Question

Please help me find the Integral of

(x+5) / (sqrt[9-(x-3)^2])

Answer 1

\[\int\limits_{}^{}(x+5)/\sqrt{9-(x-3)^2}\]

Answer 2

trying to recall the arctrigs ...

Answer 3

We learned 3
arcsin,arctan, and arcsec

I would say that this is arcsin

Answer 4

y = sin'x

siny = x

cosy y' = 1

y' = 1/cos(sin'x)

y' = 1/sqrt(1-sin^2(sin'x))

im thinking its arcsin as well

Answer 5

So I would also say that u=x-3

Answer 6

let sin(u) = x-3
du = dx

Answer 7

du = 1
a=3

Answer 8

... we want a 9sin^2, so let 3sin(u) = x-3

Answer 9

Why 9sin^2?

Answer 10

to factor out the sqrt9 to get sqrt[1-trig^2]

Answer 11

Is that a rule because in my mind sqrt9 = 3

Answer 12

sqrt[9-9a] = sqrt[ 9(1-a)] ] = 3 sqrt(1-a)

the 1-a is the format we want to work this into

Answer 13

Oh because that is in the original formula okay.
Oh wait did you multiply out (x-3)^2?

Answer 14

no, we want the trig squared, so its the innards that we are subbing

3sin(u) = x-3; x = 3sin(u)-3

3cos(u) du = dx

\[\frac{x+5}{\sqrt{9-(x-3)^2}}dx\]
\[\frac{3sin(u)-3+5}{\sqrt{9-(3sin(u))^2}}~3cos(u) du\]

Answer 15

Oh you solved for x and multiplied by u'
Wouldn't x=3sin(u)+3 because you're taking -3 to the other side of the equation?

Answer 16

lol, yes it would :)

Answer 17

Oh okay. So . . . is that it?
Or do we have to get it into the arcsin formula now?

Answer 18

we can simplify at the moment, that bottom goes 3 sqrt(1-sin^2) = 3cos, so we are left with:

3sin(u)+8 du as our integration

Answer 19

If the integral = arcsin(u/a) + c

Then is the answer arcsin(x-3)/3 + C ?

Answer 20

the usub led us in a different direction i believe, or at least simplified it tremendously we can use the wolf to dbl chk

Answer 21

Oh lol yeah I forgot about that website. Let me try it

Answer 22

integrates to: 3cos(u) + 8u, along the interval

Answer 23

or +C for the indefinite

Answer 24

so, what is u?

3sin(u) = x-3

sin(u) = x/3 - 1

u = arcsin (x/3 - 1 )

Answer 25

Okay thanks.
I"m sorry I have to go but you've been a great help :)

Answer 26

youre welcome, ill have to dbl chk my thoughts to be sure :)

Answer 27

http://www.wolframalpha.com/input/?i=d%2Fdx+%28-3cos%28arcsin+%28x%2F3+-+1+%29%29%2B8arcsin+%28x%2F3+-+1+%29%29

forgot the negative .. -3cos(u) + 8u

the wolf says it derives to a sqrt(-(x-6)x)

9 - (x^2 -6x + 9) = -(x-6)x