thanks.
Hint:

$\displaystyle \frac{x-1}{\sqrt{x}}=x^{\frac{1}{2}}-x^\frac{-1}{2}$

Now use the power rule!

3. wait, how does $\frac{x-1}{\sqrt{x}} = x^{1/2} - x^{-1/2}$?

I get that it equals $(x-1)(x^{-1/2})$... I just don't see the steps you took to get past that.

4. Originally Posted by Savior_Self
wait, how does $\frac{x-1}{\sqrt{x}} = x^{1/2} - x^{-1/2}$?

I get that it equals $(x-1)(x^{-1/2})$... I just don't see the steps you took to get past that.
Expand the brackets, using the rule that $(x^a)(x^b)=x^{a+b}$

5. Thanks. So the answer is: $\frac{2x^{3/2}}{3}-2x^{1/2}+C$

correct?

6. Originally Posted by Savior_Self
Thanks. So the answer is: $\frac{2x^{3/2}}{3}-2x^{1/2}+C$

correct?
yes you can check by taking the derivative!