Basic Integration Techniques

1. Mar 14, 2013

whatlifeforme

1. The problem statement, all variables and given/known data
I am reviewing some basic integration techniques. how would i evaluate this?

2. Relevant equations
$\displaystyle\int {\frac{1}{\sqrt{8x-x^2}} dx}$

3. The attempt at a solution
i've tried multiplying by

$\frac{\sqrt{8x-x^2}}{\sqrt{8x-x^2}}$ but that isn't getting me anywhere.

should i use something like completing the square?

2. Mar 14, 2013

Staff: Mentor

Completing the square is a good way to begin. Afterwards, a clever substitution can help.

3. Mar 14, 2013

whatlifeforme

okay. im stuck with the subtracted term.

$\frac{1}{-\sqrt{(x^2 - 8x + 16) - 16}}$

$\frac{1}{-\sqrt{(x-4)^2 - 16}}$

4. Mar 14, 2013

whatlifeforme

i don't think completing the square works here.

5. Mar 14, 2013

eumyang

Looks like you pulled a negative outside of the square root. You can't do that!!!! Try again.

6. Mar 14, 2013

phosgene

Once you've fixed up the negative, try the substitution u=(x-4) and then consider what the derivatives of the inverse trigonometric functions look like.

7. Mar 14, 2013

whatlifeforme

great. thanks phosgene.

so we are looking at:

$arcsin(\frac{x-4}{4}) + c$