Calculus with inverse trig functions

[famallama]

Homework Statement

Evaluate the integral of (1/Sqrt(5x-x^2))

Homework Equations

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

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.

 

[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)

 

[famallama]

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

 

[rock.freak667]

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

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

 

[famallama]

thank you very much