# Calculus with inverse trig functions

## 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.

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rock.freak667
Homework Helper
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)

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

rock.freak667
Homework Helper
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'?

thank you very much