Hi

the integral is Integral sign ("S") dx/ (sqrt(21-4x-x^2))

So first I completed the square so 21 - (x+2)^2 +4 so

Let u = x+2 so du = dx

so the original integral becomes S du/ sqrt( 25 - u^2)

Then I let u = 5 sin t which makes sqrt (25 - u^2) = 5cos t

du = 5 cos t dt

so then S du/ sqrt(25 - u^2) = S 5 cos t dt / 5 cos t

is this right???

= S dt = t + C

= sin ^-1 (u/5) +C = sin^-1 ((x+2)/5) + C

I find the 5 sin t = u where t = sin^-1 u/5 so if this is wrong let me know.

Thanks

Calculus beginner