Evaluate (integer sign)dx/sqrt9-8x-x^2

A.sin^-1 (x + 4/5) + C
B.sin^-1 (x - 4/5) + C
C.Ln Sqrt9-8x-x^2 + C
D.Ln (-8 - 2x) + C

B or C ?

1 answer

∫1/sqrt(9-8x-x^2)dx
=∫1/sqrt(5²-(x-4)²)dx
substitute u=x+4, du=dx
=∫1/sqrt(5²-u²)dx
=sin-1(u/5)+C
=sin-1((x+4)/5)+C