# Calculus with inverse trig functions

1. Sep 2, 2009

### famallama

1. The problem statement, all variables and given/known data
Evaluate the integral of (1/Sqrt(5x-x^2))

2. Relevant equations
[d/dx]{arcsin(x)}=(du/dx)/sqrt(1-x^2)

3. The attempt at a solution
arcsine(2x-5)/5

I did end up getting the right answer, but have no idea how I got there.

2. Sep 2, 2009

### rock.freak667

So we have

$$\int \frac{1}{\sqrt{5x-x^2}}$$

try completing the square for 5x-x2 (i.e. put it into the form a[x+h]2+k)

3. Sep 2, 2009

### famallama

I have tried that, but the 5 is what is throwing me off.

4. Sep 2, 2009

### rock.freak667

5x-x2 = -(x2-5x) = -(x+5/2)2+k. Can you find 'k'?

5. Sep 2, 2009

### famallama

thank you very much