# Math Help - A tricky trig sub integral.

1. ## A tricky trig sub integral.

Tricky for me at least:

integrate: 10x^2/sqrt(4x-x^2)

I worked it out to this:

30arcsin((x-2)/2)-5sin(2arcsin((x-2)/2))-20sqrt(4-(x-2)^2)+C

I got pretty close to the answer I know because when I asked Wolfram to differentiate this it gave me

5x^2/sqrt(4x-x^2)

Maybe I made a mistake reverting to x from theta? I was a bit confused about how to handle sin(2theta) even though I drew a diagram of the right triangle. That's why I wrote sin(arcsin...) which I'm not sure is correct? Any clarification is appreciated

2. While you were at the Wolfram site, you should've asked for a solution to your integral and at least look to see if your substitution is correct!

3. The problem is the Wolfram site's answer is so convoluted and used techniques we haven't covered. I'm doing the problem again and I think I'm coming to the right answer though! We shall see.

4. Yes I made a mistake somewhere along the way. The answer is

60arcsin((x-2)/2)-10sin(2arcsin((x-2)/2))-40sqrt(4-(x-2)^2)+C

Thanks for the suggestion!